The charge-density wave (CDW) mechanism and resulting structure of the AV₃Sb₅ family of kagome metals has posed a puzzling challenge since their discovery four years ago. In fact, the lack of consensus on the origin and structure of the CDW hinders the understanding of the emerging phenomena. Here, by employing a non-perturbative treatment of anharmonicity from first-principles calculations, we reveal that the charge-density transition in CsV₃Sb₅ is driven by the large electron-phonon coupling of the material and that the melting of the CDW state is attributed to ionic entropy and lattice anharmonicity. The calculated transition temperature is in very good agreement with experiments, implying that soft mode physics are at the core of the charge-density wave transition. Contrary to the standard assumption associated with a pure kagome lattice, the CDW is essentially three-dimensional as it is triggered by an unstable phonon at the L point. The absence of involvement of phonons at the M point enables us to constrain the resulting symmetries to six possible space groups. The unusually large electron-phonon linewidth of the soft mode explains why inelastic scattering experiments did not observe any softened phonon. We foresee that large anharmonic effects are ubiquitous and could be fundamental to understand the observed phenomena also in other kagome families.

The signature feature of the ‘strange metal’ state of high-T_c cuprates—its linear-in-temperature resistivity—has a coefficient α₁ that correlates with T_c, as expected were α₁ derived from scattering off the same bosonic fluctuations that mediate pairing. Recently, an anomalous linear-in-field magnetoresistance (=γ₁H) has also been observed, but only over a narrow doping range, leaving its relation to the strange metal state and to the superconductivity unclear. Here, we report in-plane magnetoresistance measurements on three hole-doped cuprate families spanning a wide range of temperatures, magnetic field strengths and doping. In contrast to expectations from Boltzmann transport theory, γ₁ is found to correlate universally with α₁. A phenomenological model incorporating real-space inhomogeneity is proposed to explain this correlation. Within this picture, superconductivity in hole-doped cuprates is governed not by the strength of quasiparticle interactions with a bosonic bath, but by the concentration of strange metallic carriers.

The elastic moduli provide unique insights into the thermodynamics of quantum materials, particularly into the symmetries broken at their phase transition. Here, we present a workflow to carve crystalline resonators via focused ion beam milling from small and oddly shaped crystals unsuitable for traditional measurements of elasticity. The accuracy of this technique is first established in silicon. Next, we showcase the capacity to probe changes in the electronic state with a resolution on the measured resonance frequency as small as 0.01% on YNiO₃, a rare-earth perovskite nickelate, in which bulk single crystals have typical length scales of ≈40 μm. Here, we observe a sharp 0.2% discontinuity in Young’s modulus of an YNiO₃ cantilever at a magnetic phase transition. Finally, an additional potential of using free-standing cantilevers as a tool for examining the time-dependence of chemical changes is illustrated by laser-heating YNiO₃.

The so-called “extreme magnetoresistance” (XMR) found in few conductors poses interesting conceptual challenges which address needs in technology. In contrast to the more common XMR in semi-metals, PtSn₄ stands out as a rare example of a high carrier density multi-band metal exhibiting XMR, sparking an active debate about its microscopic origin. Here we report a sharp sensitivity of its XMR upon the field angle, with an almost complete collapse only for one specific current and field direction (B//b, I//a). Corroborated by band-structure calculations, we identify a singular open orbit on one of its Fermi surface sheets as the origin of this collapse. This remarkably switchable XMR resolves the puzzle in PtSn₄ as a semi-classical effect of an ultra-pure, compensated carrier metal. It further showcases the importance of Ockham’s razor in uncommon magnetotransport phenomena and demonstrates the remarkable physical properties conventional metals can exhibit given they are superbly clean.

Diode effects are of great interest for both fundamental physics and modern technologies. Electrical diode effects (nonreciprocal transport) have been observed in Weyl systems. Optical diode effects arising from the Weyl fermions have been theoretically considered but not probed experimentally. Here, we report the observation of a nonlinear optical diode effect (NODE) in the magnetic Weyl semimetal CeAlSi, where the magnetization introduces a pronounced directionality in the nonlinear optical second-harmonic generation (SHG). We demonstrate a six-fold change of the measured SHG intensity between opposite propagation directions over a bandwidth exceeding 250 meV. Supported by density-functional theory, we establish the linearly dispersive bands emerging from Weyl nodes as the origin of this broadband effect. We further demonstrate current-induced magnetization switching and thus electrical control of the NODE. Our results advance ongoing research to identify novel nonlinear optical/transport phenomena in magnetic topological materials and further opens new pathways for the unidirectional manipulation of light.

Our understanding of quantum materials is commonly based on precise determinations of their electronic spectrum by spectroscopic means, most notably angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy. Both require atomically clean and flat crystal surfaces, which are traditionally prepared by in situ mechanical cleaving in ultrahigh vacuum chambers. We present a new approach that addresses three main issues of the current state-of-the-art methods: (1) Cleaving is a highly stochastic and, thus, inefficient process; (2) fracture processes are governed by the bonds in a bulk crystal, and many materials and surfaces simply do not cleave; and (3) the location of the cleave is random, preventing data collection at specified regions of interest. Our new workflow is based on focused ion beam machining of micro-strain lenses, in which shape (rather than crystalline) anisotropy dictates the plane of cleavage, which can be placed at a specific target layer. As proof-of-principle, we show ARPES results from micro-cleaves of Sr₂RuO₄ along the ac plane and from two surface orientations of SrTiO₃, a notoriously difficult to cleave cubic perovskite.

The kagome metals AV₃Sb₅ (A=K, Rb, Cs) present an ideal sandbox to study the interrelation between multiple coexisting correlated phases such as charge order and superconductivity. So far, no consensus on the microscopic nature of these states has been reached as the proposals struggle to explain all their exotic physical properties. Among these, field-switchable electric magneto-chiral anisotropy (eMChA) in CsV₃Sb₅ provides intriguing evidence for a rewindable electronic chirality, yet the other family members have not been likewise investigated. Here, we present a comparative study of magneto-chiral transport between CsV₃Sb₅ and KV₃Sb₅. Despite their similar electronic structure, KV₃Sb₅ displays negligible eMChA, if any, and with no field switchability. This is in stark contrast to the non-saturating eMChA in CsV₃Sb₅ even in high fields up to 35 T. In light of their similar band structures, the stark difference in eMChA suggests its origin in the correlated states. Clearly, the V kagome nets alone are not sufficient to describe the physics and the interactions with their environment are crucial in determining the nature of their low-temperature state.

Magnetic frustration allows to access novel and intriguing properties of magnetic systems and has been explored mainly in planar triangular-like arrays of magnetic ions. In this work, we describe the phosphide Ce ₆Ni ₆P ₁₇, where the Ce ⁺³ ions accommodate in a body-centered cubic lattice of Ce ₆ regular octahedra. From measurements of magnetization, specific heat, and resistivity, we determine a rich phase diagram as a function of temperature and magnetic field in which different magnetic phases are found. Besides clear evidence of magnetic frustration is obtained from entropy analysis. At zero field, a second-order antiferromagnetic transition occurs at T _N1 ≈ 1 K followed by a first-order transition at T _N2 ≈ 0.45 K. With magnetic field new magnetic phases appear, including a weakly first-order transition which ends in a classical critical point and a third magnetic phase. We also study the exact solution of the spin-1/2 Heisenberg model in an octahedron which allows us a qualitative understanding of the phase diagram and compare with the experimental results.

Spontaneously broken symmetries are at the heart of many phenomena of quantum matter and physics more generally. However, determining the exact symmetries that are broken can be challenging due to imperfections such as strain, in particular when multiple electronic orders are competing. This is exemplified by charge order in some kagome systems, where evidence of nematicity and flux order from orbital currents remains inconclusive due to contradictory measurements. Here we clarify this controversy by fabricating highly symmetric samples of a member of this family, CsV₃Sb₅, and measuring their transport properties. We find that a measurable anisotropy is absent at any temperature in the unperturbed material. However, a pronounced in-plane transport anisotropy appears when either weak magnetic fields or strains are present. A symmetry analysis indicates that a perpendicular magnetic field can indeed lead to in-plane anisotropy by inducing a flux order coexisting with more conventional bond order. Our results provide a unifying picture for the controversial charge order in kagome metals and highlight the need for materials control at the microscopic scale in the identification of broken symmetries.

An all-electric switch of the persistent electron swirl in a quantum anomalous Hall state enables researchers to flip the electronic chirality of this quantum state.

The focused ion beam (FIB) is a powerful tool for fabrication, modification, and characterization of materials down to the nanoscale. Starting with the gallium FIB, which was originally intended for photomask repair in the semiconductor industry, there are now many different types of FIB that are commercially available. These instruments use a range of ion species and are applied broadly in materials science, physics, chemistry, biology, medicine, and even archaeology. The goal of this roadmap is to provide an overview of FIB instrumentation, theory, techniques, and applications. By viewing FIB developments through the lens of various research communities, we aim to identify future pathways for ion source and instrumentation development, as well as emerging applications and opportunities for improved understanding of the complex interplay of ion–solid interactions. We intend to provide a guide for all scientists in the field that identifies common research interest and will support future fruitful interactions connecting tool development, experiment, and theory. While a comprehensive overview of the field is sought, it is not possible to cover all research related to FIB technologies in detail. We give examples of specific projects within the broader context, referencing original works and previous review articles throughout.

Efficient superconducting diodes can be designed according to established physics. However, emerging concepts must be united with known mechanisms in order to unlock functionality in rectification and frequency conversion.

Despite much experimental and theoretical work, the nature of the charge order in the kagome metals belonging to the family of materials AV₃Sb₃ (A=Cs,Rb,K) remains controversial. A crucial ingredient for the identification of the ordering in these materials is their response to external perturbations, such as strain or magnetic fields. To this end, we provide a comprehensive symmetry classification of the possible charge orders in kagome materials with a 2×2 increase of the unit cell. Motivated by the experimental reports of time-reversal symmetry breaking and rotational anisotropy, we consider the interdependence of flux and bond orders. Deriving the relevant Landau free energy for possible orders, we study the effect of symmetry-breaking perturbations such as strain and magnetic fields. Our results thus provide a road map for future tests of these intricate orders.

The quest to improve transparent conductors balances two key goals: increasing electrical conductivity and increasing optical transparency. To improve both simultaneously is hindered by the physical limitation that good metals with high electrical conductivity have large carrier densities that push the plasma edge into the ultra-violet range. Technological solutions reflect this trade-off, achieving the desired transparencies only by reducing the conductor thickness or carrier density at the expense of a lower conductance. Here we demonstrate that highly anisotropic crystalline conductors offer an alternative solution, avoiding this compromise by separating the directions of conduction and transmission. We demonstrate that slabs of the layered oxides Sr₂RuO₄ and Tl₂Ba₂CuO_6+δ are optically transparent even at macroscopic thicknesses >2 μm for c-axis polarized light. Underlying this observation is the fabrication of out-of-plane slabs by focused ion beam milling. This work provides a glimpse into future technologies, such as highly polarized and addressable optical screens.

In materials, certain approximated symmetry operations can exist in a lower-order approximation of the effective model but are good enough to influence the physical responses of the system, and these approximated symmetries were recently dubbed “quasisymmetries” [Nat. Phys. 18, 813 (2022)]. In this paper, we reveal a hierarchy structure of the quasisymmetries and the corresponding nodal structures that they enforce via two different approaches of the perturbation expansions for the effective model in the chiral crystal material CoSi. In the first approach, we treat the spin-independent linear momentum (k) term as the zero-order Hamiltonian. Its energy bands are fourfold degenerate due to an SU(2)×SU(2) quasisymmetry. We next consider both the k-independent spin-orbit coupling (SOC) and full quadratic k terms as the perturbation terms and find that the first-order perturbation leads to a model described by a self-commuting “stabilizer code” Hamiltonian with a U(1) quasisymmetry that can protect nodal planes. In the second approach, we treat the SOC-free linear k term and k-independent SOC term as the zero order. They exhibit an SU(2) quasisymmetry, which can be reduced to U(1) quasisymmetry by a choice of quadratic terms. Correspondingly, a twofold degeneracy for all the bands due to the SU(2) quasisymmetry is reduced to twofold nodal planes that are protected by the U(1) quasisymmetry. For both approaches, including higher-order perturbation will break the U(1) quasisymmetry and induce a small gap ∼1meV for the nodal planes. These quasisymmetry protected near degeneracies play an essential role in understanding recent quantum oscillation experiments in CoSi.

We thank G.P. Mikitik and Yu.V. Sharlai for contributing this note¹ and the cordial exchange about it. First and foremost, we note that the aim of our paper² is to report a methodology to diagnose topological (semi)metals using magnetic quantum oscillations. Thus far, such diagnosis has been based on the phase offset of quantum oscillations, which is extracted from a “Landau fan plot”. A thorough analysis of the Onsager–Lifshitz–Roth quantization rules has shown that the famous π-phase shift can equally well arise from orbital or spin magnetic moments in topologically trivial systems with strong spin-orbit coupling or small effective masses³. Therefore, the “Landau fan plot” does not by itself constitute a proof of a topologically nontrivial Fermi surface. In the paper at hand², we report an improved analysis method that exploits the strong energy dependence of the effective mass in linearly dispersing bands. This leads to a characteristic temperature dependence of the oscillation frequency which is a strong indicator of nontrivial topology, even for multi-band metals with complex Fermi surfaces. Three materials, Cd₃As₂, Bi₂O₂Se and LaRhIn₅ served as test cases for this method. Linear band dispersions were detected for Cd₃As₂, as well as the F ≈ 7 T pocket in LaRhIn₅.

When electric conductors differ from their mirror image, unusual chiral transport coefficients appear that are forbidden in achiral metals, such as a non-linear electric response known as electronic magnetochiral anisotropy (eMChA)^1,2,3,4,5,6. Although chiral transport signatures are allowed by symmetry in many conductors without a centre of inversion, they reach appreciable levels only in rare cases in which an exceptionally strong chiral coupling to the itinerant electrons is present. So far, observations of chiral transport have been limited to materials in which the atomic positions strongly break mirror symmetries. Here, we report chiral transport in the centrosymmetric layered kagome metal CsV₃Sb₅ observed via second-harmonic generation under an in-plane magnetic field. The eMChA signal becomes significant only at temperatures below T′≈ 35 K, deep within the charge-ordered state of CsV₃Sb₅ (T_CDW ≈ 94 K). This temperature dependence reveals a direct correspondence between electronic chirality, unidirectional charge order⁷ and spontaneous time-reversal symmetry breaking due to putative orbital loop currents^8,9,10. We show that the chirality is set by the out-of-plane field component and that a transition from left- to right-handed transport can be induced by changing the field sign. CsV₃Sb₅ is the first material in which strong chiral transport can be controlled and switched by small magnetic field changes, in stark contrast to structurally chiral materials, which is a prerequisite for applications in chiral electronics.

The cascade of electronic phases in CsV₃Sb₅ raises the prospect to disentangle their mutual interactions in a clean, strongly interacting kagome lattice. When the kagome planes are stacked into a crystal, its electronic dimensionality encodes how much of the kagome physics and its topological aspects survive. The layered structure of CsV₃Sb₅ reflects in Brillouin-zone-sized quasi-two-dimensional Fermi surfaces and significant transport anisotropy. Yet here we demonstrate that CsV₃Sb₅ is a three-dimensional (3D) metal within the charge density wave (CDW) state. Small 3D pockets play a crucial role in its low-temperature magneto- and quantum transport. Their emergence at TCDW ≈ 93 K results in an anomalous sudden increase of the in-plane magnetoresistance by four orders of magnitude. The presence of these 3D pockets is further confirmed by quantum oscillations under in-plane magnetic fields, demonstrating their closed nature. These results emphasize the impact of interlayer coupling on the kagome physics in 3D materials.

Metal–oxide–semiconductor junctions are the building blocks of modern electronics and can provide a variety of functionalities, from memory to computing. The technology, however, faces constraints in terms of further miniaturization and compatibility with post–von Neumann computing architectures. Manipulation of structural—rather than electronic—states could provide a path to ultrascaled low-power functional devices, but the electrical control of such states is challenging. Here we report electronically accessible long-lived structural states in vanadium dioxide that can provide a scheme for data storage and processing. The states can be arbitrarily manipulated on short timescales and tracked beyond 10,000 s after excitation, exhibiting features similar to glasses. In two-terminal devices with channel lengths down to 50 nm, sub-nanosecond electrical excitation can occur with an energy consumption as small as 100 fJ. These glass-like functional devices could outperform conventional metal–oxide–semiconductor electronics in terms of speed, energy consumption and miniaturization, as well as provide a route to neuromorphic computation and multilevel memories.

The crystal symmetry of a material dictates the type of topological band structure it may host, and therefore, symmetry is the guiding principle to find topological materials. Here we introduce an alternative guiding principle, which we call ‘quasi-symmetry’. This is the situation where a Hamiltonian has exact symmetry at a lower order that is broken by higher-order perturbation terms. This enforces finite but parametrically small gaps at some low-symmetry points in momentum space. Untethered from the restraints of symmetry, quasi-symmetries eliminate the need for fine tuning as they enforce that sources of large Berry curvature occur at arbitrary chemical potentials. We demonstrate that quasi-symmetry in the semi-metal CoSi stabilizes gaps below 2 meV over a large near-degenerate plane that can be measured in the quantum oscillation spectrum. The application of in-plane strain breaks the crystal symmetry and gaps the degenerate point, observable by new magnetic breakdown orbits. The quasi-symmetry, however, does not depend on spatial symmetries and hence transmission remains fully coherent. These results demonstrate a class of topological materials with increased resilience to perturbations such as strain-induced crystalline symmetry breaking, which may lead to robust topological applications as well as unexpected topology beyond the usual space group classifications.

In an idealized infinite crystal, the material properties are constrained by the symmetries of the unit cell. The point-group symmetry is broken by the sample shape of any finite crystal, but this is commonly unobservable in macroscopic metals. To sense the shape-induced symmetry lowering in such metals, long-lived bulk states originating from an anisotropic Fermi surface are needed. Here we show how a strongly facetted Fermi surface and the long quasiparticle mean free path present in microstructures of PdCoO₂ yield an in-plane resistivity anisotropy that is forbidden by symmetry on an infinite hexagonal lattice. We fabricate bar-shaped transport devices narrower than the mean free path from single crystals using focused ion beam milling, such that the ballistic charge carriers at low temperatures frequently collide with both of the side walls that define the channel. Two symmetry-forbidden transport signatures appear: the in-plane resistivity anisotropy exceeds a factor of 2, and a transverse voltage appears in zero magnetic field. Using ballistic Monte Carlo simulations and a numerical solution of the Boltzmann equation, we identify the orientation of the narrow channel as the source of symmetry breaking.

A wide range of unconventional transport phenomena has recently been observed in single-crystal delafossite metals. Here, we present a theoretical framework to elucidate electron transport using a combination of first-principles calculations and numerical modeling of the anisotropic Boltzmann transport equation. Using PdCoO₂ as a model system, we study different microscopic electron and phonon scattering mechanisms and establish the mean free path hierarchy of quasiparticles at different temperatures. We treat the anisotropic Fermi surface explicitly to numerically obtain experimentally-accessible transport observables, which bridge between the “diffusive,” “ballistic,” and “hydrodynamic” transport regime limits. We illustrate that the distinction between the “quasiballistic” and “quasihydrodynamic” regimes is challenging and often needs to be quantitative in nature. From first-principles calculations, we populate the resulting transport regime plots and demonstrate how the Fermi surface orientation adds complexity to the observed transport signatures in micrometer-scale devices. Our work provides key insights into microscopic interaction mechanisms on open hexagonal Fermi surfaces and establishes their connection to the macroscopic electron transport in finite-size channels.

Superconductor/metal interfaces are usually fabricated in heterostructures that join these dissimilar materials. A conceptually different approach has recently exploited the strain sensitivity of heavy-fermion superconductors, selectively transforming regions of the crystal into the metallic state by strain gradients. The strain is generated by differential thermal contraction between the sample and the substrate. Here, we present an improved finite-element model that reliably predicts the superconducting transition temperature in CeIrIn₅ even in complex structures. Different substrates are employed to tailor the strain field into the desired shapes. Using this approach, both highly complex and strained as well as strain-free microstructures are fabricated to validate the model. This enables a high degree of control over the microscopic strain fields and forms the basis for more advanced structuring of superconductors as in Josephson junctions yet also finds natural use cases in any material class in which a modulation of the physical properties on a chip is desirable.

We demonstrate a non-linear measurement scheme of the Shubnikov–de Haas effect based on Joule self-heating that builds on ideas of the 3ω-method used in thin films. While the temperature dependence of the resistance, R(T), of clean metals at low temperatures saturates, a significant temperature dependence, dR/dT, appears at high fields due to Landau quantization. We experimentally demonstrate this effect in the semi-metal CoSi, resolving well quantum oscillations at low magnetic fields in the non-linear channel, which appear as 3rd harmonics of the current drive frequency. To ensure the dominant self-heating originates in the crystal, not at the contacts, we fabricate crystalline microbars using focused ion beam machining. These oscillations in non-linear channel encode the ratio between the dR/dT and the thermal conductivity of the material, rendering it an interesting probe in situations of the broken Wiedemann–Franz law. Our results present a quantitative methodology that is particularly suited to investigate the electronic structure of micro- and nano-materials at intermediate temperatures.

Crystalline defects can modify quantum interactions in solids, causing unintuitive, even favourable, properties such as quantum Hall effect or superconducting vortex pinning. Here we present another example of this notion—an unexpected unidirectional Kondo scattering in single crystals of 2H-NbS₂. This manifests as a pronounced low-temperature enhancement in the out-of-plane resistivity and thermopower below 40 K, hidden for the in-plane charge transport. The anomaly can be suppressed by the c-axis-oriented magnetic field, but is unaffected by field applied along the planes. The magnetic moments originate from layers of 1T-NbS₂, which inevitably form during the growth, undergoing a charge-density-wave reconstruction with each superlattice cell (David-star-shaped cluster of Nb atoms) hosting a localised spin. Our results demonstrate the unique and highly anisotropic response of a spontaneously formed Kondo-lattice heterostructure, intercalated in a layered conductor.

We present an experimental set-up for the controlled application of strain gradients by mechanical piezoactuation on 3D crystalline microcantilevers that were fabricated by focused ion beam machining. A simple sample design tailored for transport characterization under strain at cryogenic temperatures is proposed. The topological semi-metal Cd₃As₂ serves as a test bed for the method, and we report extreme strain gradients of up to 1.3% μm⁻¹ at a surface strain value of ≈0.65% at 4 K. Interestingly, the unchanged quantum transport of the cantilever suggests that the bending cycle does not induce defects via plastic deformation. This approach is a first step towards realizing transport phenomena based on structural gradients, such as artificial gauge fields in topological materials.

Intense work studying the ballistic regime of electron transport in two-dimensional systems based on semiconductors and graphene had been thought to have established most of the key experimental facts of the field. In recent years, however, additional forms of ballistic transport have become accessible in the quasi–two-dimensional delafossite metals, whose Fermi wavelength is a factor of 100 shorter than those typically studied in the previous work and whose Fermi surfaces are nearly hexagonal in shape and therefore strongly faceted. This has some profound consequences for results obtained from the classic ballistic transport experiment of studying bend and Hall resistances in mesoscopic squares fabricated from delafossite single crystals. We observe pronounced anisotropies in bend resistances and even a Hall voltage that is strongly asymmetric in magnetic field. Although some of our observations are nonintuitive at first sight, we show that they can be understood within a nonlocal Landauer-Büttiker analysis tailored to the symmetries of the square/hexagonal geometries of our combined device/Fermi surface system. Signatures of nonlocal transport can be resolved for squares of linear dimension of nearly 100 µm, approximately a factor of 15 larger than the bulk mean free path of the crystal from which the device was fabricated.

The phase offset of quantum oscillations is commonly used to experimentally diagnose topologically nontrivial Fermi surfaces. This methodology, however, is inconclusive for spin-orbit-coupled metals where π-phase-shifts can also arise from non-topological origins. Here, we show that the linear dispersion in topological metals leads to a T²-temperature correction to the oscillation frequency that is absent for parabolic dispersions. We confirm this effect experimentally in the Dirac semi-metal Cd₃As₂ and the multiband Dirac metal LaRhIn5. Both materials match a tuning-parameter-free theoretical prediction, emphasizing their unified origin. For topologically trivial Bi₂O₂Se, no frequency shift associated to linear bands is observed as expected. However, the π-phase shift in Bi₂O₂Se would lead to a false positive in a Landau-fan plot analysis. Our frequency-focused methodology does not require any input from ab-initio calculations, and hence is promising for identifying correlated topological materials.

Whereas electron-phonon scattering relaxes the electron’s momentum in metals, a perpetual exchange of momentum between phonons and electrons may conserve total momentum and lead to a coupled electron-phonon liquid. Such a phase of matter could be a platform for observing electron hydrodynamics. Here we present evidence of an electron-phonon liquid in the transition metal ditetrelide, NbGe₂, from three different experiments. First, quantum oscillations reveal an enhanced quasiparticle mass, which is unexpected in NbGe₂ with weak electron-electron correlations, hence pointing at electron-phonon interactions. Second, resistivity measurements exhibit a discrepancy between the experimental data and standard Fermi liquid calculations. Third, Raman scattering shows anomalous temperature dependences of the phonon linewidths that fit an empirical model based on phonon-electron coupling. We discuss structural factors, such as chiral symmetry, short metallic bonds, and a low-symmetry coordination environment as potential design principles for materials with coupled electron-phonon liquid.

We report a scanning superconducting quantum interference device (SQUID) microscope in a cryogen-free dilution refrigerator with a base temperature at the sample stage of at least 30 mK. The microscope is rigidly mounted to the mixing chamber plate to optimize thermal anchoring of the sample. The microscope housing fits into the bore of a superconducting vector magnet, and our design accommodates a large number of wires connecting the sample and sensor. Through a combination of vibration isolation in the cryostat and a rigid microscope housing, we achieve relative vibrations between the SQUID and the sample that allow us to image with micrometer resolution over a 150 µm range while the sample stage temperature remains at base temperature. To demonstrate the capabilities of our system, we show images acquired simultaneously of the static magnetic field, magnetic susceptibility, and magnetic fields produced by a current above a superconducting micrometer-scale device.

As conductors in electronic applications shrink, microscopic conduction processes lead to strong deviations from Ohm’s law. Depending on the length scales of momentum conserving (l_MC) and relaxing (l_MR) electron scattering, and the device size (d), current flows may shift from ohmic to ballistic to hydrodynamic regimes. So far, an in situ methodology to obtain these parameters within a micro/nanodevice is critically lacking. In this context, we exploit Sondheimer oscillations, semi-classical magnetoresistance oscillations due to helical electronic motion, as a method to obtain l_MR even when l_MR ≫ d. We extract l_MR from the Sondheimer amplitude in WP₂, at temperatures up to T ~ 40 K, a range most relevant for hydrodynamic transport phenomena. Our data on μm-sized devices are in excellent agreement with experimental reports of the bulk l_MR and confirm that WP₂ can be microfabricated without degradation. These results conclusively establish Sondheimer oscillations as a quantitative probe of l_MR in micro-devices.

In a joint effort utilizing modified sample preparation, microscopy, X-ray diffraction and micro-fabrication, it became possible to prepare single crystals of the “hidden” phase AlCr₂. High-resolution X-ray diffraction analysis is described in detail for two crystals with the similar overall composition, but different degree of disorder, which seems to be the main cause for the differing unit cell parameters. Chemical bonding analysis of AlCr₂ in comparison to prototypical MoSi₂ shows pronounced differences reflecting the interchange of main group element vs. transition metal as majority component.

In RuCl₃, inelastic neutron scattering and Raman spectroscopy reveal a continuum of non-spin-wave excitations that persists to high temperature, suggesting the presence of a spin liquid state on a honeycomb lattice. In the context of the Kitaev model, finite magnetic fields introduce interactions between the elementary excitations, and thus the effects of high magnetic fields that are comparable to the spin-exchange energy scale must be explored. Here, we report measurements of the magnetotropic coefficient—the thermodynamic coefficient associated with magnetic anisotropy—over a wide range of magnetic fields and temperatures. We find that magnetic field and temperature compete to determine the magnetic response in a way that is independent of the large intrinsic exchange-interaction energy. This emergent scale-invariant magnetic anisotropy provides evidence for a high degree of exchange frustration that favours the formation of a spin liquid state in RuCl₃.

Structural phase transitions in f-electron materials have attracted sustained attention both for practical and basic science reasons, including the fact that they offer an environment to directly investigate relationships between structure and the f-state. Here we present results for UCr₂Si₂, where structural (tetragonal → monoclinic) and antiferromagnetic phase transitions are seen at T_S=205 K and T_N=25 K, respectively. We also provide evidence for an additional second-order phase transition at T_X=280 K. We show that T_X, T_S, and T_N respond in distinct ways to the application of hydrostatic pressure and Cr→Ru chemical substitution. In particular, hydrostatic compression increases the structural ordering temperature, eventually causes it to merge with T_X, and destroys the antiferromagnetism. In contrast, chemical substitution in the series UCr_2-xRu_xSi₂ suppresses both T_S and T_N, causing them to approach zero temperature near x≈0.16 and 0.08, respectively. The distinct T−P and T−x phase diagrams are related to the evolution of the rigid Cr-Si and Si-Si substructures, where applied pressure semiuniformly compresses the unit cell, and Cr→Ru substitution results in uniaxial lattice compression along the tetragonal c-axis and an expansion in the ab-plane. These results provide insights into an interesting class of strongly correlated quantum materials in which degrees of freedom associated with f-electron magnetism, strong electronic correlations, and structural instabilities are readily controlled.

Microstructures can be carefully designed to reveal the quantum phase of the wave-like nature of electrons in a metal. Here, we report phase-coherent oscillations of out-of-plane magnetoresistance in the layered delafossites PdCoO₂ and PtCoO₂. The oscillation period is equivalent to that determined by the magnetic flux quantum, h/e, threading an area defined by the atomic interlayer separation and the sample width, where h is Planck’s constant and e is the charge of an electron. The phase of the electron wave function appears robust over length scales exceeding 10 micrometers and persisting up to temperatures of T > 50 kelvin. We show that the experimental signal stems from a periodic field modulation of the out-of-plane hopping. These results demonstrate extraordinary single-particle quantum coherence lengths in delafossites.

Layered transition metal dichalcogenides (TMDs) are commonly classified as quasi-two-dimensional materials, meaning that their electronic structure closely resembles that of an individual layer, which results in resistivity anisotropies reaching thousands. Here, we show that this rule does not hold for 1T-TaS₂—a compound with the richest phase diagram among TMDs. Although the onset of charge density wave order makes the in-plane conduction non-metallic, we reveal that the out-of-plane charge transport is metallic and the resistivity anisotropy is close to one. We support our findings with ab initio calculations predicting a pronounced quasi-one-dimensional character of the electronic structure. Consequently, we interpret the highly debated metal-insulator transition in 1T-TaS₂ as a quasi-one-dimensional instability, contrary to the long-standing Mott localisation picture. In a broader context, these findings are relevant for the newly born field of van der Waals heterostructures, where tuning interlayer interactions (e.g., by twist, strain, intercalation, etc.) leads to new emergent phenomena.

The delafossite metals PdCoO₂, PtCoO₂, and PdCrO₂ are among the highest conductivity materials known, with low-temperature mean free paths of tens of microns in the best as-grown single crystals. A key question is whether these very low resistive scattering rates result from strongly suppressed backscattering due to special features of the electronic structure or are a consequence of highly unusual levels of crystalline perfection. We report the results of experiments in which high-energy electron irradiation was used to introduce point disorder to the Pd and Pt layers in which the conduction occurs. We obtain the cross section for formation of Frenkel pairs in absolute units, and cross-check our analysis with first-principles calculations of the relevant atomic displacement energies. We observe an increase of resistivity that is linear in defect density with a slope consistent with scattering in the unitary limit. Our results enable us to deduce that the as-grown crystals contain extremely low levels of in-plane defects of approximately 0.001%. This confirms that crystalline perfection is the most important factor in realizing the long mean free paths and highlights how unusual these delafossite metals are in comparison with the vast majority of other multicomponent oxides and alloys. We discuss the implications of our findings for future materials research.

Zirconium pentatetelluride, ZrTe₅, shows remarkable sensitivity to hydrostatic pressure. In this work we address the high-pressure transport and optical properties of this compound, on samples grown by flux and chemical vapor transport. The high-pressure resistivity is measured up to 2 GPa, and the infrared transmission up to 9 GPa. The dc conductivity anisotropy is determined using a microstructured sample. Together, the transport and optical measurements allow us to discern band parameters with and without the hydrostatic pressure, in particular the Fermi level, and the effective mass in the less conducting, out-of-plane direction. The results are interpreted within a simple two-band model characterized by a Dirac-type, linear in-plane band dispersion, and a parabolic out-of-plane dispersion.

Weyl semimetals such as the TaAs family (TaAs, TaP, NbAs, NbP) host quasiparticle excitations resembling the long-sought-after Weyl fermions at special band-crossing points in the band structure denoted as Weyl nodes. They are predicted to exhibit a negative longitudinal magnetoresistance (LMR) due to the chiral anomaly if the Fermi energy is sufficiently close to the Weyl points. However, current jetting effects, i.e., current inhomogeneities caused by a strong, field-induced conductivity anisotropy in semimetals, have a similar experimental signature and therefore have hindered a determination of the intrinsic LMR in the TaAs family so far. This work investigates the longitudinal magnetoresistance of all four members of this family along the crystallographic a and c directions. Our samples are of similar quality as those previously studied in the literature and have a similar chemical potential, as indicated by matching quantum-oscillation frequencies. Care was taken to ensure homogeneous currents in all measurements. As opposed to previous studies where this was not done, we find a positive LMR that saturates in fields above 4 T in TaP, NbP, and NbAs for B||c. Using Fermi-surface geometries from band-structure calculations that had been confirmed by experiment, we show that this is the behavior expected from a classical purely orbital effect, independent of the distance of the Weyl node to the Fermi energy. The TaAs family of compounds is the first to show such a simple LMR without apparent influences of scattering anisotropy. In configurations where the orbital effect is small, i.e., for B||a in NbAs and NbP, we find a nonmonotonous LMR, including regions of negative LMR. We discuss a weak antilocalization scenario as an alternative interpretation to the chiral anomaly for these results, since it can fully account for the overall field dependence.

While electrons moving perpendicular to a magnetic field are confined to cyclotron orbits, they can move freely parallel to the field. This simple fact leads to complex current flow in clean, low carrier density semi-metals, such as long-ranged current jets forming along the magnetic field when currents pass through point-like constrictions. Occurring accidentally at imperfect current injection contacts, the phenomenon of "current jetting" plagues the research of longitudinal magneto-resistance, which is particularly important in topological conductors. Here we demonstrate the controlled generation of tightly focused electron beams in a new class of micro-devices machined from crystals of the Dirac semi-metal Cd₃As₂. The current beams can be guided by tilting a magnetic field and their range tuned by the field strength. Finite element simulations quantitatively capture the voltage induced at faraway contacts when the beams are steered towards them, supporting the picture of controlled electron jets. These experiments demonstrate direct control over the highly non-local signal propagation unique to 3D semi-metals in the current jetting regime, and may lead to applications akin to electron optics in free space.

Geometric electron optics may be implemented in solids when electron transport is ballistic on the length scale of a device. Currently, this is realized mainly in 2D materials characterized by circular Fermi surfaces. Here we demonstrate that the nearly perfectly hexagonal Fermi surface of PdCoO₂ gives rise to highly directional ballistic transport. We probe this directional ballistic regime in a single crystal of PdCoO₂ by use of focused ion beam (FIB) micro-machining, defining crystalline ballistic circuits with features as small as 250 nm. The peculiar hexagonal Fermi surface naturally leads to enhanced electron self-focusing effects in a magnetic field compared to circular Fermi surfaces. This super-geometric focusing can be quantitatively predicted for arbitrary device geometry, based on the hexagonal cyclotron orbits appearing in this material. These results suggest a novel class of ballistic electronic devices exploiting the unique transport characteristics of strongly faceted Fermi surfaces.

A recent class of topological nodal-line semimetals with the general formula MSiX (M = Zr, Hf and X = S, Se, Te) has attracted much experimental and theoretical interest due to their properties, particularly their large magnetoresistances and high carrier mobilities. The plateletlike nature of the MSiX crystals and their extremely low residual resistivities make measurements of the resistivity along the [001] direction extremely challenging. To accomplish such measurements, microstructures of single crystals were prepared using focused ion beam techniques. Microstructures prepared in this manner have very well-defined geometries and maintain their high crystal quality, verified by the observations of quantum oscillations. We present magnetoresistance and quantum oscillation data for currents applied along both [001] and [100] in ZrSiS and ZrSiSe, which are consistent with the nontrivial topology of the Dirac line-node, as determined by a measured π Berry phase. Surprisingly, we find that, despite the three dimensional nature of both the Fermi surfaces of ZrSiS and ZrSiSe, both the resistivity anisotropy under applied magnetic fields and the in-plane angular dependent magnetoresistance differ considerably between the two compounds. Finally, we discuss the role microstructuring can play in the study of these materials and our ability to make these microstructures free-standing.

Although crystals of strongly correlated metals exhibit a diverse set of electronic ground states, few approaches exist for spatially modulating their properties. In this study, we demonstrate disorder-free control, on the micrometer scale, over the superconducting state in samples of the heavy-fermion superconductor CeIrIn₅. We pattern crystals by focused ion beam milling to tailor the boundary conditions for the elastic deformation upon thermal contraction during cooling. The resulting nonuniform strain fields induce complex patterns of superconductivity, owing to the strong dependence of the transition temperature on the strength and direction of strain. These results showcase a generic approach to manipulating electronic order on micrometer length scales in strongly correlated matter without compromising the cleanliness, stoichiometry, or mean free path.

In the Ca_1−xLa_xFeAs2 (1 1 2) family of pnictide superconductors, we have investigated a highly overdoped composition (x  =  0.56), prepared by a high-pressure, high-temperature synthesis. Magnetic measurements show an antiferromagnetic transition at T_N  =  120 K, well above the one at lower doping (0.15  <  x  <  0.27).

Below the onset of long-range magnetic order at T_N, the electrical resistivity is strongly reduced and is dominated by electron–electron interactions, as evident from its temperature dependence. The Seebeck coefficient shows a clear metallic behavior as in narrow band conductors. The temperature dependence of the Hall coefficient and the violation of Kohler's rule agree with the multiband character of the material. No superconductivity was observed down to 1.8 K. The success of the high-pressure synthesis encourages further investigations of the so far only partially explored phase diagram in this family of Iron-based high temperature superconductors.

Broadband, efficient and fast conversion of light to electricity is crucial for sensing and clean energy. The bulk photovoltaic effect (BPVE) is a second-order nonlinear optical effect that intrinsically converts light into electrical current. Here, we demonstrate a large mid-infrared BPVE in microscopic devices of the Weyl semimetal TaAs. This discovery results from combining recent developments in Weyl semimetals, focused-ion beam fabrication and theoretical works suggesting a connection between BPVE and topology. We also present a detailed symmetry analysis that allows us to separate the shift current response from photothermal effects. The magnitude and wavelength range of the assigned shift current may impact optical detectors, clean energy and topology, and demonstrate the utility of Weyl semimetals for practical applications.

We present a high magnetic field study of NbP—a member of the monopnictide Weyl semimetal (WSM) family. While the monoarsenides (NbAs and TaAs) have topologically distinct left and right-handed Weyl fermi surfaces, NbP is argued to be “topologically trivial” due to the fact that all pairs of Weyl nodes are encompassed by a single Fermi surface. We use torque magnetometry to measure the magnetic response of NbP up to 60 tesla and uncover a Berry paramagnetic response, characteristic of the topological Weyl nodes, across the entire field range. At the quantum limit B* (≈32 T), τ/B experiences a change in slope when the chemical potential enters the last Landau level. Our calculations confirm that this magnetic response arises from band topology of the Weyl pocket, even though the Fermi surface encompasses both Weyl nodes at zero magnetic field. We also find that the magnetic field pulls the chemical potential to the chiral n = 0 Landau level in the quantum limit, providing a disorder-free way of accessing chiral Weyl fermions in systems that are “not quite” WSMs in zero magnetic field.

Cuprates exhibit antiferromagnetic, charge density wave (CDW), and high-temperature superconducting ground states that can be tuned by means of doping and external magnetic fields. However, disorder generated by these tuning methods complicates the interpretation of such experiments. Here, we report a high-resolution inelastic x-ray scattering study of the high-temperature superconductor YBa₂Cu₂O_6.67 under uniaxial stress, and we show that a three-dimensional long-range-ordered CDW state can be induced through pressure along the a axis, in the absence of magnetic fields. A pronounced softening of an optical phonon mode is associated with the CDW transition. The amplitude of the CDW is suppressed below the superconducting transition temperature, indicating competition with superconductivity. The results provide insights into the normal-state properties of cuprates and illustrate the potential of uniaxial-pressure control of competing orders in quantum materials.

Unusual behavior in quantum materials commonly arises from their effective low-dimensional physics, reflecting the underlying anisotropy in the spin and charge degrees of freedom. Here we introduce the magnetotropic coefficient k = ∂²F/∂θ², the second derivative of the free energy F with respect to the magnetic field orientation θ in the crystal. We show that the magnetotropic coefficient can be quantitatively determined from a shift in the resonant frequency of a commercially available atomic force microscopy cantilever under magnetic field. This detection method enables part per 100 million sensitivity and the ability to measure magnetic anisotropy in nanogram-scale samples, as demonstrated on the Weyl semimetal NbP. Measurement of the magnetotropic coefficient in the spin-liquid candidate RuCl₃ highlights its sensitivity to anisotropic phase transitions and allows a quantitative comparison to other thermodynamic coefficients via the Ehrenfest relations.

Weyl fermions are a recently discovered ingredient for correlated states of electronic matter. A key difficulty has been that real materials also contain non-Weyl quasiparticles, and disentangling the experimental signatures has proven challenging. Here we use magnetic fields up to 95 T to drive the Weyl semimetal TaAs far into its quantum limit, where only the purely chiral 0th Landau levels of the Weyl fermions are occupied. We find the electrical resistivity to be nearly independent of magnetic field up to 50 T: unusual for conventional metals but consistent with the chiral anomaly for Weyl fermions. Above 50 T we observe a two-order-of-magnitude increase in resistivity, indicating that a gap opens in the chiral Landau levels. Above 80 T we observe strong ultrasonic attenuation below 2 K, suggesting a mesoscopically textured state of matter. These results point the way to inducing new correlated states of matter in the quantum limit of Weyl semimetals.

Focused ion beam (FIB) machining promises exciting new possibilities for the study of quantum materials through precise control over the shape and geometry of single crystals on the submicrometer scale. It offers viable routes to fabricate high-quality mesoscale structures from materials that cannot yet be grown in thin-film form and to enhance the experimentally accessible signatures of new physical phenomena. Prototype devices can also be produced in a silicon-chip environment to investigate directly the materials application potential for future electronics. This review introduces the concepts of ion beam shaping of matter, discusses the role and extent of surface damage and material disorder inherent to these techniques, and gives an overview of recent experiments on FIB-structured crystals. Given the early stage of the field of FIB-fabricated quantum materials, much is yet to come, and emergent trends and future directions are also discussed.

Three-dimensional topological semi-metals carry quasiparticle states that mimic massless relativistic Dirac fermions, elusive particles that have never been observed in nature. As they appear in the solid body, they are not bound to the usual symmetries of space-time and thus new types of fermionic excitations that explicitly violate Lorentz-invariance have been proposed, the so-called type-II Dirac fermions. We investigate the electronic spectrum of the transition-metal dichalcogenide PtSe₂ by means of quantum oscillation measurements in fields up to 65 T. The observed Fermi surfaces agree well with the expectations from band structure calculations, that recently predicted a type-II Dirac node to occur in this material. A hole- and an electron-like Fermi surface dominate the semi-metal at the Fermi level. The quasiparticle mass is significantly enhanced over the bare band mass value, likely by phonon renormalization. Our work is consistent with the existence of type-II Dirac nodes in PtSe₂, yet the Dirac node is too far below the Fermi level to support free Dirac–fermion excitations.

We present the crystal structure, electronic structure, and transport properties of the material YbMnSb₂, a candidate system for the investigation of Dirac physics in the presence of magnetic order. Our measurements reveal that this system is a low-carrier-density semimetal with a two-dimensional Fermi surface arising from a Dirac dispersion, consistent with the predictions of density-functional-theory calculations of the antiferromagnetic system. The low temperature resistivity is very large, suggesting that scattering in this system is highly efficient at dissipating momentum despite its Dirac-like nature.

Electronic nematic materials are characterized by a lowered symmetry of the electronic system compared to the underlying lattice, in analogy to the directional alignment without translational order in nematic liquid crystals¹. Such nematic phases appear in the copper- and iron-based high-temperature superconductors^2,3,4, and their role in establishing superconductivity remains an open question. Nematicity may take an active part, cooperating or competing with superconductivity, or may appear accidentally in such systems. Here we present experimental evidence for a phase of fluctuating nematic character in a heavy-fermion superconductor, CeRhIn₅ (ref. 5). We observe a magnetic-field-induced state in the vicinity of a field-tuned antiferromagnetic quantum critical point at H_c ≈ 50 tesla. This phase appears above an out-of-plane critical field H* ≈ 28 tesla and is characterized by a substantial in-plane resistivity anisotropy in the presence of a small in-plane field component. The in-plane symmetry breaking has little apparent connection to the underlying lattice, as evidenced by the small magnitude of the magnetostriction anomaly at H*. Furthermore, no anomalies appear in the magnetic torque, suggesting the absence of metamagnetism in this field range. The appearance of nematic behaviour in a prototypical heavy-fermion superconductor highlights the interrelation of nematicity and unconventional superconductivity, suggesting nematicity to be common among correlated materials.

By introducing a superconducting gap in Weyl or Dirac semimetals, the superconducting state inherits the nontrivial topology of their electronic structure. As a result, Weyl superconductors are expected to host exotic phenomena, such as nonzero-momentum pairing due to their chiral node structure, or zero-energy Majorana modes at the surface. These are of fundamental interest to improve our understanding of correlated topological systems, and, moreover, practical applications in phase-coherent devices and quantum applications have been proposed. Proximity-induced superconductivity promises to allow these experiments on nonsuperconducting Weyl semimetals. We show a new route to reliably fabricate superconducting microstructures from the nonsuperconducting Weyl semimetal NbAs under ion irradiation. The significant difference in the surface binding energy of Nb and As leads to a natural enrichment of Nb at the surface during ion milling, forming a superconducting surface layer (T_c ~ 3.5 K). Being formed from the target crystal itself, the ideal contact between the superconductor and the bulk may enable an effective gapping of the Weyl nodes in the bulk because of the proximity effect. Simple ion irradiation may thus serve as a powerful tool for the fabrication of topological quantum devices from monoarsenides, even on an industrial scale.

Metals containing cerium exhibit a diverse range of fascinating phenomena including heavy fermion behavior, quantum criticality, and novel states of matter such as unconventional superconductivity. The cubic system CeIn₃ has attracted significant attention as a structurally isotropic Kondo lattice material possessing the minimum required complexity to still reveal this rich physics. By using magnetic fields with strengths comparable to the crystal field energy scale, we illustrate a strong field-induced anisotropy as a consequence of non-spherically symmetric spin interactions in the prototypical heavy fermion material CeIn₃. This work demonstrates the importance of magnetic anisotropy in modeling f-electron materials when the orbital character of the 4f wavefunction changes (e.g., with pressure or composition). In addition, magnetic fields are shown to tune the effective hybridization and exchange interactions potentially leading to new exotic field tuned effects in f-based materials.

We report growth of single crystals of the nonmagnetic metallic delafossite PdRhO₂, comparing the results from three different methods. Complete crystallographic data were obtained from single crystal X-ray diffraction, and electronic structure calculations were made using the refined structural parameters. Focused-ion beam microstructuring was used to prepare a sample for measurements of the in- and out-of-plane electrical resistivity, and the large observed anisotropy is qualitatively consistent with the cylindrical Fermi surface predicted by the calculations.

We study the intrinsic electronic anisotropy and fermiology of the quasi-one-dimensional superconductor Ta₄Pd₃Te₁₆. Below T^∗=20 K, we detect a thermodynamic phase transition that predominantly affects the conductivity perpendicular to the quasi-one-dimensional chains. The transition relates to the presence of charge order that precedes superconductivity. Remarkably, the Fermi surface pockets detected by de Haas–van Alphen oscillations are unaffected by this transition, suggesting that the ordered state does not break any translational symmetries but rather alters the scattering of the quasiparticles themselves.

The dispersion of charge carriers in a metal is distinctly different from that of free electrons owing to their interactions with the crystal lattice. These interactions may lead to quasiparticles mimicking the massless relativistic dynamics of high-energy particle physics^1,2,3, and they can twist the quantum phase of electrons into topologically non-trivial knots—producing protected surface states with anomalous electromagnetic properties^4,5,6,7,8,9. These effects intertwine in materials known as Weyl semimetals, and in their crystal-symmetry-protected analogues, Dirac semimetals¹⁰. The latter show a linear electronic dispersion in three dimensions described by two copies of the Weyl equation (a theoretical description of massless relativistic fermions). At the surface of a crystal, the broken translational symmetry creates topological surface states, so-called Fermi arcs11, which have no counterparts in high-energy physics or conventional condensed matter systems. Here we present Shubnikov–de Haas oscillations in focused-ion-beam-prepared microstructures of Cd₃As₂ that are consistent with the theoretically predicted ‘Weyl orbits’, a kind of cyclotron motion that weaves together Fermi-arc and chiral bulk states¹². In contrast to conventional cyclotron orbits, this motion is driven by the transfer of chirality from one Weyl node to another, rather than momentum transfer of the Lorentz force. Our observations provide evidence for direct access to the topological properties of charge in a transport experiment, a first step towards their potential application.

Electrons in materials with linear dispersion behave as massless Weyl- or Dirac-quasiparticles, and continue to intrigue due to their close resemblance to elusive ultra-relativistic particles as well as their potential for future electronics. Yet the experimental signatures of Weyl-fermions are often subtle and indirect, in particular if they coexist with conventional, massive quasiparticles. Here we show a pronounced anomaly in the magnetic torque of the Weyl semimetal NbAs upon entering the quantum limit state in high magnetic fields. The torque changes sign in the quantum limit, signalling a reversal of the magnetic anisotropy that can be directly attributed to the topological nature of the Weyl electrons. Our results establish that anomalous quantum limit torque measurements provide a direct experimental method to identify and distinguish Weyl and Dirac systems.

Electron transport is conventionally determined by the momentum-relaxing scattering of electrons by the host solid and its excitations. Hydrodynamic fluid flow through channels, in contrast, is determined partly by the viscosity of the fluid, which is governed by momentum-conserving internal collisions. A long-standing question in the physics of solids has been whether the viscosity of the electron fluid plays an observable role in determining the resistance. We report experimental evidence that the resistance of restricted channels of the ultrapure two-dimensional metal palladium cobaltate (PdCoO₂) has a large viscous contribution. Comparison with theory allows an estimate of the electronic viscosity in the range between 6 × 10^–3 kg m^–1 s^–1 and 3 × 10^–4 kg m^–1 s^–1, versus 1 × 10^–3 kg m^–1 s^–1 for water at room temperature.

Many exotic metallic systems have a resistivity that varies linearly with temperature, and the physics behind this is thought to be connected to high-temperature superconductivity in the cuprates and iron pnictides^{1,2,3,4,5,6,7,8,9}. Although this phenomenon has attracted considerable attention, it is unclear how the relevant physics manifests in other transport properties, for example their response to an applied magnetic field. We report measurements of the high-field magnetoresistance of the iron pnictide superconductor BaFe₂(As_1-xP_x)₂ and find that it obeys an unusual scaling relationship between applied magnetic field and temperature, with a conversion factor given simply by the ratio of the Bohr magneton and the Boltzmann constant. This suggests that magnetic fields probe the same physics that gives rise to the T-linear resistivity, providing a new experimental clue to this long-standing puzzle.

Strong electron correlations lead to a variety of distinct ground states, such as magnetism, charge order or superconductivity. Understanding the competitive or cooperative interplay between neighbouring phases is an outstanding challenge in physics. CeRhIn₅ is a prototypical example of a heavy-fermion superconductor: it orders anti-ferromagnetically below 3.8 K, and moderate hydrostatic pressure suppresses the anti-ferromagnetic order inducing unconventional superconductivity. Here we show evidence for a phase transition to a state akin to a density wave (DW) under high magnetic fields (>27 T) in high-quality single crystal microstructures of CeRhIn₅. The DW is signalled by a hysteretic anomaly in the in-plane resistivity accompanied by non-linear electrical transport, yet remarkably thermodynamic measurements suggest that the phase transition involves only small portions of the Fermi surface. Such a subtle order might be a common feature among correlated electron systems, reminiscent of the similarly subtle charge DW state in the cuprates.

Understanding the role of electron correlations in strong spin-orbit transition-metal oxides is key to the realization of numerous exotic phases including spin-orbit–assisted Mott insulators, correlated topological solids, and prospective new high-temperature superconductors. To date, most attention has been focused on the 5d iridium-based oxides. We instead consider the Pt-based delafossite oxide PtCoO₂. Our transport measurements, performed on single-crystal samples etched to well-defined geometries using focused ion beam techniques, yield a room temperature resistivity of only 2.1 microhm·cm (μΩ-cm), establishing PtCoO₂ as the most conductive oxide known. From angle-resolved photoemission and density functional theory, we show that the underlying Fermi surface is a single cylinder of nearly hexagonal cross-section, with very weak dispersion along k_z. Despite being predominantly composed of d-orbital character, the conduction band is remarkably steep, with an average effective mass of only 1.14me. Moreover, the sharp spectral features observed in photoemission remain well defined with little additional broadening for more than 500 meV below E_F, pointing to suppressed electron-electron scattering. Together, our findings establish PtCoO₂ as a model nearly-free–electron system in a 5d delafossite transition-metal oxide.

In layered superconductors the order parameter may be modulated within the unit cell, leading to nontrivial modifications of the vortex core if the interlayer coherence length ξ_c(T) is comparable to the interlayer spacing. In the iron pnictide SmFeAs(O,F) (T_c≈50  K) this occurs below a crossover temperature T^⋆≈41  K, which separates two regimes of vortices: anisotropic Abrikosov-like at high and Josephson-like at low temperatures. Yet in the transition region around T^⋆, hybrid vortices between these two characteristics appear. Only in this region around T^⋆ and for magnetic fields well aligned with the FeAs layers, we observe oscillations of the c-axis critical current j_c(H) periodic in 1/√H due to a delicate balance of intervortex forces and interaction with the layered potential. j_c(H) shows pronounced maxima when a hexagonal vortex lattice is commensurate with the underlying crystal structure. The narrow temperature window in which oscillations are observed suggests a significant suppression of the order parameter between the superconducting layers in SmFeAs(O,F), despite its low coherence length anisotropy (γ_ξ≈3–5).

In layered superconductors, Josephson junctions may be formed within the unit cell^1,2,3 as a result of sufficiently low inter-layer coupling. These intrinsic Josephson junction (iJJ) systems⁴ have attracted considerable interest for their application potential in quantum computing as well as efficient sources of THz radiation, closing the famous ‘THz gap’⁵. So far, iJJ have been demonstrated in single-band, copper-based high-Tc superconductors, mainly in Bi–Sr–Ca–Cu–O (refs 6, 7, 8). Here we report clear experimental evidence for iJJ behaviour in the iron-based superconductor (V₂Sr₄O₆)Fe₂As₂. The intrinsic junctions are identified by periodic oscillations of the flux-flow voltage on increasing a well-aligned in-plane magnetic field⁹. The periodicity is explained by commensurability effects between the Josephson vortex lattice and the crystal structure, which is a hallmark signature of Josephson vortices confined into iJJ stacks^10,11. This finding adds the pnictide (V₂Sr₄O₆)Fe₂As₂ to the copper-based iJJ materials of interest for Josephson junction applications. In particular, novel devices based on multi-band Josephson coupling may be realized.

Iron pnictides are layered high T_c superconductors with moderate material anisotropy and thus Abrikosov vortices are expected in the mixed state. Yet, we have discovered a distinct change in the nature of the vortices from Abrikosov-like to Josephson-like in the pnictide superconductor SmFeAs(O,F) with T_c~48–50 K on cooling below a temperature T^*~41–42 K, despite its moderate electronic anisotropy γ~4–6. This transition is hallmarked by a sharp drop in the critical current and accordingly a jump in the flux-flow voltage in a magnetic field precisely aligned along the FeAs layers, indicative of highly mobile vortices. T^* coincides well with the temperature where the coherence length ξ_c perpendicular to the layers matches half of the FeAs-layer spacing. For fields slightly out-of-plane (> 0.1°– 0.15°) the vortices are completely immobilized as well-pinned Abrikosov segments are introduced when the vortex crosses the FeAs layers. We interpret these findings as a transition from well-pinned, slow moving Abrikosov vortices at high temperatures to weakly pinned, fast flowing Josephson vortices at low temperatures. This vortex dynamics could become technologically relevant as superconducting applications will always operate deep in the Josephson regime.

We report Shubnikov-de Haas oscillation measurements within the high magnetic field (μ₀H>39 T) magnetically polarized regime of URu₂Si₂, made possible using mesoscopic samples prepared by means of focused ion beam lithography. A significant change in the Fermi surface topology relative to the “hidden-order” phase is observed, signaling a transformation into a high magnetic field regime in which 5f-electrons are removed from the Fermi surface. URu₂Si₂ is therefore a rare example of an actinide compound in which a transformation of 5f-electrons can be directly observed at low temperatures, setting the stage for the unconventional ordering and high magnetic field quantum criticality in this material.

We report the synthesis, structure, and physical properties of single crystals of CePt₂In₇. Single crystal x-ray diffraction analysis confirms the tetragonal I4/mmm structure of CePt₂In₇ with unit cell parameters a = 4.5886(6) Å, c = 21.530(6) Å and V = 453.32(14) Å³. The magnetic susceptibility, heat capacity, Hall effect and electrical resistivity measurements are all consistent with CePt₂In₇ undergoing an antiferromagnetic order transition at T_N = 5.5 K, which is field independent up to 9 T. Above T_N, the Sommerfeld coefficient of specific heat is γ ≈ 300 mJ mol⁻¹ K⁻², which is characteristic of an enhanced effective mass of itinerant charge carriers. The electrical resistivity is typical of heavy-fermion behavior and gives a residual resistivity ρ₀ ∼ 0.2 µΩ cm, indicating good crystal quality. CePt₂In₇ also shows moderate anisotropy of the physical properties that is comparable to structurally related CeMIn₅ (M = Co, Rh, Ir) heavy-fermion superconductors.

Single crystals of the LnFeAsO (Ln1111, Ln = Pr, Nd, and Sm) family with lateral dimensions up to 1 mm were grown from NaAs and KAs flux at high pressure. The crystals are of good structural quality and become superconducting when O is partially substituted by F (PrFeAsO_1−xF_x and NdFeAsO_1−xF_x) or when Fe is substituted by Co (SmFe_1−xCo_xAsO). From magnetization measurements, we estimate the temperature dependence and anisotropy of the upper critical field and the critical current density of underdoped PrFeAsO_0.7F_0.3 crystal with T_c ≈ 25 K. Single crystals of SmFe_1−xCo_xAsO with maximal T_c up to 16.3 K for x ≈ 0.08 were grown. From transport and magnetic measurements, we estimate the critical fields and their anisotropy and find these superconducting properties to be quite comparable to the ones in SmFeAsO_1−xF_x with a much higher T_c ≈ 50 K. The magnetically measured critical current densities are as high as 10⁹ A/m² at 2 K up to 7 T, with indication of the usual fishtail effect. The upper critical field estimated from resistivity measurements is anisotropic with slopes of ∼−8.7 T/K (H||ab plane) and ∼−1.7 T/K (H||c axis). This anisotropy (∼5) is similar to that in other Ln1111 crystals with various higher T_c's.

When a tetrathiofulvalene (TTF) crystal is placed onto a 7,7,8,8‐tetracyanoquinodimethane (TCNQ) crystal at room temperature, a highly conducting layer is formed. In this study, we explore to what degree this is due to physical contact or transfer by sublimation of one species onto the other crystal. We have performed a variety of time‐dependent surface conductivity measurements, including TTF lamination on TCNQ at room temperature and low temperatures, as well as deposition of TTF molecules from the gas phase. Crystal-to-crystal contact insignificantly modifies material conductivity while TTF sublimation onto TCNQ is shown to dominate electronic modification.