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P.H.M. and M.D.B. received PhD studentship support from the UK Engineering and Physical Science Research Council via Grant No. EP/L015110/1. C.P. and P.J.W.M. are supported by the European Research Council under the European Union's Horizon 2020 research and innovation programme (Microstructured Topological Materials Grant No. 715730). E. Z. acknowledges support from the International Max Planck Research School for Chemistry and Physics of Quantum Materials (IMPRS-CPQM). Irradiation experiments performed on the SIRIUS platform were supported by the French National Network of Accelerators for Irradiation and Analysis of Molecules and Materials (EMIR&A) under Project No. EMIR 2019 18-7099. The delafossite metal PtCoO2 is among the highest-purity materials known, with low-temperature mean free path up to 5 μm in the best as-grown single crystals. It exhibits a strongly faceted, nearly hexagonal Fermi surface. This property has profound consequences for nonlocal transport within this material, such as in the classic ballistic-regime measurement of bend resistance in mesoscopic squares. Here, we report the results of experiments in which high-energy electron irradiation was used to introduce pointlike disorder into such squares, reducing the mean free path and therefore the strength of the ballistic-regime transport phenomena. We demonstrate that high-energy electron irradiation is a well-controlled technique to cross from nonlocal to local transport behavior and therefore determine the nature and extent of unconventional transport regimes. Using this technique, we confirm the origins of the directional ballistic effects observed in delafossite metals and demonstrate how the strongly faceted Fermi surface both leads to unconventional transport behavior and enhances the length scale over which such effects are important. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society. Publisher PDF

In RuCl$_3$, 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, magnetic fields introduce finite interactions between the elementary excitations, and thus the effects of high magnetic fields - comparable to the spin exchange energy scale - must be explored. Here we report measurements of the magnetotropic coefficient - the second derivative of the free energy with respect to magnetic field orientation - 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 favors the formation of a spin liquid state in RuCl$_3$., Comment: arXiv admin note: substantial text overlap with arXiv:1901.09245. Nature Physics

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 CeIrIn$_5$ 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 full control over the microscopic strain fields, and forms the basis for more advanced structuring of superconductors as in Josephson junctions., Comment: 8 pages, 4 figures

In photoelectron spectroscopy, the measured electron momentum range is intrinsically related to the excitation photon energy. Low photon energies $, 11 pages, 7 figures

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, new 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 non-intuitive at first sight, we show that they can be understood within a non-local Landauer-B\"uttiker analysis tailored to the symmetries of the square/hexagonal geometries of our combined device/Fermi surface system. Signatures of non-local transport can be resolved for squares of linear dimension of nearly 100 $\mu$m, approximately a factor of 15 larger than the bulk mean free path of the crystal from which the device was fabricated., Comment: 23 pages, 9 figures (including supplementary information)

This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Award No. DE-SC0015947 (scanning SQUID imaging and implementation of millikelvin microscopes) and the Cornell Center of Materials Research with funding from the NSF MRSEC program under Award No. DMR-1719875 (SQUID and microscope design). Fabrication of the microstructures was supported by the Max Planck Society and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) (Grant No. MO 3077/1-1) and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 715730). 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. Publisher PDF

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 PdCoO

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., Electrons in PdCoO2 can travel a long way before being scattered, and their band structure is such that they can travel in only one of three directions. As a result, the current flow through this nanoscale conductor can be very efficient.

Funding: This project was funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant no. 715730, MiTopMat) and also was supported by the Max Planck Society. A.P.M. and R.M. acknowledge support from the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter (EXC 2147). M.D.B., P.M., and V.S. acknowledge studentship funding from the EPSRC under grant no. EP/L015110/1. A.S. was supported by the Israel Science Foundation, the European Research Council (Project LEGOTOP), and the DFG through projectno.CRC-183. M.K. acknowledges support from the SIRIUS irradiation facility through project no. EMIR 2019 18-7099. 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. Postprint

The ultra-pure metallic oxide PdCoO\(_2\), exhibits strongly anisotropic in-plane ballistic behaviour governed by the underlying hexagonal Fermi surface. This restricts the electron motion into mainly three directions and significantly influences the physics of ballistic electron transport. In the following, the consequences of directional ballistics will be demonstrated by studying the in-plane anisotropy induced entirely by electron-boundary interactions in the ballistic regime. Moreover, the real space ballistic trajectories can directly be probed by bending the electrons onto cyclotron orbits in a magnetic field, which is a technique known as transverse electron focusing (TEF) and will subsequently be discussed in detail.

Focused ion beam (FIB) micro-machining has become an invaluable tool for studying quantum materials due to its capability to precisely define the shape and dimensions of single crystals on the sub-micrometer scale. In particular, high-quality mesoscale electrical transport devices can be fabricated from newly synthesised compounds or materials which are too small to manipulate otherwise. Moreover, by designing the microstructure accordingly, one can enhance the experimentally accessible signatures of the sought after physical phenomena. Further, this then enables prototype devices to be directly produced on standardised chips in order to investigate the application potential of a material for future electronics.

Strong electron interactions in CeIrIn\(_\text {5}\) give rise to heavily renormalised quasiparticles at low temperatures. Moreover, CeIrIn\(_\text {5}\) exhibits heavy fermion superconductivity below \(T_c = 0.4\) K. Due to the relatively low energy scale set by the hybridisation of the cerium 4f moments with the conduction electrons, the low temperature properties of CeIrIn\(_\text {5}\) can readily be tuned by non-thermal parameters. In particular, the superconductivity is exceptionally sensitive to the application of uniaxial pressure, such that \(T_c\) can be increased by 100% with only 7 kbar. Here I will demonstrate how the pressure sensitivity can be exploited to locally manipulate the electronic potential landscape and thereby spatially modulate the superconducting properties of CeIrIn\(_\text {5}\).

International audience; Zirconium pentatetelluride, ZrTe 5 , 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.

The high-pressure synthesis and incommensurately modulated structure are reported for the new compound Sr2Pt8−x As, with x = 0.715 (5). The structure consists of Sr2Pt3As layers alternating with Pt-only corrugated grids. Ab initio calculations predict a metallic character with a dominant role of the Pt d electrons. The electrical resistivity (ρ) and Seebeck coefficient confirm the metallic character, but surprisingly, ρ showed a near-flat temperature dependence. This observation fits the description of the Mooij correlation for electrical resistivity in disordered metals, originally developed for statistically distributed point defects. The discussed material has a long-range crystallographic order, but the high concentration of Pt vacancies, incommensurately ordered, strongly influences the electronic conduction properties. This result extends the range of validity of the Mooij correlation to long-range ordered incommensurately modulated vacancies. Motivated by the layered structure, the resistivity anisotropy was measured in a focused-ion-beam micro-fabricated well oriented single crystal. A low resistivity anisotropy indicates that the layers are electrically coupled and conduction channels along different directions are intermixed.

In the Ca

In the Ca1−xLaxFeAs2 (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 TN = 120 K, well above the one at lower doping (0.15 Below the onset of long-range magnetic order at TN, 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.

K.R.S., M.K., P.J.W.M., and A.P.M were supported by the Max-Planck-Society. P.J.W.M. acknowledges support by the Swiss National Science Foundation (Grant Nos. PP00P2_176789). M.D.B. acknowledges studentship funding from EPSRC under Grant No. EP/I007002/1. Work at Princeton was supported by NSF through the Princeton Center for Complex Materials, a Materials Research Science and Engineering Center Grant No. DMR-1420541. 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. Publisher PDF

This article reports an investigation of the new compound Sr2Pt8−xAs (x = 0.715), characterized by an incommensurately modulated structure and a temperature-independent electrical resistivity. The observation of saturated resistivity in this metallic system is described in the context of the Mooij correlation, which originates from the aperiodic potential of the incommensurately modulated vacancies in one of the Pt positions., The high-pressure synthesis and incommensurately modulated structure are reported for the new compound Sr2Pt8−xAs, with x = 0.715 (5). The structure consists of Sr2Pt3As layers alternating with Pt-only corrugated grids. Ab initio calculations predict a metallic character with a dominant role of the Pt d electrons. The electrical resistivity (ρ) and Seebeck coefficient confirm the metallic character, but surprisingly, ρ showed a near-flat temperature dependence. This observation fits the description of the Mooij correlation for electrical resistivity in disordered metals, originally developed for statistically distributed point defects. The discussed material has a long-range crystallographic order, but the high concentration of Pt vacancies, incommensurately ordered, strongly influences the electronic conduction properties. This result extends the range of validity of the Mooij correlation to long-range ordered incommensurately modulated vacancies. Motivated by the layered structure, the resistivity anisotropy was measured in a focused-ion-beam micro-fabricated well oriented single crystal. A low resistivity anisotropy indicates that the layers are electrically coupled and conduction channels along different directions are intermixed.

Unusual behavior of quantum materials commonly arises from their effective low-dimensional physics, which reflects the underlying anisotropy in the spin and charge degrees of freedom. Torque magnetometry is a highly sensitive technique to directly quantify the anisotropy in quantum materials, such as the layered high-T$_c$ superconductors, anisotropic quantum spin-liquids, and the surface states of topological insulators. Here we introduce the magnetotropic coefficient $k=\partial^2 F/\partial \theta^2$, the second derivative of the free energy F with respect to the angle $\theta$ between the sample and the applied magnetic field, and report a simple and effective method to experimentally detect it. A sub-$\mu$g crystallite is placed at the tip of a commercially available atomic force microscopy cantilever, and we show that $k$ can be quantitatively inferred from a shift in the resonant frequency under magnetic field. While related to the magnetic torque $\tau=\partial F/\partial \theta$, $k$ takes the role of torque susceptibility, and thus provides distinct insights into anisotropic materials akin to the difference between magnetization and magnetic susceptibility. The thermodynamic coefficient $k$ is discontinuous at second-order phase transitions and subject to Ehrenfest relations with the specific heat and magnetic susceptibility. We apply this simple yet quantitative method on the exemplary cases of the Weyl-semimetal NbP and the spin-liquid candidate RuCl$_3$, yet it is broadly applicable in quantum materials research., Comment: 7 pages including 6 figures and methods section

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 CeIrIn

Novel ion beam–based method induces superconductivity in Weyl semimetal microstructures., 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 (Tc ~ 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.

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., Weyl semimetals should exhibit unusual electronic behaviour but conditions where these effects dominate are difficult to achieve. Ramshaw et al. use high magnetic fields to drive TaAs into the quantum limit, finding evidence for the predicted chiral anomaly and an unanticipated increase in resistivity at the highest fields.

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 $c$ direction. 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 (QO) 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 behaviour expected from a classical purely orbital effect, independent on 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 non-monotonous LMR including regions of negative LMR. We discuss a weak antilocalisation scenario as an alternative interpretation than the chiral anomaly for these results, since it can fully account for the overall field dependence.

The ability to spatially modulate the electronic properties of solids has led to landmark discoveries in condensed matter physics as well as new electronic applications. Although crystals of strongly correlated metals exhibit a diverse set of electronic ground states, few approaches to spatially modulating their properties exist. Here we demonstrate spatial control over the superconducting state in mesoscale samples of the canonical heavy-fermion superconductor CeIrIn5. We use a focused ion beam (FIB) to pattern crystals on the microscale, which tailors the strain induced by differential thermal contraction into specific areas of the device. The resulting non-uniform strain fields induce complex patterns of superconductivity due to the strong dependence of the transition temperature on the strength and direction of strain. Electrical transport and magnetic imaging of devices with different geometry show that the obtained spatial modulation of superconductivity agrees with predictions based on finite element simulations. These results present a generic approach to manipulating electronic order on micrometer length scales in strongly correlated matter.