Measurement of the magnetic octupole susceptibility of PrV2Al20.

Revealing the presence of magnetic octupole order and associated octupole fluctuations in solids is a highly challenging task due to the lack of simple external fields that can couple to magnetic octupoles. Here, we demonstrate a methodology for probing the magnetic octupole susceptibility of a candidate material, PrV2Al20, using a product of magnetic field Hi and shear strain ϵjk as a composite effective field, while employing an adiabatic elastocaloric effect to probe the response. We observe Curie-Weiss behavior in the obtained octupolar susceptibility down to approximately 3 K. Although octupole order does not appear to be the leading multipolar channel in PrV2Al20, our results nevertheless reveal the presence of strong magnetic octupole fluctuations and hence demonstrate that octupole order is at least a competing state. More broadly, our results highlight how anisotropic strain can be combined with magnetic fields to probe elusive 'hidden' electronic orders.

Emergent tetragonality in a fundamentally orthorhombic material.

Symmetry plays a key role in determining the physical properties of materials. By Neumann's principle, the properties of a material remain invariant under the symmetry operations of the space group to which the material belongs. Continuous phase transitions are associated with a spontaneous reduction in symmetry. Less common are examples where proximity to a continuous phase transition leads to an increase in symmetry. We find signatures of an emergent tetragonal symmetry close to a charge density wave (CDW) bicritical point in a fundamentally orthorhombic material, ErTe3, for which the two distinct CDW phase transitions are tuned via anisotropic strain. We first establish that tension along the a axis favors an abrupt rotation of the CDW wave vector from the c to a axis and infer the presence of a bicritical point where the two continuous phase transitions meet. We then observe a divergence of the nematic elastoresistivity approaching this putative bicritical point, indicating an emergent tetragonality in the critical behavior.

Elastocaloric signatures of symmetric and antisymmetric strain-tuning of quadrupolar and magnetic phases in DyB2C2.

The adiabatic elastocaloric effect measures the temperature change of a given system with strain and provides a thermodynamic probe of the entropic landscape in the temperature-strain space. Here, we demonstrate that the DC bias strain-dependence of AC elastocaloric effect allows decomposition of the latter into symmetric (rotation-symmetry-preserving) and antisymmetric (rotation-symmetry-breaking) strain channels, using a tetragonal [Formula: see text]-electron intermetallic DyB[Formula: see text]C[Formula: see text]-whose antiferroquadrupolar order breaks local fourfold rotational symmetries while globally remaining tetragonal-as a showcase example. We capture the strain evolution of its quadrupolar and magnetic phase transitions using both singularities in the elastocaloric coefficient and its jumps at the transitions, and the latter we show follows a modified Ehrenfest relation. We find that antisymmetric strain couples to the underlying order parameter in a biquadratic (linear-quadratic) manner in the antiferroquadrupolar (canted antiferromagnetic) phase, which are attributed to a preserved (broken) global tetragonal symmetry, respectively. The broken tetragonal symmetry in the magnetic phase is further evidenced by elastocaloric strain-hysteresis and optical birefringence. Additionally, within the staggered quadrupolar order, the observed elastocaloric response reflects a quadratic increase of entropy with antisymmetric strain, analogous to the role magnetic field plays for Ising antiferromagnetic orders by promoting pseudospin flips. Our results demonstrate AC elastocaloric effect as a compact and incisive thermodynamic probe into the coupling between electronic degrees of freedom and strain in free energy, which holds the potential for investigating and understanding the symmetry of a wide variety of ordered phases in broader classes of quantum materials.

Layered metals as polarized transparent conductors.

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 Tl2Ba2CuO6+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.

Directional ballistic transport in the two-dimensional metal PdCoO2.

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.

Low-symmetry nonlocal transport in microstructured squares of delafossite metals.

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.

Temperature dependence of quantum oscillations from non-parabolic dispersions.

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.

Scanning SQUID microscopy in a cryogen-free dilution refrigerator.

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.

Expanding the momentum field of view in angle-resolved photoemission systems with hemispherical analyzers.

In photoelectron spectroscopy, the measured electron momentum range is intrinsically related to the excitation photon energy. Low photon energies <10 eV are commonly encountered in laser-based photoemission and lead to a momentum range that is smaller than the Brillouin zones of most materials. This can become a limiting factor when studying condensed matter with laser-based photoemission. An additional restriction is introduced by widely used hemispherical analyzers that record only electrons photoemitted in a solid angle set by the aperture size at the analyzer entrance. Here, we present an upgrade to increase the effective solid angle that is measured with a hemispherical analyzer. We achieve this by accelerating the photoelectrons toward the analyzer with an electric field that is generated by a bias voltage on the sample. Our experimental geometry is comparable to a parallel plate capacitor, and therefore, we approximate the electric field to be uniform along the photoelectron trajectory. With this assumption, we developed an analytic, parameter-free model that relates the measured angles to the electron momenta in the solid and verify its validity by comparing with experimental results on the charge density wave material TbTe3. By providing a larger field of view in momentum space, our approach using a bias potential considerably expands the flexibility of laser-based photoemission setups.

h/e oscillations in interlayer transport of delafossites.

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.

Super-geometric electron focusing on the hexagonal Fermi surface of PdCoO2.

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.

Spatial control of heavy-fermion superconductivity in CeIrIn5.

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.

Persistent antiferromagnetic order in heavily overdoped Ca1-x La x FeAs2.

In the Ca1-x La x FeAs2 (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.

Resonant torsion magnetometry in anisotropic 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.

Sr2Pt8-x As: a layered incommensurately modulated metal with saturated resistivity.

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.

Quantum limit transport and destruction of the Weyl nodes in TaAs.

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.

Inducing superconductivity in Weyl semimetal microstructures by selective ion sputtering.

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.