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Competing and intertwined orders are ubiquitous in strongly correlated electron systems, such as the charge, spin, and superconducting orders in the high-Tc cuprates. Recent scanning tunneling microscopy (STM) measurements provide evidence for a charge density wave (CDW) that coexists with superconductivity in the heavy Fermion metal UTe2. This CDW persists up to at least 7.5 K and, as a CDW breaks the translational symmetry of the lattice, its disappearance is necessarily accompanied by thermodynamic phase transition. Here, we report high-precision thermodynamic measurements of the elastic moduli of UTe2. We observe no signature of a phase transition in the elastic moduli down to a level of 1 part in 10^7, strongly implying the absence of bulk CDW order in UTe2. We suggest that the CDW and associated pair density wave (PDW) observed by STM may be confined to the surface of UTe2.

A major puzzle in understanding the high-Tc is the microscopic origin of the linear-in-temperature (T-linear) resistivity in the strange metal state, extending to very high temperatures. Existing theoretical discussions imply a universal "Planckian" relaxation rate, i.e., independent of doping. However, the slope of the T-linear resistivity itself is strongly doping dependent. Here, we show that a universal Planckian relaxation rate can be reconciled with the observed transport behavior if the effective mass scales inversely with the doping, 1/p, over the entire doping range, as proposed by Anderson [P. W. Anderson, Science 235, 1196 (1987)] in the context of doped Mott insulators. The 1/p mass scaling is also directly observed in the behavior of the entropy in the overdoped cuprates. This implies that while the 1/p mass scaling in the cuprates is the consequence of strong short-range repulsive interactions, the relaxation rate itself is an emergent property of different physical origin., Comment: 14 pages including 9 figures

Early efforts to realize exotic quantum ground states in frustrated magnets focused on frustration arising from the lattice geometry alone. Attention has shifted to bond-dependent anisotropic interactions, as well as further-neighbor interactions, on non-geometrically-frustrated lattices due to their greater versatility. The honeycomb magnet BaCo$_2$(AsO$_4$)$_2$ recently emerged as a candidate host for both bond-dependent (e.g. Kitaev) and third-neighbor ($J_3$) interactions, and has become a model experimental system due to its relatively low levels of disorder. Understanding the relative importance of different exchange interactions holds the key to achieving novel ground states, such as quantum spin liquids. Here, we use the magnetotropic susceptibility to map out the intermediate and high-field phase diagram of BaCo$_2$(AsO$_4$)$_2$ as a function of the out-of-plane magnetic field direction at $T = 1.6$ K. We show that the experimental data are qualitatively consistent with classical Monte Carlo results of the XXZ-$J_1$-$J_3$ model with small Kitaev and off-diagonal exchange couplings included. However, the calculated critical fields are systematically larger than the experimental values. Infinite-DMRG computations on the quantum model reveal that quantum corrections from a nearby ferromagnetic state are likely responsible for the suppressed critical fields. Together, our experiment and theory analyses demonstrate that, while quantum fluctuations play an important role in determining the phase diagram, most of the physics of BaCo$_2$(AsO$_4$)$_2$ can be understood in terms of the classical dynamics of long-range ordered states, leaving little room for the possibility of a quantum spin liquid., Comment: 16 pages, 12 figures

The iron-based high-$T_c$ superconductors exhibit rich phase diagrams with intertwined phases, including magnetism, nematicity and superconductivity. The superconducting $T_c$ in many of these materials is maximized in the regime of strong nematic fluctuations, making the role of nematicity in influencing the superconductivity a topic of intense research. Here, we use the AC elastocaloric effect (ECE) to map out the phase diagram of Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ near optimal doping. The ECE signature at $T_c$ on the overdoped side, where superconductivity condenses without any nematic order, is quantitatively consistent with other thermodynamic probes that indicate a single-component superconducting state. In contrast, on the slightly underdoped side, where superconductivity condenses within the nematic phase, ECE reveals a second thermodynamic transition proximate to and below $T_c$. We rule out magnetism and re-entrant tetragonality as the origin of this transition, and find that our observations strongly suggest a phase transition into a multicomponent superconducting state. This implies the existence of a sub-dominant pairing instability that competes strongly with the dominant $s^\pm$ instability. Our results thus motivate a re-examination of the pairing state and its interplay with nematicity in this extensively studied iron-based superconductor, while also demonstrating the power of ECE in uncovering strain-tuned phase diagrams of quantum materials.

We compute the rotational anisotropy of the free energy of $\alpha$-RuCl$_3$ in an external magnetic field. This quantity, known as the magnetotropic susceptibility, $k$, relates to the second derivative of the free energy with respect to the angle of rotation. We have used approximation-free, auxiliary-field quantum Monte Carlo simulations for a realistic model of $\alpha$-RuCl$_3$ and optimized the path integral to alleviate the negative sign problem. This allows us to reach temperatures down to $30~\rm{K}$ -- an energy scale below the dominant Kitaev coupling. We demonstrate that the magnetotropic susceptibility in this model of $\alpha$-RuCl$_3$ displays unique scaling, $k = Tf(B/T)$, with distinct scaling functions $f$ at high and low temperatures. In comparison, for the XXZ Heisenberg model, the scaling $k = Tf(B/T)$ breaks down at a temperature scale where the uniform spin susceptibility deviates from the Curie law (i.e. at the energy scale of the exchange interactions) and never recovers at low temperatures. Our findings suggest that correlations in $\alpha$-RuCl$_3$ lead to degrees of freedom that respond isotropically to a magnetic field. One possible interpretation for the apparent scale-invariance observed in experiments could be fractionalization of the spin degrees of freedom in the extended Kitaev model., Comment: 6 pages, 4 figures, supplemental material

The electronic density of states, and, hence, the quasiparticle mass on the Fermi surface, is strongly enhanced through electronic correlations in quantum-critical metals. The nature of electronic correlations in such systems can be constrained by comparing different probes of the electronic density of states. Comparative studies in high-Tc superconductors present a significant challenge because of the masking effect of the superconducting phase. In contrast, the normal state can be readily accessed in the unconventional superconductor CeCoIn5, because the energy scale associated with superconductivity is small. Here we use thermal impedance spectroscopy to simultaneously access the electronic density of states in CeCoIn5 in two independent ways; via the nuclear spin-lattice relaxation rate and via the electronic specific heat. We establish that the temperature- and magnetic field dependence of the nuclear spin-lattice relaxation rate is determined entirely by the electronic density of states on the Fermi surface, where mass enhancement is cut off at high magnetic fields. Surprisingly, the specific heat reveals excess entropy in addition to that associated with the density of states on the Fermi surface. The electronic nature of this excess entropy is evidenced by its suppression in the superconducting state. We postulate that a second 'flavor' of boson generates the observed quantum critical physics beyond the mass renormalization on the Fermi surface in CeCoIn5, and suggest such a multi-flavor character for a broader range of quantum critical metals., Comment: 55 pages

The microscopic mechanism of Cooper pairing in a superconductor leaves its fingerprint on the symmetry of the order parameter. UTe$_2$ has been inferred to have a multi-component order parameter that entails exotic effects like time reversal symmetry breaking. However, recent experimental observations in newer-generation samples have raised questions about this interpretation, pointing to the need for a direct experimental probe of the order parameter symmetry. Here, we use pulse-echo ultrasound to measure the elastic moduli of UTe$_2$ in samples that exhibit both one and two superconducting transitions. We demonstrate the absence of thermodynamic discontinuities in the shear elastic moduli of both single- and double-transition samples, providing direct evidence that UTe$_2$ has a single-component superconducting order parameter. We further show that superconductivity is highly sensitive to compression strain along the $a$ and $c$ axes, but insensitive to strain along the $b$ axis. This leads us to suggest a single-component, odd-parity order parameter -- specifically the B$_{2u}$ order parameter -- as most compatible with our data., Comment: 27 pages, 17 figures, 5 tables

Studying superconductivity in Dirac semimetals is an important step in understanding quantum matter with topologically non-trivial order parameters. We report on the properties of the superconducting phase in single crystals of the Dirac material LaCuSb2 prepared by the self-flux method. We find that chemical and hydrostatic pressure drastically suppress the superconducting transition. Furthermore, due to large Fermi surface anisotropy, magnetization and muon spin relaxation measurements reveal Type-II superconductivity for applied magnetic fields along the $a$-axis, and Type-I superconductivity for fields along the $c$-axis. Specific heat confirms the bulk nature of the transition, and its deviation from single-gap $s$-wave BCS theory suggests multigap superconductivity. Our tight-binding model points to an anisotropic gap function arising from the spin-orbital texture near the Dirac nodes, providing an explanation for the appearance of an anomaly in specific heat well below $T_c$. Given the existence of superconductivity in a material harboring Dirac fermions, LaCuSb2 proves an interesting material candidate in the search for topological superconductivity., Comment: 58 pages, 5 main figures, supplemental information attached

Resonant ultrasound spectroscopy (RUS) is a powerful technique for measuring the full elastic tensor of a given material in a single experiment. Previously, this technique was limited to regularly-shaped samples such as rectangular parallelepipeds, spheres, and cylinders. We demonstrate a new method for determining the elastic moduli of irregularly-shaped samples, extending the applicability of RUS to a much larger set of materials. We apply this new approach to the recently-discovered unconventional superconductor UTe$_2$ and provide its elastic tensor at both 300 and 4 kelvin., Comment: 18 pages, 3 figures, 12 tables

The quasiparticle density of states in correlated and quantum-critical metals directly probes the effect of electronic correlations on the Fermi surface. Measurements of the nuclear spin-lattice relaxation rate provide one such experimental probe of quasiparticle mass through the electronic density of states. By far the most common way of accessing the spin-lattice relaxation rate is via nuclear magnetic resonance and nuclear quadrupole resonance experiments, which require resonant excitation of nuclear spin transitions. Here we report non-resonant access to spin-lattice relaxation dynamics in AC-calorimetric measurements. The nuclear spin-lattice relaxation rate is inferred in our measurements from its effect on the frequency dispersion of the thermal response of the calorimeter-sample assembly. We use fast, lithographically-defined nanocalorimeters to access the nuclear spin-lattice relaxation times in metallic indium from 0.3~K to 7~K and in magnetic fields up to 35~T.

Surface acoustic waves (SAWs) provide a contactless method for measuring the wavevector-dependent conductivity. This technique has been used to discover emergent length scales in the fractional quantum Hall regime of traditional, semiconductor-based heterostructures. SAWs would appear to be an ideal match for van der Waals (vdW) heterostructures, but the right combination of substrate and experimental geometry to allow access to the quantum transport regime has not yet been found. We demonstrate that SAW resonant cavities fabricated on LiNbO$_3$ substrates can be used to access the quantum Hall regime of high-mobility, hexagonal boron nitride (hBN) encapsulated graphene heterostructures. Our work establishes SAW resonant cavities as a viable platform for performing contactless conductivity measurements in the quantum transport regime of vdW materials., Comment: 2 figures

$\alpha$-RuCl3 is a magnetic insulator exhibiting quantum spin liquid phases possibly found in the Kitaev honeycomb model. Much of the effort towards determining Hamiltonian parameters has focused on low magnetic field ordered phases. We study this problem in the high magnetic field limit where mean-field theory is better justified. We do so by machine-learning model parameters from over 200,000 low dimensional data points by combining available magnetization, torque, and torsion data sets. Our machine, an artificial neural network-mean-field theory (ANN-MFT) encoder, maps thermodynamic conditions (temperature and field vector) to model parameters via a fully connected time-reversal covariant (equivariant) neural network and then predicts observable values using mean-field theory. To train the machine, we use PyTorch to enable backpropagation through mean-field theory with a pure PyTorch implementation of the Newton-Raphson method. The results at $20$ K and $34.5$ T are consistent with other parameter inference studies in the literature at low magnetic field but strikingly have magnitudes that scale with temperature from 1.3 K up to 80 K in the $34.5-60$ T range. We conclude that the data presents physics beyond the scope of the mean-field theory and that strong interactions dominate the physics of $\alpha$-RuCl$_3$ up to field strengths of at least 60 Tesla., Comment: 12 pages, 8 figures, 2 code listings

A variety of low-temperature, normal-state properties of optimally and overdoped cuprate superconductors, including the DC and optical transport responses, are sufficiently anomalous that they might seem to be inconsistent with any quasiparticle description. However, we show by explicit construction that the most salient phenomena can be accounted for in a system with localized "strange scatterers" embedded into a Fermi liquid with a conventional quasiparticle description. Such scatterers could originate from "two-level systems" associated with an electronic glassy state with short-range charge-order correlations., Comment: Aspects of the proposed model which we had previously identified as "unnatural" appear to us now to be impossible to realize from any physically plausible microscopic origin. Accordingly, this paper has been withdrawn. We thank Patrick Lee and Chandra Varma for focusing our attention on the seriousness of these issues.

Superconducting nickelates are a new family of strongly correlated electron materials with a phase diagram closely resembling that of superconducting cuprates. While analogy with the cuprates is natural, very little is known about the metallic state of the nickelates, making these comparisons difficult. We probe the electronic dispersion of thin-film superconducting 5-layer ($n=5$) and metallic 3-layer ($n=3$) nickelates by measuring the Seebeck coefficient, $S$. We find a temperature-independent and negative $S/T$ for both $n=5$ and $n=3$ nickelates. These results are in stark contrast to the strongly temperature-dependent $S/T$ measured at similar electron filling in the cuprate La$_{1.36}$Nd$_{0.4}$Sr$_{0.24}$CuO$_4$. The electronic structure calculated from density functional theory can reproduce the temperature dependence, sign, and amplitude of $S/T$ in the nickelates using Boltzmann transport theory. This demonstrates that the electronic structure obtained from first-principles calculations provides a reliable description of the Fermiology of superconducting nickelates, and suggests that, despite indications of strong electronic correlations, there are well-defined quasiparticles in the metallic state. Finally, we explain the differences in the Seebeck coefficient between nickelates and cuprates as originating in strong dissimilarities in impurity concentrations. Our study demonstrates that the high elastic scattering limit of the Seebeck coefficient reflects only the underlying band structure of a metal, analogous to the high magnetic field limit of the Hall coefficient. This opens a new avenue for Seebeck measurements to probe the electronic band structures of relatively disordered quantum materials., Comment: 13 pages, 10 figures

A solid object's geometry, density, and elastic moduli completely determine its spectrum of normal modes. Solving the inverse problem - determining a material's elastic moduli given a set of resonance frequencies and sample geometry - relies on the ability to compute resonance spectra accurately and efficiently. Established methods for calculating these spectra are either fast but limited to simple geometries, or are applicable to arbitrarily shaped samples at the cost of being prohibitively slow. Here, we describe a method to rapidly compute the normal modes of irregularly shaped objects using entirely open-source software. Our method's accuracy compares favorably with existing methods for simple geometries and shows a significant improvement in speed over existing methods for irregular geometries., Comment: 16 pages, 3 figures

The magnetotropic susceptibility is the thermodynamic coefficient associated with the rotational anisotropy of the free energy in an external magnetic field, and is closely related to the magnetic susceptibility. It emerges naturally in frequency-shift measurements of oscillating mechanical cantilevers, which are becoming an increasingly important tool in the quantitative study of the thermodynamics of modern condensed matter systems. Here we discuss the basic properties of the magnetotropic susceptibility as they relate to the experimental aspects of frequency-shift measurements, as well as to the interpretation of those experiments in terms of the intrinsic properties of the system under study.

Anomalous transport behavior -- both longitudinal and Hall -- is the defining characteristic of the strange-metal state of High-Tc cuprates. The temperature, frequency, and magnetic field dependence of the resistivity is understood within strange metal phenomenology as resulting from energy-scale competition to set the inelastic relaxation rate. The anomalously strong temperature dependence of the Hall coefficient, however, is at odds with this phenomenology. Here we report measurements of the Hall resistivity in the strange metal state of cuprates over a broad range of magnetic fields and temperatures. The observed field and temperature dependent Hall resistivity at very high magnetic fields reveals a distinct high-field regime which is controlled by energy-scale competition. This extends the strange metal phenomenology in the cuprates to include the Hall resistivity and suggests, in particular, that the direct effect of magnetic field on the relaxation dynamics of quantum fluctuations may be at least partially responsible for the anomalous Hall resistivity of the strange metal state.

Piezomagnetism couples strain linearly to magnetic order producing magnetization. Thus, unlike magnetostriction, it enables bidirectional control of a net magnetic moment. If this effect becomes large at room temperature, it may be technologically relevant, similar to its electric analogue, piezoelectricity. To date, however, the studies of the piezomagnetic effect have been primarily restricted to antiferromagnetic (AF) insulators at cryogenic temperatures. Here we report the discovery of a large piezomagnetism in a metal at room temperature. Strikingly, by using the AF Weyl semimetal Mn$_3$Sn, known for its nearly magnetization-free anomalous Hall effect (AHE), we find that an application of small uniaxial strain of the order of 0.1 % can control both the sign and size of the AHE. Our experiment and theory show that the piezomagnetism can control the AHE distinctly from the magnetization, which will be useful for spintronics applications., Comment: 25 pages, 4 figures, To appear in Nature Physics

We measure the full elastic tensors of Mn$_3$Ge and Mn$_3$Sn as a function of temperature through their respective antiferromagnetic phase transitions. Large discontinuities in the bulk moduli at the N\'eel transitions indicate strong magnetoelastic coupling in both compounds. Strikingly, the discontinuities are nearly a factor of 10 larger in Mn$_3$Ge than in Mn$_3$Sn. We use the magnitudes of the discontinuities to calculate the pressure derivatives of the N\'eel temperature, which are 39 K/GPa 14.3 K/GPa for Mn$_3$Ge and Mn$_3$Sn, respectively. We measured in-plane shear modulus $c_{66}$, which couples strongly to the magnetic order, in magnetic fields up to 18 T and found quantitatively similar behavior in both compounds. Recent measurements have demonstrated strong piezomagnetism in Mn$_3$Sn: our results suggest that Mn$_3$Ge may be an even better candidate for this effect., Comment: 17 pages, 8 figures

One of the main developments in unconventional superconductivity in the past two decades has been the discovery that most unconventional superconductors form phase diagrams that also contain other strongly correlated states. Many systems of interest are therefore close to more than one instability, and tuning between the resultant ordered phases is the subject of intense research1. In recent years, uniaxial pressure applied using piezoelectric-based devices has been shown to be a particularly versatile new method of tuning, leading to experiments that have advanced our understanding of the fascinating unconventional superconductor Sr$_2$RuO$_4$. Here we map out its phase diagram using high-precision measurements of the elastocaloric effect in what we believe to be the first such study including both the normal and the superconducting states. We observe a strong entropy quench on entering the superconducting state, in excellent agreement with a model calculation for pairing at the Van Hove point, and obtain a quantitative estimate of the entropy change associated with entry to a magnetic state that is observed in proximity to the superconductivity. The phase diagram is intriguing both for its similarity to those seen in other families of unconventional superconductors and for extra features unique, so far, to Sr$_2$RuO$_4$., Comment: 34 pages, 23 figures, published version, manuscript and supplementary information in one document

Topological semimetals are predicted to exhibit unconventional electrodynamics, but a central experimental challenge is singling out the contributions from the topological bands. TaAs is the prototypical example, where 24 Weyl points and 8 trivial Fermi surfaces make the interpretation of any experiment in terms of band topology ambiguous. We report magneto-infrared reflection spectroscopy measurements on TaAs. We observed sharp inter-Landau level transitions from a single pocket of Weyl Fermions in magnetic fields as low as 0.4 tesla. We determine the W2 Weyl point to be 8.3 meV below the Fermi energy, corresponding to a quantum limit - the field required to reach the lowest LL - of 0.8 Tesla - unprecedentedly low for Weyl Fermions. LL spectroscopy allows us to isolate these Weyl Fermions from all other carriers in TaAs and our result provides a new way for directly exploring the more exotic quantum phenomena in Weyl semimetals, such as the chiral anomaly.

Recent experiments suggest that the superconducting order parameter of Sr$_2$RuO$_4$ has two components. A two-component order parameter has multiple degrees of freedom in the superconducting state that can result in low-energy collective modes or the formation of domain walls -- a possibility that would explain a number of experimental observations including the smallness of the time reversal symmetry breaking signal at T$_\mathrm{c}$ and telegraph noise in critical current experiments. We perform ultrasound attenuation measurements across the superconducting transition of Sr$_2$RuO$_4$ using resonant ultrasound spectroscopy (RUS). We find that the attenuation for compressional sound increases by a factor of seven immediately below T$_\mathrm{c}$, in sharp contrast with what is found in both conventional ($s$-wave) and high-T$_\mathrm{c}$ ($d$-wave) superconductors. We find our observations to be most consistent with the presence of domain walls between different configurations of the superconducting state. The fact that we observe an increase in sound attenuation for compressional strains, and not for shear strains, suggests an inhomogeneous superconducting state formed of two distinct, accidentally-degenerate superconducting order parameters that are not related to each other by symmetry. Whatever the mechanism, a factor of seven increase in sound attenuation is a singular characteristic with which any potential theory of the superconductivity in Sr$_2$RuO$_4$ must be reconciled.

We measure the Shubnikov-de Haas effect in thin-film Sr$_2$RuO$_4$ grown on an (LaAlO$_3$)$_{0.29}$-(SrAl$_{1/2}$Ta$_{1/2}$O$_3$)$_{0.71}$ (LSAT) substrate. We detect all three known Fermi surfaces and extract the Fermi surface volumes, cyclotron effective masses, and quantum lifetimes. We show that the electronic structure is nearly identical to that of single-crystal Sr$_2$RuO$_4$, and that the quasiparticle lifetime is consistent with the Tc of comparably clean, single-crystal Sr$_2$RuO$_4$. Unlike single-crystal Sr$_2$RuO$_4$, where the quantum and transport lifetimes are roughly equal, we find that the transport lifetime is $1.3\pm0.1$ times longer than the quantum lifetime. This suggests that extended (rather than point) defects may be the dominant source of quasiparticle scattering in these films. To test this idea, we perform cross-sectional STEM and find that out-of-phase boundaries extending the entire thickness of the film occur with a density that is consistent with the quantum mean free path. The long quasiparticle lifetimes make these films ideal for studying the unconventional superconducting state in Sr$_2$RuO$_4$ through the fabrication of devices -- such as planar tunnel junctions and SQUIDs., Comment: 12 pages, 8 figures

A variety of "strange metals" exhibit resistivity that decreases linearly with temperature as $T\rightarrow 0$, in contrast with conventional metals where resistivity decreases as $T^2$. This $T$-linear resistivity has been attributed to charge carriers scattering at a rate given by $\hbar/\tau=\alpha k_{\rm B} T$, where $\alpha$ is a constant of order unity. This simple relationship between the scattering rate and temperature is observed across a wide variety of materials, suggesting a fundamental upper limit on scattering---the "Planckian limit"---but little is known about the underlying origins of this limit. Here we report a measurement of the angle-dependent magnetoresistance (ADMR) of Nd-LSCO---a hole-doped cuprate that displays $T$-linear resistivity down to the lowest measured temperatures. The ADMR unveils a well-defined Fermi surface that agrees quantitatively with angle-resolved photoemission spectroscopy (ARPES) measurements and reveals a $T$-linear scattering rate that saturates the Planckian limit, namely $\alpha = 1.2 \pm 0.4$. Remarkably, we find that this Planckian scattering rate is isotropic, i.e. it is independent of direction, in contrast with expectations from "hot-spot" models. Our findings suggest that $T$-linear resistivity in strange metals emerges from a momentum-independent inelastic scattering rate that reaches the Planckian limit., Comment: 27 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:2004.01725

Using high magnetic fields up to 60 T, we report magneto-transport and photoluminescence (PL) studies of a two-dimensional electron gas (2DEG) in a GaN/AlGaN heterojunction grown by molecular-beam epitaxy. Transport measurements demonstrate that the quantum limit can be exceeded (Landau level filling factor $\nu < 1$), and show evidence for the $\nu =2/3$ fractional quantum Hall state. Simultaneous optical and transport measurements reveal synchronous quantum oscillations of both the PL intensity and longitudinal resistivity in the integer quantum Hall regime. PL spectra directly reveal the dispersion of occupied Landau levels in the 2DEG and therefore the electron mass. These results demonstrate the utility of high (pulsed) magnetic fields for detailed measurements of quantum phenomena in high-density 2DEGs., Comment: 5 pages, 4 figures

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

The nature of the pseudogap phase remains a major barrier to our understanding of cuprate high-temperature superconductivity. Whether or not this metallic phase is defined by any of the reported broken symmetries, the topology of its Fermi surface remains a fundamental open question. Here we use angle-dependent magnetoresistance (ADMR) to measure the Fermi surface of the cuprate Nd-LSCO. Above the critical doping $p^*$ -- outside of the pseudogap phase -- we fit the ADMR data and extract a Fermi surface geometry that is in quantitative agreement with angle-resolved photoemission. Below $p^*$ -- within the pseudogap phase -- the ADMR is qualitatively different, revealing a clear transformation of the Fermi surface. Changes in the quasiparticle lifetime across $p^*$ are ruled out as the cause of this transformation. Instead we find that our data are most consistent with a reconstruction of the Fermi surface by a $Q=(\pi, \pi)$ wavevector., Comment: 32 pages, 11 figures

Sr$_2$RuO$_4$ has stood as the leading candidate for a spin-triplet superconductor for 26 years. Recent NMR experiments have cast doubt on this candidacy, however, and it is difficult to find a theory of superconductivity that is consistent with all experiments. What is needed are symmetry-based experiments that can rule out broad classes of possible superconducting order parameters. Here we use resonant ultrasound spectroscopy to measure the entire symmetry-resolved elastic tensor of Sr$_2$RuO$_4$ through the superconducting transition. We observe a thermodynamic discontinuity in the shear elastic modulus $c_{66}$, requiring that the superconducting order parameter is two-component. A two-component $p$-wave order parameter, such as $p_x+i p_y$, naturally satisfies this requirement. As this order parameter appears to be precluded by recent NMR experiments, we suggest that two other two-component order parameters, namely $\left\{d_{xz},d_{yz}\right\}$ or $\left\{d_{x^2-y^2},g_{xy(x^2-y^2)}\right\}$, are now the prime candidates for the order parameter of Sr$_2$RuO$_4$.

A variety of precise experiments have been carried out to establish the character of the superconducting state in Sr2RuO4. Many of these appear to imply contradictory conclusions concerning the symmetries of this state. Here, we propose that these results can be reconciled if we assume that there is a near-degeneracy between a d_{x^2-y^2} (B_{1g} in group theory nomenclature) and a g_{xy(x^2-y^2)} (A_{2g}) superconducting state. From a weak-coupling perspective, such an accidental degeneracy can occur at a point at which a balance between the on-site and nearest-neighbor repulsions triggers a d-wave to g-wave transition., Comment: 24 pages, 2 figures

Layered heavy-metal square-lattice compounds have recently emerged as potential Dirac fermion materials due to bonding within those sublattices. We report quantum transport and spectroscopic data on the layered Sb square-lattice material LaCuSb$_{2}$. Linearly dispersing band crossings, necessary to generate Dirac fermions, are experimentally observed in the electronic band structure observed using angle-resolved photoemission spectroscopy (ARPES), along with a quasi-two-dimensional Fermi surface. Weak antilocalization that arises from two-dimensional transport is observed in the magnetoresistance, as well as regions of linear dependence, both of which are indicative of topologically non-trivial effects. Measurements of the Shubnikov-de Haas (SdH) quantum oscillations show low effective mass electrons on the order of 0.065$m_{e}$, further confirming the presence of Dirac fermions in this material.

Many unconventional superconductors exhibit a common set of anomalous charge transport properties that characterize them as `strange metals', which provides hope that there is single theory that describes them. However, model-independent connections between the strange metal and superconductivity have remained elusive. In this letter, we show that the Hall effect of the unconventional superconductor BaFe$_2$(As$_{1-x}$P$_x$)$_2$ contains an anomalous contribution arising from the correlations within the strange metal. This term has a distinctive dependence on magnetic field, which allows us to track its behavior across the doping-temperature phase diagram, even under the superconducting dome. These measurements demonstrate that the strange metal Hall component emanates from a quantum critical point and, in the zero temperature limit, decays in proportion to the superconducting critical temperature. This creates a clear and novel connection between quantum criticality and superconductivity, and suggests that similar connections exist in other strange metal superconductors., Comment: 11 pages, 3 Figures, Supplementary Information on request

Uniaxial pressure applied along an Ru-Ru bond direction induces an elliptical distortion of the largest Fermi surface of Sr$_2$RuO$_4$, eventually causing a Fermi surface topological transition, also known as a Lifshitz transition, into an open Fermi surface. There are various anomalies in low-temperature properties associated with this transition, including maxima in the superconducting critical temperature and in resistivity. In the present paper, we report new measurements, employing new uniaxial stress apparatus and new measurements of the low-temperature elastic moduli, of the strain at which this Lifshitz transition occurs: a longitudinal strain $\varepsilon_{xx}$ of $(-0.44\pm0.06)\cdot10^{-2}$, which corresponds to a B$_{1g}$ strain $\varepsilon_{xx} - \varepsilon_{yy}$ of $(-0.66\pm0.09)\cdot10^{-2}$. This is considerably smaller than the strain corresponding to a Lifshitz transition in density functional theory calculations, even if the spin-orbit coupling is taken into account. Using dynamical mean-field theory we show that electronic correlations reduce the critical strain. It turns out that the orbital anisotropy of the local Coulomb interaction on the Ru site is furthermore important to bring this critical strain close to the experimental number, and thus well into the experimentally accessible range of strains.

The unusual correlated state that emerges in URu$_2$Si$_2$ below T$_{HO}$ = 17.5 K is known as "hidden order" because even basic characteristics of the order parameter, such as its dimensionality (whether it has one component or two), are "hidden". We use resonant ultrasound spectroscopy to measure the symmetry-resolved elastic anomalies across T$_{HO}$. We observe no anomalies in the shear elastic moduli, providing strong thermodynamic evidence for a one-component order parameter. We develop a machine learning framework that reaches this conclusion directly from the raw data, even in a crystal that is too small for traditional resonant ultrasound. Our result rules out a broad class of theories of hidden order based on two-component order parameters, and constrains the nature of the fluctuations from which unconventional superconductivity emerges at lower temperature. Our machine learning framework is a powerful new tool for classifying the ubiquitous competing orders in correlated electron systems.

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: superseded by arXiv:2005.04228

We examine recent magnetic torque measurements in two compounds, $\gamma$-Li$_2$IrO$_3$ and RuCl$_3$, which have been discussed as possible realizations of the Kitaev model. The analysis of the reported discontinuity in torque, as an external magnetic field is rotated across the $c-$axis in both crystals, suggests that they have a translationally-invariant chiral spin-order of the from $<{\bf S}_i. ({\bf S}_j ~\times ~ {\bf S}_k)> \ne 0$ in the ground state and persisting over a very wide range of magnetic field and temperature. An extra-ordinary $|B|B^2$ dependence of the torque for small fields, beside the usual $B^2$ part, is predicted due to the chiral spin-order, and found to be consistent with experiments upon further analysis of the data. Other experiments such as inelastic scattering and thermal Hall effect and several questions raised by the discovery of chiral spin-order, including its topological consequences are discussed., Comment: Clearer figures of the experimental data provided. Also clearer exposition and comment on related recent work

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., Comment: 29 pages, 14 figures

Theories of the strange metal, the parent state of many high temperature superconductors, invariably involve an important role for correlations in the spin and charge degrees of freedom. The most distinctive signature of this state in the charge transport sector is a resistance that varies linearly in temperature, but this phenomenon does not clearly point to one mechanism as temperature is a scalar quantity that influences every possible mechanism for momentum relaxation. In a previous work we identified an unusual scaling relationship between magnetic field and temperature in the in-plane resistivity of the unconventional superconductor BaFe$_2$(As$_{1-x}$P$_{x}$)$_2$, providing an opportunity to use the vector nature of the magnetic field to acquire additional clues about the mechanisms responsible for scattering in the strange metal state. Here we extend this work by investigating other components of the conductivity tensor under different orientations of the magnetic field. We find that the scaling phenomenon involves only the out-of-plane component of the magnetic field and is, strikingly, independent of the direction of the applied current. This suggests that the origin of the strange magnetotransport is in the action of the magnetic field on the correlated behavior of spin and charge degrees of freedom, rather than on the simple cyclotron motion of individual quasiparticles., Comment: 5 pages, 3 figures

The Fermi surface topology of a Weyl semimetal (WSM) depends strongly on the position of the chemical potential. If it resides close to the band touching points (Weyl nodes), as it does in TaAs, separate Fermi surfaces of opposite chirality emerge, leading to novel phenomena such as the chiral magnetic effect. If the chemical potential lies too far from the nodes, however, the chiral Fermi surfaces merge into a single large Fermi surface with no net chirality. This is realized in the WSM NbP, where the Weyl nodes lie far below the Fermi energy and where the transport properties in low magnetic fields show no evidence of chiral Fermi surfaces. Here we show that the behavior of NbP in high magnetic fields is nonetheless dominated by the presence of the Weyl nodes. Torque magnetometry up to 60 tesla reveals a change in the slope of $\tau/B$ at the quantum limit B$^\star$ ($\approx 32\,\rm{T}$), where the chemical potential enters the $n=0$ Landau level. Numerical simulations show that this behaviour results from the magnetic field pulling the chemical potential to the chiral $n=0$ Landau level belonging to the Weyl nodes. These results show that high magnetic fields can uncover topological singularities in the underlying band structure of a potential WSM, and can recover topologically non-trivial experimental properties, even when the position of the chemical potential precludes their observation in zero magnetic field., Comment: 6 pages including 5 figures

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

Electronic nematics are exotic states of matter where electronic interactions break a rotational symmetry of the underlying lattice, in analogy to the directional alignment without translational order in nematic liquid crystals. Intriguingly such phases appear in the copper- and iron-based superconductors, and their role in establishing high-temperature 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 nematic character in the heavy fermion superconductor CeRhIn5. We observe a field-induced breaking of the electronic tetragonal symmetry of in the vicinity of an antiferromagnetic (AFM) quantum phase transition at Hc~50T. This phase appears in out-of-plane fields of H*~28T and is characterized by substantial in-plane resistivity anisotropy. The anisotropy can be aligned by a small in-plane field component, with no apparent connection to the underlying crystal structure. Furthermore no anomalies are observed in the magnetic torque, suggesting the absence of metamagnetic transitions in this field range. These observations are indicative of an electronic nematic character of the high field state in CeRhIn5. The appearance of nematic behavior in a phenotypical heavy fermion superconductor highlights the interrelation of nematicity and unconventional superconductivity, suggesting nematicity to be a commonality in such materials.

The anomalous metallic state in high-temperature superconducting cuprates is masked by the onset of superconductivity near a quantum critical point. Use of high magnetic fields to suppress superconductivity has enabled a detailed study of the ground state in these systems. Yet, the direct effect of strong magnetic fields on the metallic behavior at low temperatures is poorly understood, especially near critical doping, $x=0.19$. Here we report a high-field magnetoresistance study of thin films of \LSCO cuprates in close vicinity to critical doping, $0.161\leq x\leq0.190$. We find that the metallic state exposed by suppressing superconductivity is characterized by a magnetoresistance that is linear in magnetic field up to the highest measured fields of $80$T. The slope of the linear-in-field resistivity is temperature-independent at very high fields. It mirrors the magnitude and doping evolution of the linear-in-temperature resistivity that has been ascribed to Planckian dissipation near a quantum critical point. This establishes true scale-invariant conductivity as the signature of the strange metal state in the high-temperature superconducting cuprates., Comment: 10 pages, 3 figures

Weyl fermions are a new 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. We use magnetic fields up to 95 tesla to drive the Weyl semimetal TaAs far into its quantum limit (QL), where only the purely chiral 0th Landau levels (LLs) of the Weyl fermions are occupied. We find the electrical resistivity to be nearly independent of magnetic field up to 50 tesla: unusual for conventional metals but consistent with the chiral anomaly for Weyl fermions. Above 50 tesla we observe a two-order-of-magnitude increase in resistivity, indicating that a gap opens in the chiral LLs. Above 80 tesla we observe strong ultrasonic attenuation below 2 kelvin, suggesting a mesoscopically-textured state of matter. These results point the way to inducing new correlated states of matter in the QL of Weyl semimetals.

We use the Nernst effect to delineate the boundary of the pseudogap phase in the temperature-doping phase diagram of cuprate superconductors. New data for the Nernst coefficient $\nu(T)$ of YBa$_{2}$Cu$_{3}$O$_{y}$ (YBCO), La$_{1.8-x}$Eu$_{0.2}$Sr$_x$CuO$_4$ (Eu-LSCO) and La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ (Nd-LSCO) are presented and compared with previous data including La$_{2-x}$Sr$_x$CuO$_4$ (LSCO). The temperature $T_\nu$ at which $\nu/T$ deviates from its high-temperature behaviour is found to coincide with the temperature at which the resistivity deviates from its linear-$T$ dependence, which we take as the definition of the pseudogap temperature $T^\star$- in agreement with gap opening detected in ARPES data. We track $T^\star$ as a function of doping and find that it decreases linearly vs $p$ in all four materials, having the same value in the three LSCO-based cuprates, irrespective of their different crystal structures. At low $p$, $T^\star$ is higher than the onset temperature of the various orders observed in underdoped cuprates, suggesting that these orders are secondary instabilities of the pseudogap phase. A linear extrapolation of $T^\star(p)$ to $p=0$ yields $T^\star(p\to 0)\simeq T_N(0)$, the N\'eel temperature for the onset of antiferromagnetic order at $p=0$, suggesting that there is a link between pseudogap and antiferromagnetism. With increasing $p$, $T^\star(p)$ extrapolates linearly to zero at $p\simeq p_{\rm c2}$, the critical doping below which superconductivity emerges at high doping, suggesting that the conditions which favour pseudogap formation also favour pairing. We also use the Nernst effect to investigate how far superconducting fluctuations extend above $T_{\rm c}$, as a function of doping, and find that a narrow fluctuation regime tracks $T_{\rm c}$, and not $T^\star$. This confirms that the pseudogap phase is not a form of precursor superconductivity., Comment: 24 pages and 26 figures including Appendix

Predictions of a topological electronic structure in the skutterudite TPn$_3$ family (T=transition metal, Pn=pnictogen) are investigated via magnetoresistance, quantum oscillations and angle-resolved photoemission experiments of RhSb$_3$, an unfilled skutterudite semimetal with low carrier density. Electronic band structure calculations and symmetry analysis of RhSb$_3$ indicate this material to be a zero-gap semimetal protected by symmetry with inverted valence/conduction bands that touch at the $\Gamma$ point close to the Fermi level. Transport experiments reveal an unsaturated linear magnetoresistance that approaches a factor of 200 at 60~T magnetic fields, and quantum oscillations observable up to 150~K that are consistent with a large Fermi velocity ($\sim 1.3\times 10^6$ m/s), high carrier mobility ($\sim 14$ m$^2$/Vs), and the existence of a small three dimensional hole pocket. A very small, sample-dependent effective mass falls to values as low as $0.018(2)$ of the bare electron mass and scales with Fermi wavevector. This, together with a non-zero Berry's phase and location of the Fermi level in the linear region of the valence band, suggests RhSb$_3$ as representative of a new class of toplogical semimeals with symmetry-enforced Fermi degeneracy at the high symmetry points., Comment: 9 pages, 4 figures

The complexity of the antiferromagnetic orders observed in the honeycomb iridates is a double-edged sword in the search for a quantum spin-liquid ground state: both attesting that the magnetic interactions provide many of the necessary ingredients, but simultaneously impeding access. As a result, focus has been drawn to the unusual magnetic orders and the hints they provide to the underlying spin correlations. However, the study of any particular broken symmetry state generally provides little clue as to the possibilities of other nearby ground states \cite{Anderson}. Here we use extreme magnetic fields to reveal the extent of the spin correlations in $\gamma$-lithium iridate. We find that a magnetic field with a small component along the magnetic easy-axis melts long-range order, revealing a bistable, strongly correlated spin state. Far from the usual destruction of antiferromagnetism via spin polarization, the correlated spin state possesses only a small fraction of the total moment, without evidence for long-range order up to the highest attainable magnetic fields (>90 T)., Comment: 11 pages including references and 4 figures

Magneto-quantum oscillation experiments in high temperature superconductors show a strong thermally-induced suppression of the oscillation amplitude approaching critical dopings---in support of a quantum critical origin of their phase diagrams. We suggest that, in addition to a thermodynamic mass enhancement, these experiments may directly indicate the increasing role of quantum fluctuations that suppress the oscillation amplitude through inelastic scattering. We show that the traditional theoretical approaches beyond Lifshitz-Kosevich to calculate the oscillation amplitude in correlated metals result in a contradiction with the third law of thermodynamics and suggest a way to rectify this problem., Comment: PRB Rapid commun. (2017)

In the context of the relaxation time approximation to Boltzmann transport theory, we examine the behavior of the Hall number, $n_H$, of a metal in the neighborhood of a Lifshitz transition from a closed Fermi surface to open sheets. We find a universal non-analytic dependence of $n_H$ on the electron density in the high field limit, but a non-singular dependence at low fields. The existence of an assumed nematic transition produces a doping dependent $n_H$ similar to that observed in recent experiments in the high temperature superconductor YBa$_2$Cu$_3$O$_{7-x}$., Comment: References added, text modified to include extended discussion of the modified Figure 4. 5 pages, 4 figures, with 13 pages of Supplemental Material