Elastocaloric determination of the phase diagram of Sr2RuO4.

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 tuning2,3, leading to experiments that have advanced our understanding of the fascinating unconventional superconductor Sr2RuO4 (refs. 4-9). 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 Sr2RuO4.

Linear-in temperature resistivity from an isotropic Planckian scattering rate.

A variety of 'strange metals' exhibit resistivity that decreases linearly with temperature as the temperature decreases to zero1-3, in contrast to conventional metals where resistivity decreases quadratically with temperature. This linear-in-temperature resistivity has been attributed to charge carriers scattering at a rate given by h/τ = αkBT, where α is a constant of order unity, h is the Planck constant and kB is the Boltzmann constant. 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'4,5-but little is known about the underlying origins of this limit. Here we report a measurement of the angle-dependent magnetoresistance of La1.6-xNd0.4SrxCuO4-a hole-doped cuprate that shows linear-in-temperature resistivity down to the lowest measured temperatures6. The angle-dependent magnetoresistance shows a well defined Fermi surface that agrees quantitatively with angle-resolved photoemission spectroscopy measurements7 and reveals a linear-in-temperature scattering rate that saturates at the Planckian limit, namely α = 1.2 ± 0.4. Remarkably, we find that this Planckian scattering rate is isotropic, that is, it is independent of direction, in contrast to expectations from 'hotspot' models8,9. Our findings suggest that linear-in-temperature resistivity in strange metals emerges from a momentum-independent inelastic scattering rate that reaches the Planckian limit.

Giant elastocaloric effect at low temperatures in TmVO4 and implications for cryogenic cooling.

Adiabatic decompression of paraquadrupolar materials has significant potential as a cryogenic cooling technology. We focus on TmVO[Formula: see text], an archetypal material that undergoes a continuous phase transition to a ferroquadrupole-ordered state at 2.15 K. Above the phase transition, each Tm ion contributes an entropy of [Formula: see text] due to the degeneracy of the crystal electric field groundstate. Owing to the large magnetoelastic coupling, which is a prerequisite for a material to undergo a phase transition via the cooperative Jahn-Teller effect, this level splitting, and hence the entropy, can be readily tuned by externally induced strain. Using a dynamic technique in which the strain is rapidly oscillated, we measure the adiabatic elastocaloric response of single-crystal TmVO[Formula: see text], and thus experimentally obtain the entropy landscape as a function of strain and temperature. The measurement confirms the suitability of this class of materials for cryogenic cooling applications and provides insight into the dynamic quadrupole strain susceptibility.

Nanocalorimetry using microscopic optical wireless integrated circuits.

We present in situ calorimetry, thermal conductivity, and thermal diffusivity measurements of materials using temperature-sensing optical wireless integrated circuits (OWiCs). These microscopic and untethered optical sensors eliminate input wires and reduce parasitic effects. Each OWiC has a mass of ∼100 ng, a 100-µm-scale footprint, and a thermal response time of microseconds. We demonstrate that they can measure the thermal properties of nearly any material, from aerogels to metals, on samples as small as 100 ng and over thermal diffusivities covering four orders of magnitude. They also function over a broad temperature range, and we present proof-of-concept measurements of the thermodynamic phase transitions in both liquid crystal 5CB and gadolinium.

Resonant Ultrasound Spectroscopy for Irregularly Shaped Samples and Its Application to Uranium Ditelluride.

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 practically limited to regularly shaped samples such as rectangular parallelepipeds, spheres, and cylinders [W. M. Visscher et al. J. Acoust. Soc. Am. 90, 2154 (1991)JASMAN0001-496610.1121/1.401643]. 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.

Quantum Oscillations in Graphene Using Surface Acoustic Wave Resonators.

Surface acoustic waves (SAWs) provide a contactless method for measuring wave-vector-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 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 encapsulated, graphene heterostructures. Our work establishes SAW resonant cavities as a viable platform for performing contactless conductivity measurements in the quantum transport regime of van der Waals materials.

Electronic in-plane symmetry breaking at field-tuned quantum criticality in CeRhIn5.

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

Extent of Fermi-surface reconstruction in the high-temperature superconductor HgBa2CuO4+δ.

High magnetic fields have revealed a surprisingly small Fermi surface in underdoped cuprates, possibly resulting from Fermi-surface reconstruction due to an order parameter that breaks translational symmetry of the crystal lattice. A crucial issue concerns the doping extent of such a state and its relationship to the principal pseudogap and superconducting phases. We employ pulsed magnetic-field measurements on the cuprate [Formula: see text]Cu[Formula: see text] to identify signatures of Fermi-surface reconstruction from a sign change of the Hall effect and a peak in the temperature-dependent planar resistivity. We trace the termination of Fermi-surface reconstruction to two hole concentrations where the superconducting upper critical fields are found to be enhanced. One of these points is associated with the pseudogap endpoint near optimal doping. These results connect the Fermi-surface reconstruction to both superconductivity and the pseudogap phenomena.

Rapid method for computing the mechanical resonances of irregular objects.

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.

Remarkably Weak Anisotropy in Thermal Conductivity of Two-Dimensional Hybrid Perovskite Butylammonium Lead Iodide Crystals.

Two-dimensional (2D) hybrid organic-inorganic perovskites consisting of alternating organic and inorganic layers are a new class of layered structures. They have attracted increasing interest for photovoltaic, optoelectronic, and thermoelectric applications, where knowing their thermal transport properties is critical. We carry out both experimental and computational studies on thermal transport properties of 2D butylammonium lead iodide crystals and find their thermal conductivity is ultralow (below 0.3 W m-1 K-1) with very weak anisotropy (around 1.5) among layered crystals. Further analysis reveals that the unique structure with the preferential alignment of organic chains and complicated energy landscape leads to moderately smaller phonon lifetimes in the out-of-plane direction and comparable phonon group velocities in in-plane and out-of-plane directions. These new findings may guide the future design of novel hybrid materials with desired thermal conductivity for various applications.

Anomalous thermal diffusivity in underdoped YBa2Cu3O6+x.

The thermal diffusivity in the [Formula: see text] plane of underdoped YBCO crystals is measured by means of a local optical technique in the temperature range of 25-300 K. The phase delay between a point heat source and a set of detection points around it allows for high-resolution measurement of the thermal diffusivity and its in-plane anisotropy. Although the magnitude of the diffusivity may suggest that it originates from phonons, its anisotropy is comparable with reported values of the electrical resistivity anisotropy. Furthermore, the anisotropy drops sharply below the charge order transition, again similar to the electrical resistivity anisotropy. Both of these observations suggest that the thermal diffusivity has pronounced electronic as well as phononic character. At the same time, the small electrical and thermal conductivities at high temperatures imply that neither well-defined electron nor phonon quasiparticles are present in this material. We interpret our results through a strongly interacting incoherent electron-phonon "soup" picture characterized by a diffusion constant [Formula: see text], where [Formula: see text] is the soup velocity, and scattering of both electrons and phonons saturates a quantum thermal relaxation time [Formula: see text].

Bounding the pseudogap with a line of phase transitions in YBa2Cu3O6+δ.

Close to optimal doping, the copper oxide superconductors show 'strange metal' behaviour, suggestive of strong fluctuations associated with a quantum critical point. Such a critical point requires a line of classical phase transitions terminating at zero temperature near optimal doping inside the superconducting 'dome'. The underdoped region of the temperature-doping phase diagram from which superconductivity emerges is referred to as the 'pseudogap' because evidence exists for partial gapping of the conduction electrons, but so far there is no compelling thermodynamic evidence as to whether the pseudogap is a distinct phase or a continuous evolution of physical properties on cooling. Here we report that the pseudogap in YBa2Cu3O6+δ is a distinct phase, bounded by a line of phase transitions. The doping dependence of this line is such that it terminates at zero temperature inside the superconducting dome. From this we conclude that quantum criticality drives the strange metallic behaviour and therefore superconductivity in the copper oxide superconductors.

Origin of the multiple configurations that drive the response of δ-plutonium's elastic moduli to temperature.

The electronic and thermodynamic complexity of plutonium has resisted a fundamental understanding for this important elemental metal. A critical test of any theory is the unusual softening of the bulk modulus with increasing temperature, a result that is counterintuitive because no or very little change in the atomic volume is observed upon heating. This unexpected behavior has in the past been attributed to competing but never-observed electronic states with different bonding properties similar to the scenario with magnetic states in Invar alloys. Using the recent observation of plutonium dynamic magnetism, we construct a theory for plutonium that agrees with relevant measurements by using density-functional-theory (DFT) calculations with no free parameters to compute the effect of longitudinal spin fluctuations on the temperature dependence of the bulk moduli in δ-Pu. We show that the softening with temperature can be understood in terms of a continuous distribution of thermally activated spin fluctuations.

Magnetoresistance Scaling Reveals Symmetries of the Strongly Correlated Dynamics in BaFe_{2}(As_{1-x}P_{x})_{2}.

The phenomenon of T-linear resistivity commonly observed in a number of strange metals has been widely seen as evidence for the breakdown of the quasiparticle picture of metals. This study shows that a recently discovered H/T scaling relationship in the magnetoresistance of the strange metal BaFe_{2}(As_{1-x}P_{x})_{2} is independent of the relative orientations of current and magnetic field. Rather, its magnitude and form depend only on the orientation of the magnetic field with respect to a single crystallographic axis: the direction perpendicular to the magnetic iron layers. This finding suggests that the magnetotransport scaling does not originate from the conventional averaging or orbital velocity of quasiparticles as they traverse a Fermi surface, but rather from dissipation arising from two-dimensional correlations.

Fragile charge order in the nonsuperconducting ground state of the underdoped high-temperature superconductors.

The normal state in the hole underdoped copper oxide superconductors has proven to be a source of mystery for decades. The measurement of a small Fermi surface by quantum oscillations on suppression of superconductivity by high applied magnetic fields, together with complementary spectroscopic measurements in the hole underdoped copper oxide superconductors, point to a nodal electron pocket from charge order in YBa2Cu3(6+δ). Here, we report quantum oscillation measurements in the closely related stoichiometric material YBa2Cu4O8, which reveals similar Fermi surface properties to YBa2Cu3(6+δ), despite the nonobservation of charge order signatures in the same spectroscopic techniques, such as X-ray diffraction, that revealed signatures of charge order in YBa2Cu3(6+δ). Fermi surface reconstruction in YBa2Cu4O8 is suggested to occur from magnetic field enhancement of charge order that is rendered fragile in zero magnetic fields because of its potential unconventional nature and/or its occurrence as a subsidiary to more robust underlying electronic correlations.

Avoided valence transition in a plutonium superconductor.

The d and f electrons in correlated metals are often neither fully localized around their host nuclei nor fully itinerant. This localized/itinerant duality underlies the correlated electronic states of the high-Tc cuprate superconductors and the heavy-fermion intermetallics and is nowhere more apparent than in the 5f valence electrons of plutonium. Here, we report the full set of symmetry-resolved elastic moduli of PuCoGa5--the highest Tc superconductor of the heavy fermions (Tc = 18.5 K)--and find that the bulk modulus softens anomalously over a wide range in temperature above Tc. The elastic symmetry channel in which this softening occurs is characteristic of a valence instability--therefore, we identify the elastic softening with fluctuations of the plutonium 5f mixed-valence state. These valence fluctuations disappear when the superconducting gap opens at Tc, suggesting that electrons near the Fermi surface play an essential role in the mixed-valence physics of this system and that PuCoGa5 avoids a valence transition by entering the superconducting state. The lack of magnetism in PuCoGa5 has made it difficult to reconcile with most other heavy-fermion superconductors, where superconductivity is generally believed to be mediated by magnetic fluctuations. Our observations suggest that valence fluctuations play a critical role in the unusually high Tc of PuCoGa5.

Broken rotational symmetry in the pseudogap phase of a high-T(c) superconductor.

The nature of the pseudogap phase is a central problem in the effort to understand the high-transition-temperature (high-T(c)) copper oxide superconductors. A fundamental question is what symmetries are broken when the pseudogap phase sets in, which occurs when the temperature decreases below a value T*. There is evidence from measurements of both polarized neutron diffraction and the polar Kerr effect that time-reversal symmetry is broken, but at temperatures that differ significantly from one another. Broken rotational symmetry was detected from both resistivity measurements and inelastic neutron scattering at low doping, and from scanning tunnelling spectroscopy at low temperature, but showed no clear relation to T*. Here we report the observation of a large in-plane anisotropy of the Nernst effect in YBa(2)Cu(3)O(y) that sets in precisely at T* throughout the doping phase diagram. We show that the CuO chains of the orthorhombic lattice are not responsible for this anisotropy, which is therefore an intrinsic property of the CuO(2) planes. We conclude that the pseudogap phase is an electronic state that strongly breaks four-fold rotational symmetry. This narrows the range of possible states considerably, pointing to stripe or nematic order.

Electron pockets in the Fermi surface of hole-doped high-Tc superconductors.

High-temperature superconductivity in copper oxides occurs when the materials are chemically tuned to have a carrier concentration intermediate between their metallic state at high doping and their insulating state at zero doping. The underlying evolution of the electron system in the absence of superconductivity is still unclear, and a question of central importance is whether it involves any intermediate phase with broken symmetry. The Fermi surface of the electronic states in the underdoped 'YBCO' materials YBa2Cu3O(y) and YBa2Cu4O8 was recently shown to include small pockets, in contrast with the large cylinder that characterizes the overdoped regime, pointing to a topological change in the Fermi surface. Here we report the observation of a negative Hall resistance in the magnetic-field-induced normal state of YBa2Cu3O(y) and YBa2Cu4O8, which reveals that these pockets are electron-like rather than hole-like. We propose that these electron pockets most probably arise from a reconstruction of the Fermi surface caused by the onset of a density-wave phase, as is thought to occur in the electron-doped copper oxides near the onset of antiferromagnetic order. Comparison with materials of the La2CuO4 family that exhibit spin/charge density-wave order suggests that a Fermi surface reconstruction also occurs in those materials, pointing to a generic property of high-transition-temperature (T(c)) superconductors.