Phonon drag thermal Hall effect in metallic strontium titanate.

SrTiO3, a quantum paralectric, displays a detectable phonon thermal Hall effect (THE). Here, we show that the amplitude of the THE is extremely sensitive to stoichiometry. It drastically decreases upon substitution of a tiny fraction of Sr atoms with Ca, which stabilizes the ferroelectric order. It drastically increases by an even lower density of oxygen vacancies, which turn the system to a dilute metal. The enhancement in the metallic state exceeds by far the sum of the electronic and the phononic contributions. We explain this observation as an outcome of three features: 1) Heat is mostly transported by phonons; 2) the electronic Hall angle is extremely large; and 3) there is substantial momentum exchange between electrons and phonons. Starting from Herring's picture of phonon drag, we arrive to a quantitative account of the enhanced THE. Thus, phonon drag, hitherto detected as an amplifier of thermoelectric coefficients, can generate a purely thermal transverse response in a dilute metal with a large Hall angle. Our results reveal a hitherto-unknown consequence of momentum-conserving collisions between electrons and phonons.

T-Square Dependence of the Electronic Thermal Resistivity of Metallic Strontium Titanate.

The temperature dependence of the phase space for electron-electron (e-e) collisions leads to a T-square contribution to electrical resistivity of metals. Umklapp scattering is identified as the origin of momentum loss due to e-e scattering in dense metals. However, in dilute metals like lightly doped strontium titanate, the origin of T-square electrical resistivity in the absence of umklapp events is yet to be pinned down. Here, by separating electron and phonon contributions to heat transport, we extract the electronic thermal resistivity in niobium-doped strontium titanate and show that it also displays a T-square temperature dependence. Its amplitude correlates with the T-square electrical resistivity. The Wiedemann-Franz law strictly holds in the zero-temperature limit, but not at finite temperature, because the two T-square prefactors are different by a factor of ≈3, like in other Fermi liquids. Recalling the case of ^{3}He, we argue that T-square thermal resistivity does not require umklapp events. The approximate recovery of the Wiedemann-Franz law in the presence of disorder would account for a T-square electrical resistivity without umklapp.

Onsager Reciprocal Relation between Anomalous Transverse Coefficients of an Anisotropic Antiferromagnet.

Whenever two irreversible processes occur simultaneously, time-reversal symmetry of microscopic dynamics gives rise, on a macroscopic level, to Onsager's reciprocal relations, which impose constraints on the number of independent components of any transport coefficient tensor. Here, we show that in the antiferromagnetic YbMnBi_{2}, which displays a strong temperature-dependent anisotropy, Onsager's reciprocal relations are strictly satisfied for anomalous electric (σ_{ij}^{A}) and anomalous thermoelectric (α_{ij}^{A}) conductivity tensors. In contradiction with what was recently reported by Pan et al. [Nat. Mater. 21, 203 (2022)NMAACR1476-112210.1038/s41563-021-01149-2], we find that σ_{ij}^{A}(H)=σ_{ji}^{A}(-H) and α_{ij}^{A}(H)=α_{ji}^{A}(-H). This equality holds in the whole temperature window irrespective of the relative weights of the intrinsic or extrinsic mechanisms. The α_{ij}^{A}/σ_{ij}^{A} ratio is close to k_{B}/e at room temperature but peaks to an unprecedented magnitude of 2.9k_{B}/e at ∼150 K, which may involve nondegenerate carriers of small Fermi surface pockets.

Critical point for Bose-Einstein condensation of excitons in graphite.

An exciton is an electron-hole pair bound by attractive Coulomb interaction. Short-lived excitons have been detected by a variety of experimental probes in numerous contexts. An excitonic insulator, a collective state of such excitons, has been more elusive. Here, thanks to Nernst measurements in pulsed magnetic fields, we show that in graphite there is a critical temperature (T = 9.2 K) and a critical magnetic field (B = 47 T) for Bose-Einstein condensation of excitons. At this critical field, hole and electron Landau subbands simultaneously cross the Fermi level and allow exciton formation. By quantifying the effective mass and the spatial separation of the excitons in the basal plane, we show that the degeneracy temperature of the excitonic fluid corresponds to this critical temperature. This identification would explain why the field-induced transition observed in graphite is not a universal feature of three-dimensional electron systems pushed beyond the quantum limit.

Thermalization and possible signatures of quantum chaos in complex crystalline materials.

Analyses of thermal diffusivity data on complex insulators and on strongly correlated electron systems hosted in similar complex crystal structures suggest that quantum chaos is a good description for thermalization processes in these systems, particularly in the high-temperature regime where the many phonon bands and their interactions dominate the thermal transport. Here we observe that for these systems diffusive thermal transport is controlled by a universal Planckian timescale [Formula: see text] and a unique velocity [Formula: see text] Specifically, [Formula: see text] for complex insulators, and [Formula: see text] in the presence of strongly correlated itinerant electrons ([Formula: see text] and [Formula: see text] are the phonon and electron velocities, respectively). For the complex correlated electron systems we further show that charge diffusivity, while also reaching the Planckian relaxation bound, is largely dominated by the Fermi velocity of the electrons, hence suggesting that it is only the thermal (energy) diffusivity that describes chaos diffusivity.

Wide Critical Fluctuations of the Field-Induced Phase Transition in Graphite.

In the immediate vicinity of the critical temperature (T_{c}) of a phase transition, there are fluctuations of the order parameter that reside beyond the mean-field approximation. Such critical fluctuations usually occur in a very narrow temperature window in contrast to Gaussian fluctuations. Here, we report on a study of specific heat in graphite subject to a high magnetic field when all carriers are confined in the lowest Landau levels. The observation of a BCS-like specific heat jump in both temperature and field sweeps establishes that the phase transition discovered decades ago in graphite is of the second order. The jump is preceded by a steady field-induced enhancement of the electronic specific heat. A modest (20%) reduction in the amplitude of the magnetic field (from 33 to 27 T) leads to a threefold decrease of T_{c} and a drastic widening of the specific heat anomaly, which acquires a tail spreading to two times T_{c}. We argue that the steady departure from the mean-field BCS behavior is the consequence of an exceptionally large Ginzburg number in this dilute metal, which grows steadily as the field lowers. Our fit of the critical fluctuations indicates that they belong to the 3DXY universality class as in the case of the ^{4}He superfluid transition.

Universal Bound to the Amplitude of the Vortex Nernst Signal in Superconductors.

A liquid of superconducting vortices generates a transverse thermoelectric response. This Nernst signal has a tail deep in the normal state due to superconducting fluctuations. Here, we present a study of the Nernst effect in two-dimensional heterostructures of Nb-doped strontium titanate (STO) and in amorphous MoGe. The Nernst signal generated by ephemeral Cooper pairs above the critical temperature has the magnitude expected by theory in STO. On the other hand, the peak amplitude of the vortex Nernst signal below T_{c} is comparable in both and in numerous other superconductors despite the large distribution of the critical temperature and the critical magnetic fields. In four superconductors belonging to different families, the maximum Nernst signal corresponds to an entropy per vortex per layer of ≈k_{B}ln2.

Phonon Thermal Hall Effect in Strontium Titanate.

It has been known for more than a decade that phonons can produce an off-diagonal thermal conductivity in the presence of a magnetic field. Recent studies of thermal Hall conductivity, κ_{xy}, in a variety of contexts, however, have assumed a negligibly small phonon contribution. We present a study of κ_{xy} in quantum paraelectric SrTiO_{3}, which is a nonmagnetic insulator and find that its peak value exceeds what has been reported in any other insulator, including those in which the signal has been qualified as "giant." Remarkably, κ_{xy}(T) and κ(T) peak at the same temperature and the former decreases faster than the latter at both sides of the peak. Interestingly, in the case of La_{2}CuO_{4} and α-RuCl_{3}, κ_{xy}(T) and κ(T) peak also at the same temperature. We also studied KTaO_{3} and found a small signal, indicating that a sizable κ_{xy}(T) is not a generic feature of quantum paraelectrics. Combined to other observations, this points to a crucial role played by antiferrodistortive domains in generating κ_{xy} of this solid.

Thermal Transport and Phonon Hydrodynamics in Strontium Titanate.

We present a study of thermal conductivity, κ, in undoped and doped strontium titanate in a wide temperature range (2-400 K) and detecting different regimes of heat flow. In undoped SrTiO_{3}, κ evolves faster than cubic with temperature below its peak and in a narrow temperature window. Such behavior, previously observed in a handful of solids, has been attributed to a Poiseuille flow of phonons, expected to arise when momentum-conserving scattering events outweigh momentum-degrading ones. The effect disappears in the presence of dopants. In SrTi_{1-x}Nb_{x}O_{3}, a significant reduction in lattice thermal conductivity starts below the temperature at which the average inter-dopant distance and the thermal wavelength of acoustic phonons become comparable. In the high-temperature regime, thermal diffusivity becomes proportional to the inverse of temperature, with a prefactor set by sound velocity and Planckian time (τ_{p}=(ℏ/k_{B}T)).

Anomalous Nernst and Righi-Leduc Effects in Mn_{3}Sn: Berry Curvature and Entropy Flow.

We present a study of electric, thermal and thermoelectric response in noncollinear antiferromagnet Mn_{3}Sn, which hosts a large anomalous Hall effect (AHE). Berry curvature generates off-diagonal thermal (Righi-Leduc) and thermoelectric (Nernst) signals, which are detectable at room temperature and invertible with a small magnetic field. The thermal and electrical Hall conductivities respect the Wiedemann-Franz law, implying that the transverse currents induced by the Berry curvature are carried by Fermi surface quasiparticles. In contrast to conventional ferromagnets, the anomalous Lorenz number remains close to the Sommerfeld number over the whole temperature range of study, excluding any contribution by inelastic scattering and pointing to the Berry curvature as the unique source of AHE. The anomalous off-diagonal thermo-electric and Hall conductivities are strongly temperature dependent and their ratio is close to k_{B}/e.

Nernst effect in metals and superconductors: a review of concepts and experiments.

The Nernst effect is the transverse electric field produced by a longitudinal thermal gradient in the presence of a magnetic field. At the beginning of this century, Nernst experiments on cuprates were analyzed assuming that: (i) the contribution of quasi-particles to the Nernst signal is negligible; and (ii) Gaussian superconducting fluctuations cannot produce a Nernst signal well above the critical temperature. Both these assumptions were contradicted by subsequent experiments. This paper reviews experiments documenting multiple sources of a Nernst signal, which, according to the Bridgman relation, measures the flow of transverse entropy caused by a longitudinal particle flow. Along the lines of Landauer's approach to transport phenomena, the magnitude of the transverse magneto-thermoelectric response is linked to the quantum of thermoelectric conductance and a number of material-dependent length scales: the mean free path, the Fermi wavelength, the de Broglie thermal wavelength and the superconducting coherence length. Extremely mobile quasi-particles in dilute metals generate a widely-documented Nernst signal. Fluctuating Cooper pairs in the normal state of superconductors have been found to produce a detectable Nernst signal with an amplitude conforming to the Gaussian theory, first conceived by Ussishkin, Sondhi and Huse. In addition to these microscopic sources, mobile Abrikosov vortices, mesoscopic objects simultaneously carrying entropy and magnetic flux, can produce a sizeable Nernst response. Finally, in metals subject to a magnetic field strong enough to truncate the Fermi surface to a few Landau tubes, each exiting tube generates a peak in the Nernst response. The survey of these well-established sources of the Nernst signal is a helpful guide to identify the origin of the Nernst signal in other controversial cases.

Colossal Seebeck Coefficient of Hopping Electrons in (TMTSF)_{2} PF_{6}.

We report on a study of the Seebeck coefficient and resistivity in the quasi-one-dimensional conductor (TMTSF)_{2} PF_{6} extended deep into the spin-density-wave state. The metal-insulator transition at T_{SDW}=12 K leads to a reduction in carrier concentration by 7 orders of magnitude. Below 1 K, charge transport displays the behavior known as variable range hopping. Until now, the Seebeck response of electrons in this regime has barely been explored and is even less understood. We find that, in this system, residual carriers, hopping from one trap to another, generate a Seebeck coefficient as large as 400 k_{B}/e. The results provide the first solid evidence for a long-standing prediction according to which hopping electrons in the presence of the Coulomb interaction can generate a sizable Seebeck coefficient in the zero-temperature limit.

Origin of the Large Anisotropic g Factor of Holes in Bismuth.

The ratio of the Zeeman splitting to the cyclotron energy (M=ΔE_{Z}/ℏω_{c}) for holelike carriers in bismuth has been quantified with great precision by many experiments performed during the past five decades. It exceeds 2 when the magnetic field is along the trigonal axis and vanishes in the perpendicular configuration. Theoretically, however, M is expected to be isotropic and equal to unity in a two-band Dirac model. We argue that a solution to this half-a-century-old puzzle can be found by extending the k·p theory to multiple bands. Our model not only gives a quantitative account of the magnitude and anisotropy of M for holelike carriers in bismuth, but also explains its contrasting evolution with antimony doping and pressure, both probed by new experiments reported here. The present results have important implications for the magnitude and anisotropy of M in other systems with strong spin-orbit coupling.

Quantum Oscillations, Thermoelectric Coefficients, and the Fermi Surface of Semimetallic WTe2.

We present a study of angle-resolved quantum oscillations of electric and thermoelectric transport coefficients in semimetallic WTe2, which has the particularity of displaying a large B(2) magnetoresistance. The Fermi surface consists of two pairs of electronlike and holelike pockets of equal volumes in a "Russian doll" structure. The carrier density, Fermi energy, mobility, and the mean-free path of the system are quantified. An additional frequency is observed above a threshold field and attributed to the magnetic breakdown across two orbits. In contrast to all other dilute metals, the Nernst signal remains linear in the magnetic field even in the high-field (ωcτ≫1) regime. Surprisingly, none of the pockets extend across the c axis of the first Brillouin zone, making the system a three-dimensional metal with moderate anisotropy in Fermi velocity, yet a large anisotropy in the mean-free path.

Landau spectrum and twin boundaries of bismuth in the extreme quantum limit.

The Landau spectrum of bismuth is complex and includes many angle-dependent lines in the extreme quantum limit. The adequacy of single-particle theory to describe this spectrum in detail has been an open issue. Here, we present a study of angle-resolved Nernst effect in bismuth, which maps the angle-resolved Landau spectrum for the entire solid angle up to 28 T. The experimental map is in good agreement with the results of a theoretical model with parabolic dispersion for holes and an extended Dirac Hamiltonian for electrons. The angular dependence of additional lines in the Landau spectrum allows us to uncover the mystery of their origin. They correspond to the lines expected for the hole Landau levels in a secondary crystal tilted by 108°, the angle between twinned crystals in bismuth. According to our results, the electron reservoirs of the two identical tilted crystals have different chemical potentials, and carriers across the twin boundary have different concentrations. An exceptional feature of this junction is that it separates two electron-hole compensated reservoirs. The link between this edge singularity and the states wrapping a three-dimensional electron gas in the quantum limit emerges as an outstanding open question.

How heat propagates in liquid 3He.

In Landau's Fermi liquid picture, transport is governed by scattering between quasi-particles. The normal liquid 3He conforms to this picture but only at very low temperature. Here, we show that the deviation from the standard behavior is concomitant with the fermion-fermion scattering time falling below the Planckian time, ℏ k B T and the thermal diffusivity of this quantum liquid is bounded by a minimum set by fundamental physical constants and observed in classical liquids. This points to collective excitations (a sound mode) as carriers of heat. We propose that this mode has a wavevector of 2kF and a mean free path equal to the de Broglie thermal length. This would provide an additional conducting channel with a T 1/2 temperature dependence, matching what is observed by experiments. The experimental data from 0.007 K to 3 K can be accounted for, with a margin of 10%, if thermal conductivity is the sum of two contributions: one by quasi-particles (varying as the inverse of temperature) and another by sound (following the square root of temperature).

Two phase transitions induced by a magnetic field in graphite.

Different instabilities have been speculated for a three-dimensional electron gas confined to its lowest Landau level. The phase transition induced in graphite by a strong magnetic field, and believed to be a charge density wave, is the only experimentally established case of such instabilities. Studying the magnetoresistance in graphite for the first time up to 80 T, we find that the magnetic field induces two successive phase transitions, consisting of two distinct ordered states each restricted to a finite field window. In both states, an energy gap opens up in the out-of-plane conductivity and coexists with an unexpected in-plane metallicity for a fully gap bulk system. Such peculiar metallicity may arise as a consequence of edge-state transport expected to develop in the presence of a bulk gap.

The phonon thermal Hall angle in black phosphorus.

The origin of phonon thermal Hall Effect (THE) observed in a variety of insulators is yet to be identified. Here, we report on the observation of a thermal Hall conductivity in a non-magnetic elemental insulator, with an amplitude exceeding what has been previously observed. In black phosphorus (BP), the longitudinal (κii), and the transverse, κij, thermal conductivities peak at the same temperature and at this peak temperature, the κij/κjj/B is ≈ 10-4-10-3 T-1. Both these features are shared by other insulators displaying THE, despite an absolute amplitude spreading over three orders of magnitude. The absence of correlation between the thermal Hall angle and the phonon mean-free-path imposes a severe constraint for theoretical scenarios of THE. We show that in BP a longitudinal and a transverse acoustic phonon mode anti-cross, facilitating wave-like transport across modes. The anisotropic charge distribution surrounding atomic bonds can pave the way for coupling between phonons and the magnetic field.

Tuning the anomalous Nernst and Hall effects with shifting the chemical potential in Fe-doped and Ni-doped Co3Sn2S2.

Co3Sn2S2is believed to be a magnetic Weyl semimetal. It displays large anomalous Hall, Nernst and thermal Hall effects with a remarkably large anomalous Hall angle. Here, we present a comprehensive study of how substituting Co by Fe or Ni affects the electrical and thermoelectric transport. We find that doping alters the amplitude of the anomalous transverse coefficients. The maximum decrease in the amplitude of the low-temperature anomalous Hall conductivityσijAis twofold. Comparing our results with theoretical calculations of the Berry spectrum assuming a rigid shift of the Fermi level, we find that given the modest shift in the position of the chemical potential induced by doping, the experimentally observed variation occurs five times faster than expected. Doping affects the amplitude and the sign of the anomalous Nernst coefficient. Despite these drastic changes, the amplitude of theαijA/σijAratio at the Curie temperature remains close to≈0.5kB/e, in agreement with the scaling relationship observed across many topological magnets.