Weak signal extraction enabled by deep neural network denoising of diffraction data.

The removal or cancellation of noise has wide-spread applications in imaging and acoustics. In applications in everyday life, such as image restoration, denoising may even include generative aspects, which are unfaithful to the ground truth. For scientific use, however, denoising must reproduce the ground truth accurately. Denoising scientific data is further challenged by unknown noise profiles. In fact, such data will often include noise from multiple distinct sources, which substantially reduces the applicability of simulation-based approaches. Here we show how scientific data can be denoised by using a deep convolutional neural network such that weak signals appear with quantitative accuracy. In particular, we study X-ray diffraction and resonant X-ray scattering data recorded on crystalline materials. We demonstrate that weak signals stemming from charge ordering, insignificant in the noisy data, become visible and accurate in the denoised data. This success is enabled by supervised training of a deep neural network with pairs of measured low- and high-noise data. We additionally show that using artificial noise does not yield such quantitatively accurate results. Our approach thus illustrates a practical strategy for noise filtering that can be applied to challenging acquisition problems.

Unveiling the double-peak structure of quantum oscillations in the specific heat.

Quantum oscillation phenomenon is an essential tool to understand the electronic structure of quantum matter. Here we report a systematic study of quantum oscillations in the electronic specific heat Cel in natural graphite. We show that the crossing of a single spin Landau level and the Fermi energy give rise to a double-peak structure, in striking contrast to the single peak expected from Lifshitz-Kosevich theory. Intriguingly, the double-peak structure is predicted by the kernel term for Cel/T in the free electron theory. The Cel/T represents a spectroscopic tuning fork of width 4.8kBT which can be tuned at will to resonance. Using a coincidence method, the double-peak structure can be used to accurately determine the Landé g-factors of quantum materials. More generally, the tuning fork can be used to reveal any peak in fermionic density of states tuned by magnetic field, such as Lifshitz transition in heavy-fermion compounds.

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.

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.

Boundary conductance in macroscopic bismuth crystals.

The interface between a solid and vacuum can become electronically distinct from the bulk. This feature, encountered in the case of quantum Hall effect, has a manifestation in insulators with topologically protected metallic surface states. Non-trivial Berry curvature of the Bloch waves or periodically driven perturbation are known to generate it. Here, by studying the angle-dependent magnetoresistance in prismatic bismuth crystals of different shapes, we detect a robust surface contribution to electric conductivity when the magnetic field is aligned parallel to a two-dimensional boundary between the three-dimensional crystal and vacuum. The effect is absent in antimony, which has an identical crystal symmetry, a similar Fermi surface structure and equally ballistic carriers, but an inverted band symmetry and a topological invariant of opposite sign. Our observation confirms that the boundary interrupting the cyclotron orbits remains metallic in bismuth, which is in agreement with what was predicted by Azbel decades ago. However, the absence of the effect in antimony indicates an intimate link between band symmetry and this boundary conductance.

Non-universal current flow near the metal-insulator transition in an oxide interface.

In systems near phase transitions, macroscopic properties often follow algebraic scaling laws, determined by the dimensionality and the underlying symmetries of the system. The emergence of such universal scaling implies that microscopic details are irrelevant. Here, we locally investigate the scaling properties of the metal-insulator transition at the LaAlO3/SrTiO3 interface. We show that, by changing the dimensionality and the symmetries of the electronic system, coupling between structural and electronic properties prevents the universal behavior near the transition. By imaging the current flow in the system, we reveal that structural domain boundaries modify the filamentary flow close to the transition point, preventing a fractal with the expected universal dimension from forming.

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.

Thermal resistivity and hydrodynamics of the degenerate electron fluid in antimony.

Detecting hydrodynamic fingerprints in the flow of electrons in solids constitutes a dynamic field of investigation in contemporary condensed matter physics. Most attention has been focused on the regime near the degeneracy temperature when the thermal velocity can present a spatially modulated profile. Here, we report on the observation of a hydrodynamic feature in the flow of quasi-ballistic degenerate electrons in bulk antimony. By scrutinizing the temperature dependence of thermal and electric resistivities, we detect a size-dependent departure from the Wiedemann-Franz law, unexpected in the momentum-relaxing picture of transport. This observation finds a natural explanation in the hydrodynamic picture, where upon warming, momentum-conserving collisions reduce quadratically in temperature both viscosity and thermal diffusivity. This effect has been established theoretically and experimentally in normal-state liquid 3He. The comparison of electrons in antimony and fermions in 3He paves the way to a quantification of momentum-conserving fermion-fermion collision rate in different Fermi liquids.

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.

Finite-temperature violation of the anomalous transverse Wiedemann-Franz law.

The Wiedemann-Franz (WF) law has been tested in numerous solids, but the extent of its relevance to the anomalous transverse transport and the topological nature of the wave function, remains an open question. Here, we present a study of anomalous transverse response in the noncollinear antiferromagnet Mn3Ge extended from room temperature down to sub-kelvin temperature and find that the anomalous Lorenz ratio remains close to the Sommerfeld value up to 100 K but not above. The finite-temperature violation of the WF correlation is caused by a mismatch between the thermal and electrical summations of the Berry curvature and not by inelastic scattering. This interpretation is backed by our theoretical calculations, which reveals a competition between the temperature and the Berry curvature distribution. The data accuracy is supported by verifying the anomalous Bridgman relation. The anomalous Lorenz ratio is thus an extremely sensitive probe of the Berry spectrum of a solid.

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.

Chiral domain walls of Mn3Sn and their memory.

Magnetic domain walls are topological solitons whose internal structure is set by competing energies which sculpt them. In common ferromagnets, domain walls are known to be of either Bloch or Néel types. Little is established in the case of Mn3Sn, a triangular antiferromagnet with a large room-temperature anomalous Hall effect, where domain nucleation is triggered by a well-defined threshold magnetic field. Here, we show that the domain walls of this system generate an additional contribution to the Hall conductivity tensor and a transverse magnetization. The former is an electric field lying in the same plane with the magnetic field and electric current and therefore a planar Hall effect. We demonstrate that in-plane rotation of spins inside the domain wall would explain both observations and the clockwise or anticlockwise chirality of the walls depends on the history of the field orientation and can be controlled.

Magnetoresistance and valley degree of freedom in bulk bismuth.

In this paper, we first review fundamental aspects of magnetoresistance in multi-valley systems based on the semiclassical theory. Then we will review experimental evidence and theoretical understanding of magnetoresistance in an archetypal multi-valley system, where the electric conductivity is set by the sum of the contributions of different valleys. Bulk bismuth has three valleys with an extremely anisotropic effective mass. As a consequence the magnetoconductivity in each valley is extremely sensitive to the orientation of the magnetic field. Therefore, a rotating magnetic field plays the role of a valley valve tuning the contribution of each valley to the total conductivity. In addition to this simple semiclassical effect, other phenomena arise in the high-field limit as a consequence of an intricate Landau spectrum. In the vicinity of the quantum limit, the orientation of magnetic field significantly affects the distribution of carriers in each valley, namely, the valley polarization is induced by the magnetic field. Moreover, experiment has found that well beyond the quantum limit, one or two valleys become totally empty. This is the only case in condensed matter physics where a Fermi sea is completely dried up by a magnetic field without a metal-insulator transition. There have been two long-standing problems on bismuth near the quantum limit: the large anisotropic Zeeman splitting of holes, and the extra peaks in quantum oscillations, which cannot be assigned to any known Landau levels. These problems are solved by taking into account the interband effect due to the spin-orbit couplings for the former, and the contributions from the twinned crystal for the latter. Up to here, the whole spectrum can be interpreted within the one-particle theory. Finally, we will discuss transport and thermodynamic signatures of breaking of the valley symmetry in this system. By this term, we refer to the observed spontaneous loss of threefold symmetry at high magnetic field and low temperature. Its theoretical understanding is still missing. We will discuss possible explanations.

Emptying Dirac valleys in bismuth using high magnetic fields.

The Fermi surface of elemental bismuth consists of three small rotationally equivalent electron pockets, offering a valley degree of freedom to charge carriers. A relatively small magnetic field can confine electrons to their lowest Landau level. This is the quantum limit attained in other dilute metals upon application of sufficiently strong magnetic field. Here we report on the observation of another threshold magnetic field never encountered before in any other solid. Above this field, Bempty, one or two valleys become totally empty. Drying up a Fermi sea by magnetic field in the Brillouin zone leads to a manyfold enhancement in electric conductance. We trace the origin of the large drop in magnetoresistance across Bempty to transfer of carriers between valleys with highly anisotropic mobilities. The non-interacting picture of electrons with field-dependent mobility explains most results but the Coulomb interaction may play a role in shaping the fine details.

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.

SOLID-STATE PHYSICS. Scalable T² resistivity in a small single-component Fermi surface.

Scattering among electrons generates a distinct contribution to electrical resistivity that follows a quadratic temperature (T) dependence. In strongly correlated electron systems, the prefactor A of this T(2) resistivity scales with the magnitude of the electronic specific heat, γ. Here we show that one can change the magnitude of A by four orders of magnitude in metallic strontium titanate (SrTiO3) by tuning the concentration of the carriers and, consequently, the Fermi energy. The T(2) behavior persists in the single-band dilute limit despite the absence of two known mechanisms for T(2) behavior: distinct electron reservoirs and Umklapp processes. The results highlight the absence of a microscopic theory for momentum decay through electron-electron scattering in various Fermi liquids.

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.

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.

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.