Wiedemann-Franz Research Articles

Large oscillatory thermal hall effect in kagome metals

The thermal Hall effect recently provided intriguing probes to the ground state of exotic quantum matters. These observations of transverse thermal Hall signals lead to the debate on the fermionic versus bosonic origins of these phenomena. The recent report of quantum oscillations (QOs) in Kitaev spin liquid points to a possible resolution. The Landau level quantization would most likely capture only the fermionic thermal transport effect. However, the QOs in the thermal Hall effect are generally hard to detect. In this work, we report the observation of a large oscillatory thermal Hall effect of correlated Kagome metals. We detect a 180-degree phase change of the oscillation and demonstrate the phase flip as an essential feature for QOs in the thermal transport properties. More importantly, the QOs in the thermal Hall channel are more profound than those in the electrical Hall channel, which strongly violates the Wiedemann–Franz (WF) law for QOs. This result presents the oscillatory thermal Hall effect as a powerful probe to the correlated quantum materials.

A criterion for strange metallicity in the Lorenz ratio

The Wiedemann-Franz (WF) law, stating that the Lorenz ratio L = κ/(Tσ) between the thermal and electrical conductivities in a metal approaches a universal constant {L}_{0}={pi }^{2}{k}_{B}^{2}/(3{e}^{2}) at low temperatures, is often interpreted as a signature of fermionic Landau quasi-particles. In contrast, we show that various models of weakly disordered non-Fermi liquids also obey the WF law at T → 0. Instead, we propose using the leading low-temperature correction to the WF law, L(T) − L0 (proportional to the inelastic scattering rate), to distinguish different types of strange metals. As an example, we demonstrate that in a solvable model of a marginal Fermi-liquid, L(T) − L0 ∝ − T. Using the quantum Boltzmann equation (QBE) approach, we find analogous behavior in a class of marginal- and non-Fermi liquids with a weakly momentum-dependent inelastic scattering. In contrast, in a Fermi-liquid, L(T) − L0 is proportional to − T2. This holds even when the resistivity grows linearly with T, due to T − linear quasi-elastic scattering (as in the case of electron-phonon scattering at temperatures above the Debye frequency). Finally, by exploiting the QBE approach, we demonstrate that the transverse Lorenz ratio, Lxy = κxy/(Tσxy), exhibits the same behavior.

Transport properties in the Horndeski holographic two-currents model

The transport features of the holographic two-currents model are investigated in the Horndeski gravity framework. This system displays metallic or insulating characteristics depending on whether the Horndeski coupling parameter gamma is negative or positive, but is unaffected by other system parameters such as the strength of the momentum dissipation hat{k}, the doping chi and the coupling between two gauge fields theta . Secondly, we demonstrate that the thermal conductivities are affected not only by the inherent properties of the black hole, but also by the model parameters. Furthermore, we are particularly interested in the Lorentz ratios’ properties. As expected, the Wiedemann–Franz (WF) law is violated, as it is in the majority of holographic systems. Particularly intriguing is the fact that several Lorentz ratio bounds reported in the typical axions model still remain true in our current theories. We would like to highlight out, however, that the lower bound for hat{bar{L}}_A is affected by the system parameters chi , theta and gamma , which differs from the case of the typical axions model.

Quantum theory of nonlinear thermal response

The Linear behavior of thermal transport has been widely explored, both theoretically and ex?perimentally. On the other hand, the nonlinear thermal response has not been fully discussed. In light of the thermal vector potential theory [Phys. Rev. Lett. 114, 196601 (2015)], we develop a general formulation to calculate the linear and nonlinear dynamic thermal responses. In the DC limit, we recover the well-known Mott relation and the Wiedemann-Franz (WF) law at the linear order response, which link the thermoelectric conductivity {\eta}, thermal conductivity \k{appa} and electric conductivity {\sigma} together. To be specific, the linear Mott relation describes the linear {\eta} is proportional to the first derivative of {\sigma} with respect to Fermi energy (for brevity we call the first derivative, the others are similar); and the linear WF law shows the linear \k{appa} is proportional to the zero derivative (i.e. the {\sigma} itself). We found there are higher-order Mott relation and WF law which follow an order-dependent relation. At the second order, the Mott relation indicates that the second order {\sigma} is proportional to the zero derivative of the second order {\eta}; but the second WF law shows that the second {\sigma} is proportional to the first derivative of \k{appa}. At the third order, the derivative order in?creases once. Although we only did explicit calculate up to the third order response, we can deduce that the n-th order electric conductivity is proportional to the n-2-th derivative of the n-th order thermoelectric conductivity for the nonlinear Mott relation; and the n-th order electric conductivity is proportional to the n-1-th derivative of the n-th order thermal conductivity for the nonlinear WF law.

Violation of the magnonic Wiedemann-Franz law in the strong nonlinear regime

The celebrated Wiedemann-Franz (WF) law which governs the relation between charge and heat transport traces back to the experimental discovery in 1853 by Wiedemann and Franz. Despite the fundamental difference of the quantum-statistical properties between fermions and bosons, the linear-in-$T$ behavior of the WF law at low temperatures has recently been found to be the universal property by the discovery of the WF law for magnon transport. However, the WF law is for the linear response, and whether or not the universal law is valid even in the nonlinear regime of Bose systems remains an open issue. Here we provide a solution to this fundamental challenge. We show that the ratio of the thermal to spin transport coefficient of magnons in topologically trivial insulating magnets exhibits a different behavior from the linear response and the universal law breaks down in the strong nonlinear regime. This finding is within experimental reach with current device and measurement technologies. Our discovery is the key ingredient in magnon-based spintronics, in the evaluation of the figure of merit for thermomagnetic conversion elements of spintronics devices.

Transport properties of a 3-dimensional holographic effective theory with gauge-axion coupling

In this paper, we implement a 3-dimensional holographic effective theory with gauge-axion coupling. The analytical black hole solution is worked out. We investigate the Direct current (DC) thermoelectric conductivities. A novel property is that DC electric conductivity for vanishing gauge-axion coupling is temperature dependent. It is different from that of 4-dimensional axion model whose DC electric conductivity is temperature independent. In addition, the gauge-axion coupling induces a metal insulator transition (MIT) at zero temperature. The properties of other DC thermoelectric conductivities are also discussed. Moreover we find that the Wiedemann-Franz (WF) law is violated in our model.

Magnetic field-induced non-trivial electronic topology in Fe3−xGeTe2

The anomalous Hall, Nernst, and thermal Hall coefficients of the itinerant ferromagnet Fe3−xGeTe2 display anomalies upon cooling that are consistent with a topological transition that could induce deviations with respect to the Wiedemann–Franz (WF) law. This law has not yet been validated for the anomalous transport variables, with recent experimental studies yielding material-dependent results. Nevertheless, the anomalous Hall and thermal Hall coefficients of Fe3−xGeTe2 are found, within our experimental accuracy, to satisfy the WF law for magnetic fields μ0H applied along its c axis. Remarkably, large anomalous transport is also observed for μ0H||a axis with the field aligned along the gradient of the chemical potential generated by thermal gradients or electrical currents, a configuration that should not lead to their observation. These anomalous planar quantities are found to not scale with the component of the planar magnetization (M||), showing instead a sharp decrease beyond μ0H||= 4 T or the field required to align the magnetic moments along μ0H||. We argue that chiral spin structures associated with Bloch domain walls lead to a field-dependent spin chirality that produces a novel type of topological transport in the absence of interaction between the magnetic field and electrical or thermal currents. Locally chiral spin structures are captured by our Monte Carlo simulations incorporating small Dzyaloshinskii–Moriya and biquadratic exchange interactions. These observations reveal not only a new way to detect and expose topological excitations, but also a new configuration for heat conversion that expands the current technological horizon for thermoelectric energy applications.

Large violation of the Wiedemann–Franz law in Heusler, ferromagnetic, Weyl semimetal Co2MnAl

The Wiedemann–Franz (WF) law relates the electronic component of the thermal conductivity to the electrical conductivity in metals through the Lorenz number. The WF law has proven to be remarkably robust, however violations have been observed in many topological materials. In this work, we report thermoelectric measurements conducted on Heusler, ferromagnetic, Weyl semimetal Co2MnAl which shows a drastic, temperature dependent violation of the WF law below 300 K. We then discuss our result in the context of known physical explanations for WF law violation. Both the magnitude and temperature dependence of the violation in Co2MnAl are extreme, indicating that there may be more than one effect contributing to the violation in this system.

Enhanced Electron Heat Conduction in TaS3 1D Metal Wire.

The 1D wire TaS3 exhibits metallic behavior at room temperature but changes into a semiconductor below the Peierls transition temperature (Tp), near 210 K. Using the 3ω method, we measured the thermal conductivity of TaS3 as a function of temperature. Electrons dominate the heat conduction of a metal. The Wiedemann–Franz law states that the thermal conductivity of a metal is proportional to the electrical conductivity σ with a proportional coefficient of L0, known as the Lorenz number—that is, . Our characterization of the thermal conductivity of metallic TaS3 reveals that, at a given temperature T, the thermal conductivity κ is much higher than the value estimated in the Wiedemann–Franz (W-F) law. The thermal conductivity of metallic TaS3 was approximately 12 times larger than predicted by W-F law, implying . This result implies the possibility of an existing heat conduction path that the Sommerfeld theory cannot account for.

Wiedemann-Franz law in scattering theory revisited

The violation of Wiedemann-Franz (WF) law has been widely discussed in quantum transport experiments as an indication of deviation from Fermi-liquid behavior. The conventional form of WF law is only concerned with the transmission function at Fermi-level which, however, vanishes in many practical situations. We reinvestigate the WF law in noninteracting quantum systems with vanishing zero energy transmission and report a universal number $21/5$ as an upper bound of Lorenz ratio $\mathscr{R}$ in weakly energy-dependent scattering theory. We provide different experimental realizations for the observation of $\mathscr{R}=21/5$ namely the transport setups with graphene, the multi-level quantum dot and double quantum dot. The reported universal Lorenz ratio paves an efficient way of experimentally obtaining the information about the associated quantum interferences in the system. Our work also provides enough evidence which concludes that the violation of WF law does not necessarily imply the non-Fermi-liquid nature of underlying transport processes; equally, the Fermi-liquid transport characteristics cannot be concluded by an observed validation of WF law.

Disorder recovers the Wiedemann-Franz law in the metallic phase of VO2

At temperatures higher than 341 K, vanadium dioxide (${\mathrm{VO}}_{2}$) is a strongly correlated metal with resistivity exceeding the Mott-Ioffe-Regel limit. Its electronic thermal conductivity is lower than that predicted by the Wiedemann-Franz (WF) law, and can be explained by nonquasiparticle transport where heat and charge currents follow separate diffusive modes. In contradiction, the Wiedemann-Franz law is a direct consequence of quasiparticle transport where charge carriers are elastically scattered. In this work, we enhance elastic electron scattering in ${\mathrm{VO}}_{2}$ by introducing atomic disorder with ion irradiation. A gradual and eventually full recovery of the WF law is observed at high defect densities. This observation provides an example that connects hydrodynamic quasiparticle transport to nonquasiparticle transport in metallic systems.

Thermodynamic efficiency of mesoscopic thermoelectric generators with broken time-reversal symmetry: Insights from an ecological optimization

We study the performance optimization for mesoscopic thermoelectric generators (MTGs) with broken time-reversal symmetry by using an ecological criterion, and some specific properties of the thermoelectric system are further revealed. We discuss the working regimes of time-reversal symmetric mesoscopic (macroscopic) thermoelectric generators, and find that a larger thermodynamic efficiency can be obtained only when the Wiedemann–Franz (WF) law is strongly violated. Furthermore, a definite dependence of the optimal bound efficiency (power) on the asymmetry parameter and the generalized thermoelectric figure of merit is analytically determined, and it is found that the usual value [Formula: see text] can be readily overcome. A larger efficiency can be obtained with the further enhancement of broken time-reversal symmetry, although the power output does not synchronize with efficiency. Interestingly, both the increase of the number [Formula: see text] of terminals and the external magnetic field open up the possibility to physically enhance the performance of thermoelectric generators, and the underlying physical origin of the improved energy conversion is also provided. The obtained results can contribute to a profound insight of thermodynamic performance for MTGs.

Wiedemann-Franz Law for Molecular Hopping Transport.

The Wiedemann-Franz (WF) law is a fundamental result in solid-state physics that relates the thermal and electrical conductivity of a metal. It is derived from the predominant transport mechanism in metals: the motion of quasi-free charge-carrying particles. Here, an equivalent WF relationship is developed for molecular systems in which charge carriers are moving not as free particles but instead hop between redox sites. We derive a concise analytical relationship between the electrical and thermal conductivity generated by electron hopping in molecular systems and find that the linear temperature dependence of their ratio as expressed in the standard WF law is replaced by a linear dependence on the nuclear reorganization energy associated with the electron hopping process. The robustness of the molecular WF relation is confirmed by examining the conductance properties of a paradigmatic molecular junction. This result opens a new way to analyze conductivity in molecular systems, with possible applications advancing the design of molecular technologies that derive their function from electrical and/or thermal conductance.

Large transverse thermoelectric figure of merit in a topological Dirac semimetal

Thermoelectric (TE) conversion in conducting materials is of eminent importance for providing renewable energy and solid-state cooling. Although traditionally, the Seebeck effect plays a key role for the TE figure of merit zST, it encounters fundamental constraints hindering its conversion efficiency. Most notably, there are the charge compensation of electrons and holes that diminishes this effect, and the intertwinement of the corresponding electrical and thermal conductivities through the Wiedemann-Franz (WF) law which makes their independent optimization in zST impossible. Here, we demonstrate that in the Dirac semimetal Cd3As2 the Nernst effect, i.e., the transverse counterpart of the Seebeck effect, can generate a large TE figure of merit zNT. At room temperature, zNT = 0.5 in a small field of 2 T; it significantly surmounts its longitudinal counterpart zST for any field and further increases upon warming. A large Nernst effect is generically expected in topological semimetals, benefiting from both the bipolar transport of compensated electrons and holes and their high mobilities. In this case, heat and charge transport are orthogonal, i.e., not intertwined by the WF law anymore. More importantly, further optimization of zNT by tuning the Fermi level to the Dirac node can be anticipated due to not only the enhanced bipolar transport, but also the anomalous Nernst effect arising from a pronounced Berry curvature. A combination of the former topologically trivial and the latter nontrivial advantages promises to open a new avenue towards high-efficient transverse thermoelectricity.

Wiedemann-Franz law and Fermi liquids

We consider in depth the applicability of the Wiedemann-Franz (WF) law, namely that the electronic thermal conductivity ($\kappa$) is proportional to the product of the absolute temperature ($T$) and the electrical conductivity ($\sigma$) in a metal with the constant of proportionality, the so-called Lorenz number $L_0$, being a materials-independent universal constant in all systems obeying the Fermi liquid (FL) paradigm. It has been often stated that the validity (invalidity) of the WF law is the hallmark of an FL (non-Fermi-liquid (NFL)). We consider, both in two (2D) and three (3D) dimensions, a system of conduction electrons at a finite temperature $T$ coupled to a bath of acoustic phonons and quenched impurities, ignoring effects of electron-electron interactions. We find that the WF law is violated arbitrarily strongly with the effective Lorenz number vanishing at low temperatures as long as phonon scattering is stronger than impurity scattering. This happens both in 2D and in 3D for $T<T_{BG}$, where $T_{BG}$ is the Bloch-Gr\"uneisen temperature of the system. In the absence of phonon scattering (or equivalently, when impurity scattering is much stronger than the phonon scattering), however, the WF law is restored at low temperatures even if the impurity scattering is mostly small angle forward scattering. Thus, strictly at $T=0$ the WF law is always valid in a FL in the presence of infinitesimal impurity scattering. For strong phonon scattering, the WF law is restored for $T> T_{BG}$ (or the Debye temperature $T_D$, whichever is lower) as in usual metals. At very high temperatures, thermal smearing of the Fermi surface causes the effective Lorenz number to go below $L_0$ manifesting a quantitative deviation from the WF law. Our work establishes definitively that the uncritical association of an NFL behavior with the failure of the WF law is incorrect.

Magnonic noise and Wiedemann-Franz law

We theoretically establish mutual relations among magnetic momentum, heat, and fluctuations of propagating magnons in a ferromagnetic insulating junction in terms of noise and the bosonic Wiedemann-Franz (WF) law. Using the Schwinger-Keldysh formalism, we calculate all transport coefficients of a noise spectrum for both magnonic spin and heat currents, and establish Onsager relations between the thermomagnetic currents and the zero-frequency noise. Making use of the magnonic WF law and the Seebeck coefficient in the low-temperature limit, we theoretically discover universal relations, i.e. being independent of material parameters, for both the nonequilibrium and equilibrium noise, and show that each noise is described solely in terms of thermal conductance. Finally, we introduce a magnonic spin-analog of the Fano factor, noise-to-current ratio, and demonstrate that the magnonic spin-Fano factor reduces to a universal value in the low-temperature limit and it remains valid even beyond a linear response regime.

Structural, electrical, thermal, mechanical properties and micro-hardness in Sn-based Sn-Pb-Al ternary alloys

The structural, electrical, thermal, mechanical properties and micro-hardness of five different samples of Sn-Pb-Al ternary alloys (Sn-[x] wt. % Pb-10 wt. % Al) (x=40, 30, 20 and 10) with constant Al concentrations, and the eutectic Sn-Pb-Al (Sn 61.82 Pb 38.10 Al 0.08 ) ternary alloy were investigated. The electrical conductivity of the samples, depending on temperature, was measured using the four-point probe technique (4PPT). The temperature dependence of the thermal conductivities of the samples was shown using the Wiedemann-Franz (W-F) law with the data obtained from electrical measurements. Scanning Electron Microscope (SEM), X-ray diffraction (XRD), and Energy Dispersive X-ray Analysis (EDX) measurements were carried out to reveal the surface morphology, crystal structure, cell parameters, grain sizes, and chemical compositions. Tensile tests were carried out to determine the ultimate tensile strengths depending on the particle size of each component in the alloys. The results of the micro-hardness tests were found using a Vickers test machine for each component of the alloys.

Thermophysical Properties of Cold- and Vacuum Plasma-Sprayed Cu-Cr-X Alloys, NiAl and NiCrAlY Coatings I: Electrical and Thermal Conductivity, Thermal Diffusivity, and Total Hemispherical Emissivity

This two-part paper reports the thermophysical properties of several cold- and vacuum plasma-sprayed monolithic Cu- and Ni-based alloy coatings. Part I presents the electrical and thermal conductivity, thermal diffusivity, and total hemispherical emissivity data, while Part II reports the specific heat capacity data for these coatings. Metallic copper alloys and stoichiometric NiAl and NiCrAlY coatings were fabricated by either the cold spray or the vacuum plasma spray deposition processes for thermal property measurements between 77 and 1223 K. The temperature dependencies of the thermal conductivities, thermal diffusivities, electrical conductivities, and total hemispherical emissivities of these cold- and vacuum-sprayed monolithic coatings are reported in this paper. The electrical and thermal conductivity data correlate reasonably well for Cu-8%Cr-1%Al, Cu-23%Cr-5%Al, and NiAl in accordance with the Wiedemann–Franz (WF) law although a better fit is obtained using the Smith–Palmer relationship. The Lorentz numbers determined from the WF law are close to the theoretical value.

Thermal transport across a continuous metal-insulator transition

The celebrated Wiedemann-Franz (WF) law is believed to be robust in metals as long as interactions between electrons preserve their fermion-quasiparticle character. We study thermal transport and the fate of the WF law close to a continuous metal-insulator transition (MIT) in the Falicov-Kimball model (FKM) using cluster-dynamical mean-field theory (CDMFT). Surprisingly, as for electrical transport, we find robust and novel quantum critical scaling in thermal transport across the MIT. We unearth the deeper reasons for these novel findings in terms of (i) the specific structure of energy-current correlations for the FKM and (ii) the microscopic electronic processes which facil- itate energy transport while simultaneously blocking charge transport close to the MIT. However, within (C)DMFT, we also find that the WF law survives at T=0 in the incoherent metal right up to the MIT, even in absence of Landau quasiparticles.

Thermal conductivity reduction of tungsten plasma facing material due to helium plasma irradiation in PISCES using the improved 3-omega method

The near-surface region of plasma facing material (PFM) plays an important role in thermal management of fusion reactors. In this work, we measured thermal conductivity of tungsten (W) surface layers damaged by He plasma in PISCES at UCSD. We studied the damage effect on both bulk, and thin film, W. We observed that the surface morphology of both bulk and thin film was altered after exposure to He plasma with the fluence of 1 × 1026 m−2 (bulk) and 2 × 1024 m−2 (thin film). Transmission electron microscopy (TEM) analysis reveals that the depth of the irradiation damaged layer was approximately 20 nm on the bulk W exposed to He plasma at 773 K for 2000 s. In order to measure the thermal conductivity of this exceedingly thin damaged layer in the bulk W, we adopted the well-established ‘3-omega’ method and employed novel nanofabrication techniques to improve the measurement sensitivity. For the damaged W thin film sample, we measured the reduction in electrical conductivity and used the Wiedemann-Franz (W-F) law to extract the thermal conductivity. Results from both measurements show that thermal conductivity in the damaged layers was reduced by at least ∼80% compared to that of undamaged W. This large reduction in thermal conductivity can be attributed to the scattering of electrons, the dominant heat carriers in W, caused by defects introduced by He plasma irradiation.