Metallic nanostructures (the nanofilms and nanowires) are widely used in electronic devices, and their thermal transport properties are crucial for heat dissipation. However, there are still gaps in understanding thermal transport in metallic nanostructures, especially regarding the size effect and validity of the Wiedemann-Franz law. In this work, we perform mode-by-mode first-principles calculations combining the Boltzmann transport equation to understand thermal transport in metallic nanostructures. We take the gold (Au) and tungsten (W) nanostructures as prototypes. It is found that when the size of nanostructures is on the order of several tens of nanometers, the electronic/phonon thermal conductivity is smaller than the bulk value and decreases with size. The phonon contribution increases in nanostructures for those metals with small bulk phonon thermal conductivity (like Au), while the phonon contribution may increase or be suppressed in nanostructures for those metals with large bulk phonon thermal conductivity (like W). By assuming that the grain boundary does not induce inelastic electron-phonon scattering, the Wiedemann-Franz law works well in both Au and W nanostructures if the Lorentz ratio is estimated using electronic thermal conductivity. The Wiedemann-Franz law also works well in Au nanostructures when the Lorentz ratio is estimated by total thermal conductivity.
We analyze the data of the recent paper Nature 559, 205 (2018) and show that it contains an observation of thermal and electric conductivities of the doping layers in GaAs/AlGaAs heterostructures which violates the Wiedemann-Franz law. Namely, the measured thermal conductivity of the doping layers is similar to that of a metal while the electrical conductivity is exponentially small. We find that these results may be related to the exciton contribution to thermal conductivity calculated in several recent theoretical works for metallic samples.
Motivated by recent experiments [Science 355, 6330 (2017); Nat. Nanotechnol. 12, 430 (2017)], we present here an extensive theoretical analysis of the thermal conductance of atomic-size contacts made of three different metals, namely gold (Au), platinum (Pt) and aluminum (Al).
We study the effect of mesoscopic fluctuations on the validity of the Wiedemann--Franz (WF) law for quasi-one-dimensional metal wires and open quantum dots. At temperatures much less than the generalized Thouless energy, E_c, the WF law is satisfied for each specific sample but as the temperature is raised through E_c a sample-specific correction to the WF law of order 1/g appears (g is the dimensionless conductance) and then tends to zero again at high temperatures. The mesoscopic violation of the Weidemann-Franz law is even more pronounced in a ring geometry, for which Lorenz number exhibits…
We investigate nonlinear heat properties in mesoscopic conductors using a scattering theory of transport. Our approach is based on a leading-order expansion in both the electrical and thermal driving forces. Beyond linear response, the transport coefficients are functions of the nonequilibrium screening potential that builds up in the system due to interactions. Within a mean-field approximation, we self-consistently calculate the heat rectification properties of a quantum dot attached to two terminals. We discuss nonlinear contributions to the Peltier effect and find departures from the Wiede…
In one-dimensional (1D) conductors with linear E-k dispersion (Dirac systems) intrabranch thermalization is favored by elastic electron-electron interaction in contrast to electron systems with a nonlinear (parabolic) dispersion. We show that under external electric fields or thermal gradients the carrier populations of different branches, treated as Fermi gases, have different temperatures as a consequence of self-consistent carrier-heat transport. Specifically, in the presence of elastic phonon scattering, the Wiedemann-Franz law is restricted to each branch with its specific temperature and…
We study the influence of Coulomb interaction on the thermoelectric transport coefficients for a metallic single-electron transistor. By performing a perturbation expansion up to second order in the tunnel-barrier conductance, we include sequential and cotunneling processes as well as quantum fluctuations that renormalize the charging energy and the tunnel conductance. We find that Coulomb interaction leads to a strong violation of the Wiedemann-Franz law: the Lorenz ratio becomes gate-voltage dependent for sequential tunneling, and is increased by a factor 9/5 in the cotunneling regime. Final…
We study features of the thermoelectric transport through a Kitaev chain hosting Majorana bound states (MBS) at its ends. We describe the behavior of the Seebeck coefficient and the ZT figure of merit for two different configurations between MBS and normal current leads. We find an important violation of the Wiedemann-Franz law in one of these geometries, leading to sizeable values of the thermoelectric efficiency over a narrow window in chemical potential away from neutrality. These findings could lead to interesting thermoelectric-based MBSs detection devices, via measurements of the Seebeck…
We present a simple theory of thermoelectric transport in bilayer graphene and report our results for the electrical resistivity, the thermal resistivity, the Seebeck coefficient, and the Wiedemann-Franz ratio as functions of doping density and temperature. In the absence of disorder, the thermal resistivity tends to zero as the charge neutrality point is approached; the electric resistivity jumps from zero to an intrinsic finite value, and the Seebeck coefficient diverges in the same limit. Even though these results are similar to those obtained for single-layer graphene, their derivation is …
We consider the thermoelectric properties of a double-quantum-dot molecule coupled in parallel to metal electrodes with a magnetic flux threading the ring. By means of the Sommerfeld expansion we obtain analytical expressions for the electric and thermal conductances, thermopower and figure of merit for arbitrary values of the magnetic flux. We neglect electronic correlations. The Fano antiresonances in transmission demand that terms usually discarded in the Sommerfeld expansion are taken into account. We also explore the behavior of the Lorenz ratio L=κ/σT, where κ and σ are the thermal and e…
In the 2016 experiment by Crossno et al. [Science 351, 1058 (2016)], electronic contribution to the thermal conductivity of graphene was found to violate the well-known Wiedemann-Franz (WF) law for metals. At liquid nitrogen temperatures, the thermal to electrical conductivity ratio of charge-neutral samples was more than 10 times higher than predicted by the WF law, what was attributed to interactions between particles leading to collective behavior described by hydrodynamics. Here we show, by adapting the handbook derivation of the WF law to the case of massless Dirac fermions, that signific…
We report our investigations on the finite-size effects of the Lorenz number in a molecular wire. Using Landauer-Büttiker formalism, we find that for sufficiently long wires there are two validity regimes of the Wiedemann-Franz (WF) law, the cotunneling and the sequential tunneling regimes, while in small systems only the first regime survives. We compare our results with the standard Kubo formalism and explain its failure to detect the WF law in small systems. Furthermore, our studies on exponentially localized disordered wires show that the Lorenz number value L_0 predicted by the WF law is …
We analyze a well-known experimental work [J. Crossno et al., Science 351, 1058 (2016)] which reported on the failure of the Wiedemann-Franz law in graphene at $T\sim 10$-$100\,\mathrm{K}$, attributing this failure to the non-Fermi liquid nature of the Dirac fluid associated with undoped intrinsic graphene. In spite of serious theoretical efforts, the reported observations remain unexplained. Our detailed quantitative analysis based on Fermi liquid considerations, which apply to extrinsic doped graphene, establishes that one possible explanation for the reported observations is the opening of …
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 origin of energy conversion 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…
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 ob…
We study the thermal transport through a Majorana island connected to multiple external quantum wires. In the presence of a large charging energy, we find that the Wiedemann-Franz law is nontrivially violated at low temperature, contrarily to what happens for the overscreened Kondo effect and for nontopological junctions. For three wires, we find that the Lorenz ratio is rescaled by a universal factor 2/3 and we show that this behavior is due to the presence of localized Majorana modes on the island.
We report on the electrical and thermal transport properties of nickel nanoparticles with crystallite size from 23.1 to 1.3 nm. These nanoparticles show a systematic metal to insulator transition with the change in the conduction type from n to p type, colossal Seebeck coefficient, and ultralow thermal conductivity at 300 K as the crystallite size drops. The electrical resistivity analysis reveals a dramatic change in the electronic excitation spectrum indicating the opening of an energy gap, and cotunneling and Coulomb blockade of the charge carriers. Seebeck coefficient shows transport energ…
We analyze the charge and thermal transport at a junction of interacting quantum wires close to equilibrium. Within the framework of Tomonaga-Luttinger liquids, we compute the thermal conductance for a wide class of boundary conditions and detail the physical processes leading to the breakdown of the Wiedemann-Franz law at the junction. We show how connecting external reservoirs to the quantum wires affects the conductance tensors close to the various fixed points of the phase diagram of the junction. We therefore distinguish two types of violation of the Wiedemann-Franz law: a "trivial" one, …
We study thermal transport in the disordered Fermi liquid at low temperatures. Gravitational potentials are used as sources for finding the heat density and its correlation function. For a comprehensive study, we extend the renormalization group (RG) analysis developed for electric transport by including the gravitational potentials into the RG scheme. Our analysis reveals that the Wiedemann-Franz law remains valid even in the presence of quantum corrections caused by the interplay of diffusion modes and the electron electron interaction. In the present scheme this fundamental relation is clos…
Advances in optimizing thermoelectric material efficiency have seen a parallel activity in theoretical and computational advances. In the current work, it is shown that the calculation of exact Fermi-Dirac integrals enables the generalization of the Wiedemann-Franz law (WF) to optimize the dimensionless thermoelectric figure of merit ZT. This is done by optimizing the Seebeck coefficient, the electrical conductivity and the thermal conductivity. In the calculation of the thermal conductivity, both electronic and phononic contributions are included. The solutions provide insight into the releva…
We present the theory of thermoelectric transport in metals with long-lived quasiparticles, carefully addressing the interplay of electron-electron scattering as well as electron-impurity scattering, but neglecting electron-phonon scattering. In Fermi liquids with a large Fermi surface and weak electron-impurity scattering, we provide universal and simple formulas for the behavior of the thermoelectric conductivities across the ballistic-to-hydrodynamic crossover. In this regime, the electrical conductivity is relatively unchanged by hydrodynamic effects. In contrast, the thermal conductivity …
We extract experimentally the electronic thermal conductivity, $K_{e}$, in suspended graphene which we dope using a back-gate electrode. We make use of two-point dc electron transport at low bias voltages and intermediate temperatures (50 - 160 K), where the electron and lattice temperatures are decoupled. The thermal conductivity is proportional to the charge conductivity times the temperature, confirming that the Wiedemann-Franz relation is obeyed in suspended graphene. We extract an estimate of the Lorenz coefficient as 1.1 to 1.7 $\times 10^{-8}$ W $Ω$K$^{-2}$. $K_e$ shows a transistor eff…
The Wiedemann-Franz law, connecting the electronic thermal conductivity to the electrical conductivity of a disordered metal, is generally found to be well satisfied even when electron-electron (e-e) interactions are strong. In ultra-clean conductors, however, large deviations from the standard form of the law are expected, due to the fact that e-e interactions affect the two conductivities in radically different ways. Thus, the standard Wiedemann-Franz ratio between the thermal and the electric conductivity is reduced by a factor $1+τ/τ_{\rm th}^{\rm ee}$, where $1/τ$ is the momentum relaxati…
Interactions between particles in quantum many-body systems can lead to collective behavior described by hydrodynamics. One such system is the electron-hole plasma in graphene near the charge neutrality point which can form a strongly coupled Dirac fluid. This charge neutral plasma of quasi-relativistic fermions is expected to exhibit a substantial enhancement of the thermal conductivity, due to decoupling of charge and heat currents within hydrodynamics. Employing high sensitivity Johnson noise thermometry, we report the breakdown of the Wiedemann-Franz law in graphene, with a thermal conduct…
We consider the thermoelectric properties of the mixed-dimensional quantum electrodynamics of the relativistic Dirac fermion and Wilson-Fisher boson. These models are self-dual, and can form non-trivial many-body phases depending on the values of chemical potential, background magnetic field and the electromagnetic fine-structure constant. Using particle-vortex duality, we derive a variety of thermoelectric relations for strongly-interacting phases with classic paradigms such as the Wiedemann-Franz law and the Mott's relation in the dual weakly interacting regimes. Besides, at the self-dual po…
We report on coupled heat and particle transport measurements through a quantum point contact (QPC) connecting two reservoirs of resonantly interacting, finite temperature Fermi gases. After heating one of them, we observe a particle current flowing from cold to hot. We monitor the temperature evolution of the reservoirs and find that the system evolves after an initial response into a non-equilibrium steady state with finite temperature and chemical potential differences across the QPC. In this state any relaxation in the form of heat and particle currents vanishes. From our measurements we e…
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 i…
We present a quantum Hall effect of magnons in two-dimensional clean insulating magnets at finite temperature. Through the Aharonov-Casher effect, a magnon moving in an electric field acquires a geometric phase and forms Landau levels in an electric field gradient of sawtooth form. At low temperatures, the lowest energy band being almost flat carries a Chern number associated with a Berry curvature. Appropriately defining the thermal conductance for bosons, we find that the magnon Hall conductances get quantized and show a universal thermomagnetic behavior, i.e., are independent of materials, …
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. bei…
We compare the thermal conductance $G_{\rm thermal}$ (at temperature $T$) and the electrical shot noise power $P_{\rm shot}$ (at bias voltage $V\gg k_{\rm B}T/e$) of Majorana fermions on the two-dimensional surface of a three-dimensional topological superconductor. We present analytical and numerical calculations to demonstrate that, for a local coupling between the superconductor and metal contacts, $G_{\rm thermal}/P_{\rm shot}= {\cal L}T/eV$ (with ${\cal L}$ the Lorenz number). This relation is ensured by the combination of electron-hole and time-reversal symmetries, irrespective of the mic…
We calculate the thermal conductivity of interacting electrons in disordered metals. In our analysis we point out that the interaction affects thermal transport through two distinct mechanims, associated with quantum interference corrections and energy exchange of the quasi particles with the electromagnetic environment, respectively. The latter is seen to lead to a violation of the Wiedemann-Franz law. Our theory predicts a strong enhancement of the Lorenz ratio $κ/σT$ over the value which is predicted by the Wiedemann-Franz law, when the electrons encounter a large environmental impedance.
One of the main goals of spintronics is to improve transport of information carriers and to achieve new functionalities with ultra-low dissipation. A most promising strategy for this holy grail is to use pure magnon currents created and transported in insulating magnets, in the complete absence of any conducting metallic elements. Here we propose a realistic solution to this fundamental challenge by analyzing magnon and heat transport in insulating ferromagnetic junctions. We calculate all transport coefficients for magnon transport and establish Onsager relations between them. We theoreticall…
We investigate the electric and thermal transport properties in a disordered Weyl ferromagnet on an equal footing by using the Keldysh formalism in curved spacetime. In particular, we calculate the anomalous thermal Hall conductivity, which consists of the Kubo formula and the heat magnetization, without relying on the Wiedemann-Franz law. We take nonmagnetic impurities into account within the self-consistent $T$-matrix approximation and reproduce the Wiedemann-Franz law for the extrinsic Fermi-surface and intrinsic Fermi-sea terms, respectively. This is the first step towards a unified theory…
We consider in depth the applicability of the Wiedemann-Franz (WF) law, namely that the electronic thermal conductivity ($κ$) is proportional to the product of the absolute temperature ($T$) and the electrical conductivity ($σ$) 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 sys…
Using the semiclassical quantum Boltzmann theory and employing the Dirac model with twist angle-dependent Fermi velocity we obtain results for the electrical resistivity, the electronic thermal resistivity, the Seebeck coefficient, and the Wiedemann-Franz ratio in near magic angle twisted bilayer graphene, as functions of doping density (around the charge-neutrality-point) and modified Fermi velocity $\tilde v$. The $\tilde v$-dependence of the relevant scattering mechanisms, i.e. electron-hole Coulomb, long-ranged impurities, and acoustic gauge phonons, is considered in detail. We find a rang…
Hydrodynamic behavior in electronic systems is commonly accepted to be associated with extremely clean samples such that electron-electron collisions dominate and total momentum is conserved. Contrary to this, we show that in monolayer graphene the presence of disorder is essential to enable an unconventional hydrodynamic regime which exists near the charge neutrality point and is characterized by a large enhancement of the Wiedemann-Franz ratio. Although the enhancement becomes more pronounced with decreasing disorder, the very possibility of observing the effect depends crucially on the pres…
We study the electron thermal transport in granular metals at large tunnel conductance between the grains, $g_T \gg 1$ and not too low a temperature $T > g_Tδ$, where $δ$ is the mean energy level spacing for a single grain. Taking into account the electron-electron interaction effects we calculate the thermal conductivity and show that the Wiedemann-Franz law is violated for granular metals. We find that interaction effects suppress the thermal conductivity less than the electrical conductivity.
Thermoelectric properties of a two-level molecule attached to the metallic electrodes are analyzed using the equation of motion technique within the Green function formalism. Results show that the electrical conductance is strongly dependent on the electron and phonon temperatures and the electron-phonon coupling strength. In addition, it is observed that the thermal conductance peaks in the electron-hole symmetry points are vanished in the presence of the strong electron-phonon interaction. It is also found that the figure of merit is strongly suppressed in the strong electron-phonon interact…
We study the electric and thermal transport of the Dirac carriers in monolayer graphene using the Boltzmann-equation approach. Motivated by recent thermopower measurements [F. Ghahari, H.-Y.~Xie, T. Taniguchi, K. Watanabe, M.~S.~Foster, and P.~Kim, Phys.\ Rev.\ Lett.\ {\bf 116}, 136802 (2016)], we consider the effects of quenched disorder, Coulomb interactions, and electron--optical-phonon scattering. Via an unbiased numerical solution to the Boltzmann equation we calculate the electrical conductivity, thermopower, and electronic component of the thermal conductivity, and discuss the validity …
We investigate theoretically thermal and electrical conductances for the system consisting of a quantum dot (QD) connected both to a pair of Majorana fermions residing the edges of a Kitaev wire and two metallic leads. We demonstrate that both quantities reveal pronounced resonances, whose positions can be controlled by tuning of an asymmetry of the couplings of the QD and a pair of MFs. Similar behavior is revealed for the thermopower, Wiedemann-Franz law and dimensionless thermoelectric figure of merit. The considered geometry can thus be used as a tuner of heat and charge transport assisted…
We have measured the differential resistance in a two-dimensional topological insulator (2DTI) in a HgTe quantum well, as a function of the applied dc current. The transport near the charge neutrality point is characterized by a pair of counter propagating gapless edge modes. In the presence of an electric field, the energy is transported by counter propagating channels in the opposite direction. We test a hot carrier effect model and demonstrate that the energy transfer complies with the Wiedemann Franz law near the charge neutrality point in the edge transport regime.
