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. Finally, we suggest a measurement scheme for an experimental realization.
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).
Spectroscopy of Heat Transport and Violation of the Wiedemann--Franz Law in a GaAs Hydrodynamic Mesoscopic Channel
São Carlos Institute of Physics, University of São Paulo（圣保罗大学圣卡洛斯物理研究所）；Physics Department, Federal University of São Carlos（圣卡洛斯联邦大学物理系）；Ioffe Institute（约费研究所）；Institute of Physics, University of São Paulo（圣保罗大学物理研究所）；Institute of Semiconductor Physics（半导体物理研究所）
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 …
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 t…
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 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, …
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 …
Wiedemann-Franz Relation and Thermal-transistor Effect in Suspended Graphene
我们提取实验的电子热导率，$K_{e}$，在悬浮的石墨烯，我们掺杂使用背栅电极。我们利用两点直流电子输运在低偏置电压和中间温度（50 - 160 K），电子和晶格温度去耦。热导率与电荷电导率乘以温度成比例，证实了悬浮石墨烯中服从Wiedemann-Franz关系。我们提取Lorenz系数的估计值为1.1至1.7 $\times 10^{-8}$ W $Ω$ K $^{-2}$。$K_e$显示出晶体管效应，并且当电荷载流子密度在$\approx$ 0.5至1.8 $\times 10^{11}$ cm $^{-2}$范围内时，可以用背栅以大于2的因子进行调谐。
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 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…
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 develop a method of theoretically investigating the charge, energy and heat transport in the presence of the charge Kondo correlations. The Coulomb blockade oscillations of heat conductance in the single electron transistor exhibiting the charge Kondo effects are investigated. We explore the Wiedemann Franz ratio in both charge-single channel and charge-two channel Kondo regime. The close connections of our findings with the recent experiments on multi-channel charge Kondo effects are discussed.
We report on combined measurements of heat and charge transport through a single-electron transistor. The device acts as a heat switch actuated by the voltage applied on the gate. The Wiedemann-Franz law for the ratio of heat and charge conductances is found to be systematically violated away from the charge degeneracy points. The observed deviation agrees well with the theoretical expectation. With large temperature drop between the source and drain, the heat current away from degeneracy deviates from the standard quadratic dependence in the two temperatures.
