Electrical and thermal transport were studied in a vacuum-annealed polycrystalline silver wire with residual resistivity ratio 200-400, in the temperature range 0.1-1.2K and in magnetic fields up to 5T. Both at zero field and at 5T the wire exhibits the Wiedemann-Franz law with the fundamental Lorenz number, contrary to an earlier report [Gloos, K. et al, Cryogenics 30, 14 (1990)]. Our result demonstrates that silver is an excellent material for thermal links in ultra-low-temperature experiments operating at high magnetic fields.
Validation of the Wiedemann-Franz Law in solid and molten tungsten above 2000 K through thermal conductivity measurements via steady state temperature differential radiometry
We study the electronic part of the thermal conductivity kappa of metals. We present two methods for calculating kappa, a quantum Monte-Carlo (QMC) method and a method where the phonons but not the electrons are treated semiclassically (SC). We compare the two methods for a model of alkali-doped C60, A3C60, and show that they agree well. We then mainly use the SC method, which is simpler and easier to interpret. We perform SC calculations for Nb for large temperatures T and find that kappa increases with T as kappa(T)=a+bT, where a and b are constants, consistent with a saturation of the mean …
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…
Theoretical analysis of the effect of thermoelectric phenomena on the relation of effective electrical and thermal conductivity in the macroscopically inhomogeneous media is carried out. Plane-layered structures, two-dimensional self-dual and three-dimensional randomly inhomogeneous media are examined. It is shown that the relation of effective electrical to thermal conductivity, which is independent of concentration in so-called Wiedemann-Franz media, in the case of high values of internal thermoelectric figure of merit can be considerably different from the one for the local values in each p…
Breaking the Wiedemann-Franz limit in thermoelectrics via separated flat bands
TU Wien（维也纳工业大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Universität Würzburg（维尔茨堡大学）；Laboratoire des Solides Irradiés, CEA/DRF/IRAMIS, CNRS, École Polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院辐照固体实验室，法国原子能及替代能源委员会/研究与发展部/基础科学研究所，法国国家科学研究中心，巴黎理工学院）
We study the relationship between the shape of the electronic band structure and the thermoelectric properties. In order to study the band shape dependence of the thermoelectric properties generally, we first adopt models with band structures having the dispersion $E({\bf k}) \sim |{\bf k}|^n$ with $n = 2, 4$ and 6. We consider one, two- and three dimensional systems, and calculate the thermoelectric properties using the Boltzmann equation approach within the constant quasi-particle lifetime approximation. $n = 2$ corresponds to the usual parabolic band structure, while the band shape for $n =…
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…
Organic semiconductors have attracted increasing interest as thermoelectric converters in recent years due to their intrinsically low thermal conductivity compared to inorganic materials. This boom has led to encouraging practical results, in which the thermal conductivity has predominantly been treated as an empirical number. However, in an optimized thermoelectric material, the electronic component can dominate the thermal conductivity in which case the figure of merit $ZT$ becomes a function of thermopower and Lorentz factor only. Hence design of effective organic thermoelectric materials r…
The journey through the nontrivial band topology beyond the conventional band structure has resulted in the recent discovery of three-dimensional Dirac semimetal phase in Na$_{3}$Bi and Cd$_{3}$As$_{2}$. The bulk state of which is semi-metallic obeying linear energy dispersion, while the surface state is topology protected Fermi arc. Due to the unique band topology, they show different exotic electronic properties of both fundamental and technological interest. From electrical and thermal transport measurements, we have demonstrated a remarkable violation of Wiedemann-Franz law (WFL) under app…
The Wiedemann-Franz (WF) law links the ratio of electronic charge and heat conductivity to fundamental constants. It has been tested in numerous solids, but the extent of its relevance to the anomalous transverse transport, which represents the topological nature of the wave function, remains an open question. Here we present a study of anomalous transverse response in the noncollinear antiferromagnet Mn$_{3}$Ge 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-temp…
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…
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 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…
We study the low temperature thermal conductivity of single-layer transition metal dichalcogenides. In the low temperature regime where heat is carried primarily through transport of electrons, thermal conductivity is linked to electrical conductivity through the Wiedemann-Franz law. Using a \textit{k.p} Hamiltonian that describes the $ K $ and $ K^{'} $ valley edges, we compute the zero-frequency electric (Drude) conductivity using the Kubo formula to obtain a numerical estimate for the thermal conductivity. The impurity scattering determined transit time of electrons which enters the Drude e…
Electronic and phononic thermal conductivity are involved in the thermal conduction for metals and Wiedemann-Franz law is usually employed to predict them separately. However, Wiedemann-Franz law is shown to be invalid at intermediate temperatures. Here, to obtain the accurate thermal conductivity and Lorenz ratio for metals, the momentum relaxation time is used for electrical conductivity and energy relaxation time for electronic thermal conductivity. The mode-level first-principles calculation is conducted on two representative metals copper and aluminum. It is shown that the method can corr…
By way of the non-equilibrium Green's function simulations and analytical expressions, the quantum thermal conductance of stanene is studied. We find that, due to the existence of Dirac fermion in stanene, the ratio of electron thermal conductance and electric conductance becomes a chemical-potential-dependent quantity, violating the Wiedemann-Franz law. This finding is applicable to any two-dimensional (2D) materials that possess massless Dirac fermions. In strong contrast to the negligible electronic contribution in graphene, surprisingly, the electrons and phonons in stanene carry a compara…
Coupling between heat and electrical currents is at the heart of thermoelectric processes. From a thermal viewpoint this may be seen as an additional thermal flux linked to the appearance of electrical current in a given thermoelectric system. Since this additional flux is associated to the global displacement of charge carriers in the system, it can be qualified as convective in opposition to the conductive part associated with both phonons transport and heat transport by electrons under open circuit condition, as, e.g., in the Wiedemann-Franz relation. In this article we demonstrate that con…
Co$_3$Sn$_2$S$_2$ is a ferromagnetic semi-metal with Weyl nodes in its band structure and a large anomalous Hall effect below its Curie temperature of 177 K. We present a detailed study of its Fermi surface and examine the relevance of the anomalous transverse Wiedemann Franz law to it. We studied Shubnikov-de Haas oscillations along two orientations in single crystals with a mobility as high as $2.7\times$10$^3$ cm$^2$V$^{-1}$s$^{-1}$ subject to a magnetic field as large as $\sim$ 60 T. The angle dependence of the frequencies is in agreement with density functional theory (DFT) calculations a…
We investigate the minimum conductivity of graphene within a quasiclassical approach taking into account electron-hole coherence effects which stem from the chiral nature of low energy excitations. Relying on an analytical solution of the kinetic equation in the electron-hole coherent and incoherent cases we study both the electrical and thermal conductivity whose relation fullfills Wiedemann-Franz law. We found that the most of the previous findings based on the Boltzmann equation are restricted to only high mobility samples where electron-hole coherence effects are not sufficient.
Ferromagnetic ordering with a small magnetic moment is found below 14 K from SQUID measurements for the compound Ce4Sb1.5Ge1.5. The transport characteristics of a number of Ce4Sb3-xTx (T = Ge, Si, Sn, Pb, Al) systems were measured at room temperature, Ce4Sb1.5Ge1.5 demonstrating the highest Seebeck coefficient. Its transport properties (resistivity, thermal conductivity, thermoelectric power) are experimentally investigated in detail up to low temperatures. The Kondo-lattice behavior of resistivity and its anomaly at the ordering point are found. A comparison with the Wiedemann-Franz law is pe…
