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Wiedemann-Franz law is a prediction of electronic theory of electric and thermal conductivity in metals, which states that a Lorenz ratio $L=kappa/(sigma T)$, where $kappa$ is a thermal conductivity, $sigma$ --- electric conductivity and $T$ --- absolute temperature, is a universal constant in certain cases. We present here a simple experimental setup to verify this prediction in a teaching experiment.
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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-Gruneisen 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.
The recent detection of charge-density modulations in YBa2Cu3Oy and other cuprate superconductors raises new questions about the normal state of underdoped cuprates. In one class of theories, the modulations are intertwined with pairing in a dual state, expected to persist up to high magnetic fields as a vortex liquid. In support of such a state, specific heat and magnetisation data on YBa2Cu3Oy have been interpreted in terms of a vortex liquid persisting above the vortex-melting field Hvs at T = 0. Here we report high-field measurements of the electrical and thermal Hall conductivities in YBa2Cu3O6.54 that allow us to probe the Wiedemann-Franz law, a sensitive test of the presence of superconductivity in a metal. In the T = 0 limit, we find that the law is satisfied for fields immediately above Hvs. This rules out the existence of a vortex liquid and it places strict constraints on the nature of the normal state in underdoped cuprates.
Transport coefficients serve as important probes in characterizing the QCD matter created in high-energy heavy-ion collisions. Thermal and electrical conductivities as transport coefficients have got special significance in studying the time evolution of the created matter. We have adopted color string percolation approach for the estimation of thermal conductivity ($kappa$), electrical conductivity ($sigma_{el}$) and their ratio, which is popularly known as Wiedemann-Franz law in condensed matter physics. The ratio $kappa/sigma_{el}T$, which is also known as Lorenz number ($mathbb{L}$) is studied as a function of temperature and is compared with various theoretical calculations. We observe that the thermal conductivity for hot QCD medium is almost temperature independent in the present formalism and matches with the results obtained in ideal equation of state (EOS) for quark-gluon plasma with fixed coupling constant ($alpha_s$). The obtained Lorenz number is compared with the Stefan-Boltzmann limit for an ideal gas. We observe that a hot QCD medium with color degrees of freedom behaves like a free electron gas.
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 $1+tau/tau_{rm th}^{rm ee}$, where $1/tau$ is the momentum relaxation rate, and $1/tau_{rm th}^{rm ee}$ is the relaxation time of the thermal current due to e-e collisions. Here we study the density and temperature dependence of $1/tau_{rm th}^{rm ee}$ in the important case of doped, clean single layers of graphene, which exhibit record-high thermal conductivities. We show that at low temperature $1/tau_{rm th}^{rm ee}$ is $8/5$ of the quasiparticle decay rate. We also show that the many-body renormalization of the thermal Drude weight coincides with that of the Fermi velocity.
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 considerably more delicate. The singularities are removed by the inclusion of a small amount of disorder, which leads to the appearance of a window of doping densities $0<n<n_c$ (with $n_c$ tending to zero in the zero-disorder limit) in which the Wiedemann-Franz law is severely violated.
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