The Kelvin Formula for Thermopower

Thermoelectrics are important in physics, engineering, and material science due to their useful applications and inherent theoretical difficulty, especially in strongly correlated materials. Here we reexamine the framework for calculating the thermopower, inspired by ideas of Lord Kelvin from 1854. We find an approximate but concise expression, which we term as the Kelvin formula for the the Seebeck coefficient. According to this formula, the Seebeck coefficient is given as the particle number $N$ derivative of the entropy $\Sigma$, at constant volume $V$ and temperature $T$, $S_{\text{Kelvin}}=\frac{1}{q_e}\{\frac{\partial {\Sigma}}{\partial N} \}_{V,T}$. This formula is shown to be competitive compared to other approximations in various contexts including strongly correlated systems. We finally connect to a recent thermopower calculation for non-Abelian fractional quantum Hall states, where we point out that the Kelvin formula is exact.Comment: 6 pages, 2 figure

Thermopower of Two-Dimensional Electrons at ν\nu = 3/2 and 5/2

The longitudinal thermopower of ultra-high mobility two-dimensional electrons has been measured at both zero magnetic field and at high fields in the compressible metallic state at filling factor $\nu = 3/2$ and the incompressible fractional quantized Hall state at $\nu = 5/2$. At zero field our results demonstrate that the thermopower is dominated by electron diffusion for temperatures below about $T = 150$ mK. A diffusion dominated thermopower is also observed at $\nu = 3/2$ and allows us to extract an estimate of the composite fermion effective mass. At $\nu = 5/2$ both the temperature and magnetic field dependence of the observed thermopower clearly signal the presence of the energy gap of this fractional quantized Hall state. We find that the thermopower in the vicinity of $\nu = 5/2$ exceeds that recently predicted under the assumption that the entropy of the 2D system is dominated by non-abelian quasiparticle exchange statistics.Comment: 10 pages, 10 figures

Thermopower as a Possible Probe of Non-Abelian Quasiparticle Statistics in Fractional Quantum Hall Liquids

We show in this paper that thermopower is enhanced in non-Abelian quantum Hall liquids under appropriate conditions. This is because thermopower measures entropy per electron in the clean limit, while the degeneracy and entropy associated with non-Abelian quasiparticles enhance entropy when they are present. Thus thermopower can potentially probe non-Abelian nature of the quasiparticles, and measure their quantum dimension.Comment: 5 pages. Minor revisions in response to referee comments. Published versio

Quantum Nernst effect in a bismuth single crystal

We report a theoretical calculation explaining the quantum Nernst effect observed experimentally in a bismuth single crystal. Generalizing the edge-current picture in two dimensions, we show that the peaks of the Nernst coefficient survive in three dimensions due to a van Hove singularity. We also evaluate the phonon-drag effect on the Nernst coefficient numerically. Our result agrees with the experimental result for a bismuth single crystal.Comment: 4 pages, 4 figures, to be published in Proceedings of ISQM-Tokyo '0

Quantum kinetic approach to the calculation of the Nernst effect

We show that the strong Nernst effect observed recently in amorphous superconducting films far above the critical temperature is caused by the fluctuations of the superconducting order parameter. We employ the quantum kinetic approach for the derivation of the Nernst coefficient. We present here the main steps of the calculation and discuss some subtle issues that we encountered while calculating the Nernst coefficient. In particular, we demonstrate that in the limit T=0 the contribution of the magnetization ensures the vanishing of the Nernst signal in accordance with the third law of thermodynamics. We obtained a striking agreement between our theoretical calculations and the experimental data in a broad region of temperatures and magnetic fields.Comment: 24 pages, 13 figure

Fluctuations of the superconducting order parameter as an origin of the Nernst effect

We show that the strong Nernst signal observed recently in amorphous superconducting films far above the critical temperature is caused by the fluctuations of the superconducting order parameter. We demonstrate a striking agreement between our theoretical calculations and the experimental data at various temperatures and magnetic fields. Besides, the Nernst effect is interesting not only in the context of superconductivity. We discuss some subtle issues in the theoretical study of thermal phenomena that we have encountered while calculating the Nernst coefficient. In particular, we explain how the Nernst theorem (the third law of thermodynamics) imposes a strict constraint on the magnitude of the Nernst effect.Comment: 6 pages, 5 figures, extended versio

Nernst-Ettingshausen effect in two-component electronic liquids

A simple model describing the Nernst-Ettingshausen effect (NEE) in two-component electronic liquids is formulated. The examples considered include graphite, where the normal and Dirac fermions coexist, superconductor in fluctuating regime, with coexisting Cooper pairs and normal electrons, and the inter-stellar plasma of electrons and protons. We give a general expression for the Nernst constant and show that the origin of a giant NEE is in the strong dependence of the chemical potential on temperature in all cases

Thermohydrodynamics in Quantum Hall Systems

A theory of thermohydrodynamics in two-dimensional electron systems in quantizing magnetic fields is developed including a nonlinear transport regime. Spatio-temporal variations of the electron temperature and the chemical potential in the local equilibrium are described by the equations of conservation with the number and thermal-energy flux densities. A model of these flux densities due to hopping and drift processes is introduced for a random potential varying slowly compared to both the magnetic length and the phase coherence length. The flux measured in the standard transport experiment is derived and is used to define a transport component of the flux density. The equations of conservation can be written in terms of the transport component only. As an illustration, the theory is applied to the Ettingshausen effect, in which a one-dimensional spatial variation of the electron temperature is produced perpendicular to the current.Comment: 10 pages, 1 figur

Quasiparticle Hall Transport of d-wave Superconductors in Vortex State

We present a theory of quasiparticle Hall transport in strongly type-II superconductors within their vortex state. We establish the existence of integer quantum spin Hall effect in clean unconventional $d_{x^2-y^2}$ superconductors in the vortex state from a general analysis of the Bogoliubov-de Gennes equation. The spin Hall conductivity $\sigma^s_{xy}$ is shown to be quantized in units of $\frac{\hbar}{8\pi}$. This result does not rest on linearization of the BdG equations around Dirac nodes and therefore includes inter-nodal physics in its entirety. In addition, this result holds for a generic inversion-symmetric lattice of vortices as long as the magnetic field $B$ satisfies $H_{c1} \ll B \ll H_{c2}$. We then derive the Wiedemann-Franz law for the spin and thermal Hall conductivity in the vortex state. In the limit of $T \to 0$, the thermal Hall conductivity satisfies $\kappa_{x y}=\frac{4\pi^2}{3}(\frac{k_B}{\hbar})^2 T \sigma^s_{xy}$. The transitions between different quantized values of $\sigma^s_{xy}$ as well as relation to conventional superconductors are discussed.Comment: 18 pages REVTex, 3 figures, references adde

Thermoelectric Response of an Interacting Two-Dimensional Electron Gas in Quantizing Magnetic Field

We present a discussion of the linear thermoelectric response of an interacting electron gas in a quantizing magnetic field. Boundary currents can carry a significant fraction of the net current passing through the system. We derive general expressions for the bulk and boundary components of the number and energy currents. We show that the local current density may be described in terms of ``transport'' and ``internal magnetization'' contributions. The latter carry no net current and are not observable in standard transport experiments. We show that although Onsager relations cannot be applied to the local current, they are valid for the transport currents and hence for the currents observed in standard transport experiments. We relate three of the four thermoelectric response coefficients of a disorder-free interacting two-dimensional electron gas to equilibrium thermodynamic quantities. In particular, we show that the diffusion thermopower is proportional to the entropy per particle, and we compare this result with recent experimental observations.Comment: 18 pages, 2 postscript figures included. Revtex with epsf.tex and multicol.sty. In the revised version, the comparison with experimental observations at $\nu=1/2, 3/2$ is extended to include the possibility of corrections due to weak impurity scattering. The conclusions that we reach regarding the applicability of the composite fermion model at these filling fractions are not affecte