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

Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes

We present a general hydrodynamic theory of transport in the vicinity of superfluid-insulator transitions in two spatial dimensions described by "Lorentz"-invariant quantum critical points. We allow for a weak impurity scattering rate, a magnetic field B, and a deviation in the density, \rho, from that of the insulator. We show that the frequency-dependent thermal and electric linear response functions, including the Nernst coefficient, are fully determined by a single transport coefficient (a universal electrical conductivity), the impurity scattering rate, and a few thermodynamic state variables. With reasonable estimates for the parameters, our results predict a magnetic field and temperature dependence of the Nernst signal which resembles measurements in the cuprates, including the overall magnitude. Our theory predicts a "hydrodynamic cyclotron mode" which could be observable in ultrapure samples. We also present exact results for the zero frequency transport co-efficients of a supersymmetric conformal field theory (CFT), which is solvable by the AdS/CFT correspondence. This correspondence maps the \rho and B perturbations of the 2+1 dimensional CFT to electric and magnetic charges of a black hole in the 3+1 dimensional anti-de Sitter space. These exact results are found to be in full agreement with the general predictions of our hydrodynamic analysis in the appropriate limiting regime. The mapping of the hydrodynamic and AdS/CFT results under particle-vortex duality is also described.Comment: 44 pages, 4 figures; (v3) Added new subsection highlighting negative Hall resistance at hole densities smaller than 1/

Manifestation of the electric dipole moment in the decays of τ\tau leptons produced in e+e−e^+e^- annihilation

\mbox{CP}-odd asymmetries in the processes $e^+e^-\rightarrow \tau^+\pi^-\nu_\tau$, $e^+e^-\rightarrow \pi^+\tau^-\bar\nu_ \tau$, $e^+e^-\rightarrow \tau^+\rho^-\nu_\tau$, and $e^+e^-\rightarrow \rho^+\tau^-\bar\nu_\tau$ are investigated with account for longitudinal polarization of electrons (or positrons). These asymmetries is a manifestation of electric dipole form factor $F_3^\tau\equiv b$ in the $\gamma\tau^+\tau^-$ vertex. It is shown that to measure \mbox{Im}\,b, polarization is not needed, and to measure \mbox{Re}\,b, the polarization is not necessary, but simplifies the measurement of \mbox{Re}\,b.Comment: 12 pages, 1 figur

Quadrupole radiation and e+e−e^+e^- pair production in the collision of nonrelativistic nuclei

We analyze the one-photon mechanism of $e^+e^-$ pair production in the collision of nonrelativistic nuclei. The contribution of electric quadrupole radiation of virtual photon to the corresponding cross section is found. The effect of the finite nuclear size is considered in detail. A comparison is made with the contribution of electric dipole radiation of virtual photon and with the contribution of the two-photon pair production mechanism. It is shown that the contribution of electric quadrupole radiation is dominant in a wide range of relative velocities. The cross section for the production of $e^+e^-$ pair with the capture of an electron by one of the nuclei is also analyzed.Comment: 7 pages, 2 figue

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

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

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