Quasiparticle Transport Research Articles

Charge imbalance induced by a temperature gradient in superconducting aluminum

The quasiparticle transport current induced in a superconducting aluminum film by a temperature gradient has been measured by means of the spatially decaying charge imbalance generated near the end of the sample where the current is divergent. The magnitude and decay length of the charge imbalance are in good agreement with the predictions of a simple model that takes into account the nonuniformity of the temperature gradient. The inferred value of the thermopower in the superconducting state agrees reasonably well with the value measured in the normal state. Measurements of the decay length of charge imbalance induced by current injection yield a value of the inelastic relaxation time ${\ensuremath{\tau}}_{E}$ of about 2 ns. This value is substantially smaller than that obtained from other measurements for reasons that are not known.

Observation of Thermoelectrically Induced Charge Imbalance in Superconducting Aluminum

The quasiparticle transport current induced in a superconducting aluminum film by a temperature gradient has been detected by measurements of the spatially decaying charge imbalance generated near the end of the sample where the current is divergent. The results are in good agreement with theory when the nonuniformity of the temperature gradient is taken into account. In particular, the inferred value of the thermopower agrees well with the value obtained when the aluminum is in the normal state.

Thermoelectric effects in the superconducting state

A wide variety of interesting thermoelectric effects can be exist in superconductors, even though all conventional thermoelectric properties vanish. This paper discusses some of the phenomena predicted to occur in a superconductor with a temperature gradient, and reviews experiments that have been conducted to observe them. Although the present theory of non-equilibrium superconductivity has been very successful in describing most quasiparticle transport effects, the field of thermoelectricity has been characterized by large discrepancies between theory and experiment. Some of these discrepancies remain unresolved. However, a new class of effects, in which the thermoelectric response creates a charge imbalance in a superconductor, has been proposed and observed, confirming some aspects of the thermoelectric transport theory.

Comments on the effect of disorder on transport with intermediate degree of coherence: Calculation of the mean square displacement

We use the generalized master equation with a simple exponential memory but with disorder in its spatial dependence to analyze the combined effect of coherence and randomness on the transport of quasiparticles. We calculate the mean-square-displacement and find that it retains well-known properties in the presence of randomness.

QUANTUM PHYSICS OF RETARDED TRANSPORT

Many problems in hot electron physics, in particular the transport properties of sub micron devices, in volve space and time scales such that the semi-classical Boltzmann transport theory is invalid. Here we examine the temporal and spatial retardation effects associated with the evolution of the microscopic Wigner distributions for carriers using many-body Green function techniques applicable to inhomogeneous high field quasi-particle transport.

Quasiparticle excitations, the relaxation, and transport properties in the narrow-band region of the Hubbard model

Assuming that, in the narrow-band region, the exact Green's function of the Hubbard model essentially retains the two-peak structure proposed by Hubbard, we derive its consequences as rigorously as possible. When a quasielectron is added to the ground state of $N$ electrons in the narrow-band region of the Hubbard model, the whole system is shown to relax due to the strong interaction $I$, thus yielding a relaxation energy $\ensuremath{\Delta}E$ between the quasielectron and the original $N$ electrons. This explains the conclusion in the preceding paper that a gap $\ensuremath{\Delta}E$ analogous to the energy gap in superconductivity appears between the quasielectron spectrum and the chemical potential for any occupation $n$ regardless of whether the lower band is exactly filled or not and that the system cannot be a normal metal. We further found that the ground state is, in fact, a bound state, and electrons involved do not obey the Landau theory of quasiparticles. However, the electron Green's function describes the motion of an electron added to this $N$-electron ground state without the relaxation of the original $N$ electrons, and hence this added electron behaves exactly like a Landau quasiparticle and can be represented by the quasiparticle operator ${\mathrm{A}}_{k\ensuremath{\sigma}}^{\ifmmode\dagger\else\textdagger\fi{}}$ introduced by Luttinger and Nozi\`eres. Only if the original $N$ electrons are allowed to relax is the energy of the system reduced by $\ensuremath{\Delta}E$, yielding the energy gap $\ensuremath{\Delta}E$. When a quasielectron is removed from the system of $N+1$ electrons, the same relaxation energy $\ensuremath{\Delta}E$ is removed, and again the gap $\ensuremath{\Delta}E$ is introduced between the chemical potential $\ensuremath{\mu}$ and the quasihole spectrum, thus creating a gap $2\ensuremath{\Delta}E$ between the quasielectron and quasihole spectra for any occupation $n$. The Fermi level, lying at the center of the gap, never intersects the quasiparticle spectra and therefore, Luttinger's theorem that the volume within the Fermi surface is independent of interactions and equal to the value in the noninteracting limit does not apply to the Hubbard model in the narrow-band region. However, this conclusion does not immediately imply that the system is an insulator. Instead, it is shown that a current-carrying state analogous to the condensate state found by Fr\ohlich appears under certain conditions. When the number of electrons $N$ is nearly or exactly equal to the number of atoms ${N}_{a}$, quasiparticlelike behavior disappears completely, making the system insulating. The only exception is the pathological limit $I=\ensuremath{\infty}$, where a metallic state with a Fermi volume twice that in the noninteracting limit is found.

Tunneling potentials associated with thermoelectric quasiparticle transport in superconductors

A superconductor in a thermal gradient assumes a steady state with counterflowing super and normal currents. A quasiparticle transport theory is presented for this current, and the resulting nonequilibrium quasiparticle distribution function is used to discuss NIS tunneling. For zero tunneling current, we derive a bias voltage which is quadratic in ▽ T and which is of roughly the same magnitude as the linear effect recently measured by Falco.

Transport Coefficients of Normal Liquid 3He at Very Low Temperatures: --s- and p-Wave Approximation--

Shear viscosity and thermal conductivity in the very low temperature region of the normal Fermi liquid 3He are studied variationally by using the quasiparticle transport equation. s- and p-wave approximation is used for the scattering amplitude for quasiparticles on the Fermi surface and the relation between the partially expanded potentials and Landau Fermi liquid parameters is derived. It is found that the trial functions for the shear viscosity and the thermal conductivity give very good approximation to the ture solutions of the transport equation.

Generalized heat conduction equation

The linear constitutive relation between heat flux and temperature gradient known as Fourier’s law is modified to be nonlocal in time; i.e., the heat flux depends on the past history of the temperature gradient. It is shown that this leads to a generalized heat conduction equation which can be hyperbolic and thus possess a wavelike solution with finite velocity of propagation of a heat pulse. In two extreme limits of very short and very long memory the equation reduces, respectively, to the usual parabolic heat conduction equation and to a hyperbolic wave equation. For in between memory the equation has the properties of a telegraph equation characterized by a relaxation time. Such equations have arisen in treatments of second sound, exciton transport, and quasiparticle transport in 3He.

On the Applicability of the Quasi-particle Transport Equation of Superfluid 3He at Low Temperatures

On the Applicability of the Quasi-particle Transport Equation of Superfluid 3He at Low Temperatures

Fermi-liquid theory for interband transitions

Previous uses of the Landau quasiparticle theory have been confined to cases where the driving frequency is small. Here a Landau-type theory including interband transitions is derived. The quasiparticle transport equation is derived by a procedure similar to that of Luttinger and Nozieres and Jones and McClure using a bi-orthogonal expansion introduced by Layzer. Using a Ward-type relationship, the connection between quasiparticle quantities and physical densities and currents is made.

Derivation of a Quasiparticle Transport Equation for an Impure Fermi Liquid at Low Temperatures

Derivation of a Quasiparticle Transport Equation for an Impure Fermi Liquid at Low Temperatures

Transport Coefficients of a Normal Fermi Liquid: Application to LiquidHe3

The transport coefficients of a normal Fermi liquid in the extreme low-temperature limit and the leading finite-temperature contributions to the transport coefficients are studied using the quasiparticle transport equation. The scattering amplitude for quasiparticles on the Fermi surface is expressed in terms of Landau parameters, using an approximation which takes into account $s$- and $p$-wave scattering; the calculated values of the transport coefficients in the extreme low-temperature limit for liquid ${\mathrm{He}}^{3}$ are shown to be in good agreement with the experimental values. Finite-temperature contributions to the transport coefficients are expressed in terms of the solution of the transport equation in the extreme low-temperature limit, and explicit calculations are performed for the case of liquid ${\mathrm{He}}^{3}$. Assuming Landau parameters with $l\ensuremath{\ge}2$ vanish, an estimate of the Landau parameter $F_{1}^{}{}_{}{}^{a}$ for liquid ${\mathrm{He}}^{3}$ is obtained by comparing the theoretical and experimental values of the leading finite-temperature contributions to the transport coefficients.

Transport Coefficients of a Normal Fermi Liquid at Finite Temperatures

Exact solutions of the quasiparticle transport equation in the limit $T\ensuremath{\rightarrow}0$ are used to calculate finite temperature corrections to the thermal conductivity and spin-diffusion coefficients of a normal Fermi liquid by a perturbation theory method. Application of the results to liquid ${\mathrm{He}}^{3}$ yields an estimate for the Landau parameter $F_{1}^{}{}_{}{}^{a}$

Green's functions method for justifying a nonequilibrium landau theory

A Landau theory which includes nonequilibrium situations is derived. The approach of Kadanoff and Baym is used to obtain a quasi-particle transport equation with collision terms. Landau's identifications of physical quantities as various moments of the quasi-particle distribution function are justified through the use of identities involving the functional dependence of the real time functions. These identities are derived using the concept of the φ-derivability of the real time functions discussed in an earlier work.