Nonperturbative interaction effects in the thermodynamics of disordered wires

TL;DR

This paper investigates nonperturbative Coulomb interaction effects on the thermodynamics of disordered multichannel wires, revealing how these effects depend on temperature, conductance, and channel number, and providing explicit corrections to heat capacity.

Contribution

It introduces a nonperturbative analysis of interaction corrections using the replica nonlinear sigma model, focusing on the crossover from dimerized pairs to Coulomb plasma regimes.

Findings

Derived the nonperturbative correction to heat capacity in high-temperature regime.

Identified the crossover behavior between dimerized and plasma regimes.

Expressed the correction ratio as /C_0   N_{ch} G^2(L_T) e^{-2G(L_T)}.

Abstract

We study nonperturbative interaction corrections to the thermodynamic quantities of multichannel disordered wires in the presence of the Coulomb interactions. Within the replica nonlinear $\sigma$-model (NL$\sigma$M) formalism, they arise from nonperturbative soliton saddle points of the NL$\sigma$M action. The problem is reduced to evaluating the partition function of a replicated classical one dimensional Coulomb gas. The state of the latter depends on two parameters: the number of transverse channels in the wire, N_{ch}, and the dimensionless conductance, G(L_T), of a wire segment of length equal to the thermal diffusion length, L_T. At relatively high temperatures, $G(L_T) \gtrsim \ln N_{ch} $, the gas is dimerized, i.e. consists of bound neutral pairs. At lower temperatures, $\ln N_{ch} \gtrsim G(L_T) \gtrsim 1$, the pairs overlap and form a Coulomb plasma. The crossover between the two regimes occurs at a parametrically large conductance $G(L_T) \sim \ln N_{ch}$, and may be studied independently from the perturbative effects. Specializing to the high temperature regime, we obtain the leading nonperturbative correction to the wire heat capacity. Its ratio to the heat capacity for noninteracting electrons, C_0, is $\delta C/C_0\sim N_{ch}G^2(L_T)e^{-2G(L_T)}$.