Thermopower of Single-Channel Disordered and Chaotic Conductors

TL;DR

This paper analytically and numerically investigates the distribution of thermopower in disordered and chaotic quantum conductors, revealing Lorentzian and exponential behaviors at different regimes and specific distribution features for quantum dots.

Contribution

It provides a detailed analysis of thermopower distributions in disordered wires and quantum dots, including new analytical forms and numerical validation across regimes.

Findings

Thermopower distribution in disordered wires is Lorentzian at zero temperature.

Distribution crosses over to exponential with increasing temperature.

Quantum dots exhibit a cusp at S=0 and power-law tails in the distribution.

Abstract

We show (analytically and by numerical simulation) that the zero-temperature limit of the distribution of the thermopower S of a one-dimensional disordered wire in the localized regime is a Lorentzian, with a disorder-independent width of 4 pi^3 k_B^2 T/3e\Delta (where T is the temperature and \Delta the mean level spacing). Upon raising the temperature the distribution crosses over to an exponential form exp(-2|S|eT/\Delta). We also consider the case of a chaotic quantum dot with two single-channel ballistic point contacts. The distribution of S then has a cusp at S=0 and a tail |S|^{-1-\beta} log|S| for large S (with \beta=1,2 depending on the presence or absence of time-reversal symmetry).