On the Mott formula for thermopower of non-interactions electrons in quantum point contacts

TL;DR

This paper compares the thermopower of non-interacting electrons in quantum point contacts calculated via the Landauer formula with the low temperature and Mott approximations, highlighting their validity and deviations.

Contribution

It provides an analytical and numerical comparison of the thermopower formulas for non-interacting electrons in quantum point contacts, clarifying the applicability of the Mott formula.

Findings

The Mott formula accurately describes thermopower at low temperatures.

Deviations from the Mott formula indicate interaction effects or non-idealities.

Numerical results support the analytical comparisons.

Abstract

We calculate the linear response thermopower S of a quantum point contact using the Landauer formula and therefore assume non-interacting electrons. The purpose of the paper, is to compare analytically and numerically the linear thermopower S of non-interacting electrons to the low temperature approximation, S^1=(pi^2/3e)k^2 T d(ln G(mu,T=0))/dmu, and the so-called Mott expression, S^M=(pi^2/3e)k^2 T d(ln G(mu,T))/dmu, where G(mu,T) is the (temperature dependent) conductance. This comparison is important, since the Mott formula is often used to detect deviations from single-particle behavior in the thermopower of a point contact.