Three-particle collisions in quantum wires: Corrections to thermopower and conductance

TL;DR

This paper investigates how three-particle electron collisions affect thermopower and conductance in finite quantum wires, revealing positive corrections that depend on wire length and involve deep Fermi sea states.

Contribution

It provides a leading-order calculation of three-particle collision effects on thermopower and conductance in quantum wires, including the role of integrability.

Findings

Three-particle collisions lead to positive thermopower corrections.

In integrable models, three-particle collision rates are zero.

Corrections follow an activation law related to Fermi energy.

Abstract

We consider the effect of electron-electron interaction on the electron transport through a finite length single-mode quantum wire with reflectionless contacts. The two-particle scattering events cannot alter the electric current and therefore we study the effect of three-particle collisions. Within the Boltzmann equation framework, we calculate corrections to the thermopower and conductance to the leading order in the interaction and in the length of wire $L$. We check explicitly that the three-particle collision rate is identically zero in the case of several integrable interaction potentials. In the general (non-integrable) case, we find a positive contribution to the thermopower to leading order in $L$. The processes giving rise to the correction involve electron states deep in the Fermi sea. Therefore the correction follows an activation law with the characteristic energy of the order of the Fermi energy for the electrons in the wire.