Conductance of fully equilibrated quantum wires

TL;DR

This paper investigates how weak electron-electron scattering in long quantum wires causes full equilibration, leading to temperature-dependent corrections to the quantized conductance, independent of interaction specifics.

Contribution

It provides a theoretical analysis of conductance corrections due to electron-electron interactions in quantum wires, emphasizing the role of full equilibration and conservation laws.

Findings

Conductance acquires a quadratic temperature correction.

Full equilibration alters contact resistance.

Correction magnitude is independent of interaction details.

Abstract

We study the conductance of a quantum wire in the presence of weak electron-electron scattering. In a sufficiently long wire the scattering leads to full equilibration of the electron distribution function in the frame moving with the electric current. At non-zero temperature this equilibrium distribution differs from the one supplied by the leads. As a result the contact resistance increases, and the quantized conductance of the wire acquires a quadratic in temperature correction. The magnitude of the correction is found by analysis of the conservation laws of the system and does not depend on the details of the interaction mechanism responsible for equilibration.