Tunneling into a Luttinger liquid revisited

TL;DR

This paper investigates how electron interactions affect tunneling into a Luttinger liquid, revealing that contact size influences stability and conductance behavior beyond simple models.

Contribution

It extends understanding of tunneling in Luttinger liquids by analyzing stability and conductance beyond lowest-order perturbation, considering contact size effects.

Findings

Finite contact size destabilizes the fixed point.

Tunneling conductance can be nonmonotonic with temperature or bias.

Breakup of the liquid into two parts can occur due to tunneling.

Abstract

We study how electron-electron interactions renormalize tunneling into a Luttinger liquid beyond the lowest order of perturbation in the tunneling amplitude. We find that the conventional fixed point has a finite basin of attraction only in the point contact model, but a finite size of the contact makes it generically unstable to the tunneling-induced break up of the liquid into two independent parts. In the course of renormalization to the nonperturbative-in-tunneling fixed point, the tunneling conductance may show a nonmonotonic behavior with temperature or bias voltage.