Tunneling into Nonequilibrium Luttinger Liquid with Impurity

TL;DR

This paper investigates tunneling into a nonequilibrium Luttinger liquid with a defect, revealing how inelastic backscattering and plasmon emission influence tunneling rates and exponents at different energy edges.

Contribution

It provides a theoretical analysis of tunneling in a nonequilibrium LL, highlighting the effects of inelastic backscattering and plasmon emission on tunneling exponents.

Findings

Tunneling rates split into two edges with distinct exponents.

Fermi edge exponent matches equilibrium LL value.

Side edge exponent can be negative depending on Coulomb interaction strength.

Abstract

We evaluate tunneling rates into/from a voltage biased quantum wire containing weak backscattering defect. Interacting electrons in such a wire form a true nonequilibrium state of the Luttinger liquid (LL). This state is created due to inelastic electron backscattering leading to the emission of nonequilibrium plasmons with typical frequency $\hbar \omega \leq U$. The tunneling rates are split into two edges. The tunneling exponent at the Fermi edge is positive and equals that of the equilibrium LL, while the exponent at the side edge $E_F-U$ is negative if Coulomb interaction is not too strong.