Nonequilibrium transport of helical Luttinger liquids through a quantum dot

TL;DR

This paper investigates non-equilibrium transport in helical Luttinger liquids through a quantum dot, revealing a quantum phase transition influenced by interactions, with detailed analysis of current, noise, and density of states.

Contribution

It introduces a comprehensive analysis of steady-state transport in helical Luttinger liquids with a quantum dot, including effects of interactions and phase transitions.

Findings

Identifies a metal-to-insulator quantum phase transition driven by interaction strength.

Derives analytical current expressions for non-interacting dots with self-energy corrections.

Discovers singular behaviors in current noise and density of states near the transition.

Abstract

We study a steady state non-equilibrium transport between two interacting helical edge states of a two dimensional topological insulator, described by helical Luttinger liquids, through a quantum dot. For non-interacting dot the current is obtained analytically by including the self-energy correction to the dot Green's function. For interacting dot we use equation of motion method to study the influence of weak on-site Coulomb interaction on the transport. We find the metal-to-insulator quantum phase transition for attractive or repulsive interactions in the leads when the magnitude of the interaction strength characterized by a charge sector Luttinger parameter $K$ goes beyond a critical value. The critical Luttinger parameter $K_{cr}$ depends on the hoping strength between dot and the leads as well as the energy level of the dot with respect to the Fermi levels of the leads, ranging from weak interaction regime for dot level off resonance to strong interaction regime for dot in resonance with the equilibrium Fermi level. Nearby the transition various singular behaviors of current noise, dot density of state, and the decoherence rate (inverse of lifetime) of the dot are briefly discussed.