Tunneling between edge states of a 2D topological insulator and a Fermi liquid lead through a quantum dot

TL;DR

This paper investigates non-equilibrium tunneling between a quantum dot connected to a 2D topological insulator edge and a Fermi liquid, deriving analytical results for current behavior using bosonization and RG techniques.

Contribution

It introduces a method to analyze tunneling involving a topological insulator edge and provides exact results in the small bias limit with interactions.

Findings

Derived a formula for the I-V characteristic over a wide range of conditions.

Analyzed the effects of electron-electron interactions on tunneling current.

Provided insights into non-equilibrium transport in topological insulator systems.

Abstract

In this paper we study a non-equilibrium resonant tunnelling problem where a non-interacting quantum dot is connected to two leads, one being the edge of an interacting 2-D topological insulator (Luttinger liquid) and the other being a usual Fermi liquid. We show that the current passing through the system can be expressed in terms of a non-equilibrium local single-particle Green's function of the Luttinger liquid lead which can be analysed using standard bosonization- Renormalization Group (RG) technique. In particular, some exact results can be extracted in the small bias limit with repulsive electron-electron interaction. A simple formula which captures the qualitative feature of the I-V relation over whole temperature and voltage bias range is being proposed and studied.