Tunneling into and between helical edge states - fermionic approach

TL;DR

This paper investigates the electronic transport properties of junctions involving helical edge states in topological insulators using a fermionic approach, revealing fixed points, fixed lines, and conductance scaling behaviors.

Contribution

It introduces a fermionic scattering state formalism to analyze tunneling and junctions of helical edge states, extending previous models and identifying new fixed points and conductance relations.

Findings

Existence of fixed lines and fixed points in RG flow.

Proportionality relations for conductances during renormalization.

Scaling exponents and phase portraits for different junction configurations.

Abstract

We study four-terminal junction of spinless Luttinger liquid wires, which describes either a corner junction of two helical edges states of topological insulators or the tunneling from the spinful wire into the helical edge state. We use the fermionic representation and the scattering state formalism, in order to compute the renormalization group (RG) equations for the linear response conductances. We establish our approach by considering a junction between two possibly non-equivalent helical edge states and find an agreement with the earlier analysis of this situation. Tunneling from the tip of the spinful wire to the edge state is further analyzed which requires some modification of our formalism. In the latter case we demonstrate i) the existence of both fixed lines and conventional fixed points of RG equations, and ii) certain proportionality relations holding for conductances during renormalization. The scaling exponents and phase portraits are obtained in all cases.