Electron-electron interactions in partially mixed helical states

TL;DR

This paper explores how electron-electron interactions influence partially mixed helical states at the edges of topological insulators, revealing regimes of gap formation, helicity mixing, and temperature-dependent charge transport behaviors.

Contribution

It provides a theoretical analysis of interaction effects on helical edge states, identifying regimes of gap opening and helicity mixing using bosonization and RG methods.

Findings

Strong interactions induce helicity mixing and a strong gap regime.

Charge and spin density wave correlations depend on interaction strength.

Charge conductivity exhibits distinct temperature dependence in different regimes.

Abstract

We theoretically study the effect of electron-electron interactions in one-dimensional partially mixed helical states. These helical states can be realized at the edges of two-dimensional topological insulators with partially broken time-reversal symmetry, resulting in helical gapped states. Using the bosonization method and renormalization group analysis, we identify weak gap, crossover, and strong gap regimes in the phase diagram. We find that strong electron-electron interaction mixes the helicity of the states, leading to the relevant strong gap regime. We investigate the charge and spin density wave correlation functions in different relevancy regimes of the gap mediated by interactions, where in the case of strong repulsive interaction, the spin density wave dominates the charge density wave. Additionally, employing the Memory function technique, we calculate the effect of mixed helicity on the charge transport in a sufficiently long edge. We find a non-uniform temperature dependence for the charge conductivity in both the strong and weak gap regimes with distinct features.