Rashba coupling and magnetic order in correlated helical liquids

TL;DR

This study uses quantum Monte Carlo simulations to analyze how Rashba coupling influences correlated helical liquids, revealing that interactions enhance spin correlations and can induce a spectral gap, but the gap remains closed due to fluctuations.

Contribution

It provides the first comprehensive numerical analysis of Rashba coupling effects on strongly correlated helical liquids using quantum Monte Carlo methods.

Findings

Interactions enhance spin correlations in helical liquids.

Spectral weight at the Fermi level is suppressed by interactions.

The spectral gap observed is closed by order parameter fluctuations.

Abstract

We study strongly correlated helical liquids with and without Rashba coupling using quantum Monte Carlo simulations of the Kane-Mele model with a Hubbard interaction at the edge. Independent of the Rashba coupling, we find that interactions enhance spin correlations and suppress the spectral weight at the Fermi level. For sufficiently strong interactions, a gap can be observed in the single-particle spectral function. However, based on a finite-size scaling analysis and theoretical arguments, we argue that this gap is closed by order parameter fluctuations in the Luttinger liquid phase even at zero temperature, and filled in by thermally induced kinks in the order parameter in the Mott phase at finite temperatures. While the bosonization suggests an umklapp-driven Mott transition only in the presence of Rashba coupling and hence a significant impact of the latter, our numerical results are almost unaffected by Rashba coupling even at low temperatures.