Topological phases in a two-dimensional lattice: Magnetic field versus spin-orbit coupling

TL;DR

This paper investigates how spin-orbit coupling and magnetic fields influence topological states in a 2D honeycomb lattice, connecting quantum Hall and quantum spin Hall phenomena through minimal models.

Contribution

It provides a detailed analysis of the effects of intrinsic and Rashba spin-orbit couplings and Zeeman splitting on topological phases, clarifying their interplay in minimal models.

Findings

Distinct topological states induced by individual effects

Competition between spin-orbit coupling and magnetic field effects

Potential experimental realizations of the model

Abstract

In this work, we explore the rich variety of topological states that arise in two-dimensional systems, by considering the competing effects of spin-orbit couplings and a perpendicular magnetic field on a honeycomb lattice. Unlike earlier approaches, we investigate minimal models in order to clarify the effects of the intrinsic and Rashba spin-orbit couplings, and also of the Zeeman splitting, on the quantum Hall states generated by the magnetic field. In this sense, our work provides an interesting path connecting quantum Hall and quantum spin Hall physics. First, we consider the properties of each term individually and we analyze their similarities and differences. Secondly, we investigate the subtle competitions that arise when these effects are combined. We finally explore the various possible experimental realizations of our model.