Artificial Gauge Field and Quantum Spin Hall States in a Conventional Two-dimensional Electron Gas

TL;DR

This paper demonstrates how to induce artificial gauge fields and quantum spin Hall states in a conventional 2D electron gas through engineered band structures and spin-orbit interactions in quantum wells.

Contribution

It introduces a theoretical method to generate topological phases in standard 2D electron gases using antidot lattices and band engineering.

Findings

Artificial gauge fields can be induced in 2D electron gases.

Band inversions lead to topological phases with helical edge states.

Large nontrivial minigaps support quantum spin Hall states.

Abstract

Based on the Born-Oppemheimer approximation, we divide total electron Hamiltonian in a spinorbit coupled system into slow orbital motion and fast interband transition process. We find that the fast motion induces a gauge field on slow orbital motion, perpendicular to electron momentum, inducing a topological phase. From this general designing principle, we present a theory for generating artificial gauge field and topological phase in a conventional two-dimensional electron gas embedded in parabolically graded GaAs/In$_{x}$Ga$_{1-x}$As/GaAs quantum wells with antidot lattices. By tuning the etching depth and period of antidot lattices, the band folding caused by superimposed potential leads to formation of minibands and band inversions between the neighboring subbands. The intersubband spin-orbit interaction opens considerably large nontrivial minigaps and leads to many pairs of helical edge states in these gaps.