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

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.