Chern insulating state in laterally patterned semiconductor heterostructures

Hexagonally patterned two-dimensional $p$-type semiconductor systems are quantum simulators of graphene with strong and highly tunable spin-orbit interactions. We show that application of purely in-plane magnetic fields, in combination with the crystallographic anisotropy present in low-symmetry semiconductor interfaces, allows Chern insulating phases to emerge from an originally topologically insulating state after a quantum phase transition. These phases are characterized by pairs of co-propagating edge modes and Hall conductivities $\sigma_{xy} = +\frac{2 e^2}{h}, -\frac{2 e^2}{h}$ in the absence of Landau levels or cyclotron motion. With current lithographic technology, the Chern insulating transitions are predicted to occur in GaAs heterostructures at magnetic fields of $\sim 5\text{T}$.