Spin Hall utilizing U(1) and SU(2) gauge fields

We propose a two-dimensional electron gas (2DEG) system in which an external magnetic (B) field with a small chirality is applied to provide a topological U(1) U(1) gauge field that separates conduction electrons of opposite spins in the transverse direction. Additionally, the vertical electric (E) field in the 2DEG, together with spin-orbit coupling, produces a SU(2) gauge field which reinforces / opposes the effect of the topological gauge. The system thus provides a tunable spin Hall effect, where an applied gate voltage on the 2DEG can be used to modulate the transverse spin current. As this method leads to the enhancement or cancellation of intrinsic spin Hall, it naturally distinguishes the extrinsic from the intrinsic effect.