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We propose a two-dimensional electron gas (2DEG) system in which an externalmagnetic (B) field with a small chirality is applied to provide a topologicalU(1) U(1) gauge field that separates conduction electrons of opposite spins inthe transverse direction. Additionally, the vertical electric (E) field in the2DEG, together with spin-orbit coupling, produces a SU(2) gauge field whichreinforces / opposes the effect of the topological gauge. The system thusprovides a tunable spin Hall effect, where an applied gate voltage on the 2DEGcan be used to modulate the transverse spin current. As this method leads tothe enhancement or cancellation of intrinsic spin Hall, it naturallydistinguishes the extrinsic from the intrinsic effect.Comment: 11 pages, 3 figure

Spin transverse separation in a two-dimensional electron-gas using an external magnetic field with a topological chirality