Intrinsic Spin Hall Effect — Rashba 2D Model

In a 2D electron gas with Rashba spin-orbit coupling H = ℏ²k²/2m + λ(k×σ)·ẑ, the Berry curvature of the split bands gives an intrinsic spin Hall conductivity σ_SH = e/8π (in 2D). This contribution is purely geometric — requiring no impurities — and is a hallmark of topological band physics.

Rashba Band Structure E±(k)
Berry Curvature Ω±(k) [radial]
Spin Hall Conductivity σ_SH(E_F)
σ_SH = — | Fermi level in upper/lower band
Iris Lab · Spin Hall effect · Berry phase · Rashba coupling