In a 2D electron gas (2DEG) with broken structural inversion symmetry, spin-orbit coupling of the Rashba type locks the electron spin perpendicular to its momentum, splitting the Fermi surface into two helical sub-bands.
Rashba Hamiltonian: H = ℏ²k²/(2m*) + α(k × σ)·ẑ = ℏ²k²/(2m*) ± αk. This splits the parabolic dispersion into two branches: E±(k) = ℏ²k²/(2m*) ± α|k|. Each branch has a helical spin texture — the spin rotates by 2π as k circles the Fermi surface (winding number = ±1). The two Fermi circles have radii k± = m*/ℏ²(αm*/ℏ² ± √(2m*EF/ℏ²+α²m*²/ℏ⁴)^(1/2)). The Rashba effect underlies spin transistors, spin Hall effect, and topological insulator surface states.