Week 8: Hall effect in a 2D bar, from Hall voltage to edge states

Hall effect in a 2D bar: from a small Hall voltage to edge states (Datta Ch. 11, Figs. 11.1–11.6)

Linear response: the source injects extra electrons (μ₁ = 1, μ₂ = 0). They move at the Fermi speed, curve in the magnetic field (dp/dt = −qv×B, Eq. 11.1), scatter elastically and reflect at the side walls. The density across the width at mid-bar is the transverse profile of μ; its top-to-bottom difference is the Hall voltage qV_H.

Carriers:

Magnetic field: ω_cτ Mean free path λ = (π/2)vτ (bar: L = 3, W = 1)

qV_H/(μ₁ − μ₂) from two edge probes–

Datta Eq. 11.14 (valid for ω_cτ ≪ 1)–

Transmission to the drain–

Cyclotron radius r_c/W–