Week 8: A single defect, two Landauer formulas and probes

A single defect: two Landauer formulas and what a probe measures (Datta Ch. 10, Figs. 10.1–10.8)

An otherwise ballistic wire with one defect in the middle that transmits a fraction T of the electrons. As in Week 7, the density of each stream (counted) is its potential: μ⁺ for right-movers, μ⁻ for left-movers (μ₁ = 1, μ₂ = 0). Two weakly coupled probes read μ_probe = αμ⁺ + (1 − α)μ⁻ (Eq. 10.4).

Defect transmission T Left probe weighting α_L Right probe weighting α_R

Two-terminal G_2t / (q²M/h) = T (Eq. 10.2)–

Four-terminal G_4t / (q²M/h) = T/(1−T) (Eq. 10.1)–

Probe readings μ_L*, μ_R*–

Measured R_4t / R_B–