Week 13: One level, two contacts, quantum broadening

One level, two contacts: quantum broadening (Datta Part B, Ch. 18, Sec. 18.1)

A single level ε coupled to a source and a drain with escape rates γ₁/ℏ, γ₂/ℏ. Contact turns the sharp level into the Lorentzian D(E) = (γ/2π)/[(E−ε)² + (γ/2)²] (Eq. 18.23), and the current is I = (q/h) ∫ T(E)[f₁ − f₂] dE with T = γ₁γ₂/[(E−ε)² + (γ/2)²] (Eqs. 18.22, 18.30). Energies are measured from the equilibrium µ₀ = 0.

Level position ε − µ₀ (meV) Bias qV = µ₁ − µ₂ (meV) Source coupling γ₁ (meV) Drain coupling γ₂ (meV) Temperature (K)

Level occupation N (< 1)–

Current I = (q/h)∫T(f₁−f₂)dE–

Rate-equation I at E = ε (18.10b)–

Peak G (kT ≪ γ) = 4γ₁γ₂/γ² q²/h–

Width γ = γ₁ + γ₂–

Dwell time τ = ℏ/γ–

Linear-response G at µ₀ (q²/h)–

kT–