Non-Equilibrium Green Functions — Keldysh Contour

Quantum transport through a nanojunction: Landauer formula and NEGF-DFT

Transmission T(E) & Current density

Keldysh contour & self-energies

I-V characteristic

Spectral function A(E)

Lesser GF & occupancy

Bias voltage V_bias (eV) 0.50 Level energy ε₀ (eV) 0.00 Left coupling Γ_L (eV) 0.10 Right coupling Γ_R (eV) 0.10 Temperature T (K) 77

Keldysh-NEGF: Non-equilibrium transport via time-ordered Keldysh contour C = C⁺ ∪ C⁻. Retarded GF: G^r(E) = [(E-ε₀) - Σ_L^r - Σ_R^r]⁻¹. Transmission: T(E) = Γ_L·|G^r|²·Γ_R. Landauer current: I = (2e/h)∫T(E)[f_L(E)-f_R(E)]dE.
Current I: — μA | Conductance G: — G₀ | Occupancy ⟨n⟩: —