In the same manner, the stationary photocurrent proportional to intensity of light is J = − − 2 π π e τ τ ℏ ℏ ∑ ∑ i , f ∫ ∫ BZ d k ( 2 π π ) D | v i − − v f | ( f i ( k ) − − f f ( k ) ) | H i f ′ | 2 δ δ ( E f ( k ) − − E i ( k ) − − ℏ ℏ ω ω ) , where τ τ is the relaxation time, v i − − v f and f i ( k ) − − f f ( k ) are the difference of the group velocity and Fermi-Dirac distribution between possible the initial and final states. Here | H i f ′ | 2 defines the optical transition dipole. Due to the commutation relation between position r and the Hamiltonian, we can also rewrite the transition dipole and photocurrent in terms of position operator matrix using ⟨ ⟨ i | p | f ⟩ ⟩ = − − i m 0 ω ω ⟨ ⟨ i | r | f ⟩ ⟩ .