Spectral properties of a disordered insulating lattice under nonlinear electric field

Quenched disorder in a solid state system can result in Anderson localization, where electrons are exponentially localized and the system behaves like an insulator. By exactly solving a disordered electronic lattice model out of equilibrium, we investigate the effect of a DC electric field on Anderson localization in an open system and provide a minimal platform to study disorder-nonequilibrium interplay in electronic lattice systems. We perform steady-state Keldysh-Green’s function calculations on an infinite lattice with a finite range of disorder-active regions that are coupled to fermion reservoirs. Our solutions out of a fully electronic model verify Mott’s temperature scaling of the variable-range-hopping transport and the Lifshitz tail, well corroborated by the coherent potential approximation. We further reveal that a nonequilibrium electronic lattice creates a statistical evolution that shows a counterintuitive shift of the distribution edge in the opposite direction of the band edge. The rich evolution of nonthermal statistics highlights the importance of an explicit band structure and the impurity correlations in strong nonequilibrium theories.