Real-time formalism for studying the nonlinear response of "smart" materials to an electric field

Abstract

The nonlinear response of a material to a large electric field (steady or pulsed) often determines the ultimate performance of the material for electronics applications. The formalism for understanding nonlinear effects in conventional semiconductors is well understood. The formalism is less well developed for so-called ``smart'' materials that are tuned to lie close to the metal-insulator transition. Here we show that the nonlinear response of a strongly correlated electronic material can be calculated with a massively parallel algorithm by discretizing a continuous matrix operator on the Kadanoff-Baym contour in real time. We benchmark the technique by examining the solutions when the field vanishes and comparing the results to exact results from an equilibrium formalism. We briefly discuss the numerical issues associated with the case of a large electric field and present results that show how the Bloch oscillations become damped as the scattering due to electron correlations increases.