Numerical method for coherent electron dynamics with position-dependent effective-mass distributions in semiconductor heterostructures.

We develop a numerical scheme for solving the time-dependent Kohn-Sham equation in semiconductor heterostructures. Based on the efficient and accurate method recently proposed by Watanabe and Tsukada [Phys. Rev. E 65, 036705 (2002)], an extension is made for treating effective-mass mismatch between different semiconductor materials. A demonstrative calculation shows that the energy of the quantum-well state is accurately conserved during the time-evolution calculation with the present method. Examples under the existence of Hartree and exchange-correlation interactions are also shown as demonstrations of nonlinear electron dynamics in quantum wells. The present method is particularly useful for analyzing nonlinear coherent charge oscillations in semiconductor quantum wells, taking into account many-body effects.