Memory function approach to electronic diffusion in two-dimensional electron systems

Abstract

Based on an expansion of the memory function, we propose an analytical approach to analyze the role played by temperature, electron effective mass, and background dielectric constant on the diffusion constant of a two-dimensional electron gas in a uniform perpendicular external magnetic field. Using a short-time expansion of the Kubo-Greenwood formula, we are able to calculate the two-body and three-body effects from the corresponding correlation functions which are obtained from the hypernetted-chain integral equation theory and the Kirkwood superposition approximation, respectively. When our results are compared with already published molecular dynamics and Monte Carlo simulation results, the agreement is excellent. At low temperature, the diffusion constant first increases and then decreases as the magnetic field is increased but decreases monotonically with increasing magnetic field at high temperature. Our calculations show that the Lorentz force induced by an applied uniform magnetic field is enhanced by increasing the dielectric constant and decreasing the electron effective mass.