The role of the exchange-Coulomb potential in two-dimensional electron transport

Abstract

We develop a quantum kinetic theory of two-dimensional electron gases in which exchange is treated self-consistently at the Hartree-Fock level and enters as a nonlocal, momentum-dependent field in phase space. By starting from the Coulomb Hamiltonian, we derive a Hartree-Fock-Wigner equation for the electronic Wigner function and obtain a closed fluid model with exchange-corrected pressure, force, and current. For a single layer, we show that exchange renormalizes the Fermi velocity and can drive a long-wavelength plasmonic instability at low densities. In coupled layers, the same framework predicts acoustic-optical mode coupling, and an instability forming long-lived charge-imbalance patterns that are not predicted by classical Vlasov and Boltzmann models. Finally, we apply the kinetic model to the Coulomb drag problem and show how exchange substantially enhances the drag resistivity in dilute GaAs double wells, quantitatively matching experimental observations.