Impurity compensation and band-gap renormalization in double-quantum-wires

We investigate the band-gap renormalization due to electron-electron interaction in the n-type doped GaAs-based double-quantum-wire systems. Electron self-energy is calculated using the leading-order perturbation theory (GW) within the full random-phase-approximation (RPA). We include the impurity effects through Mermin expression and show that decreasing the spacing in double-wire system can compensate partly the undesirable effect of impurities on the band-gap renormalization. Therefore, it is possible to offset the effect of impurity in related devices and to adjust the band-gap. We also, apply a constant electric field to one of the wires. It is shown that the change of the band-gap renormalization in the other wire will be insignificant if the drift velocity does not exceed Fermi velocity