Bound States and Many-Body Effects in H-Shaped Quantum Wires

In this paper, bound states energies and corresponding wave functions of H-shaped quantum wires are calculated numerically in the presence of external magnetic and electric fields and within the Landau gauge. With a suitable definition of external confinement potential, we present a numerical algorithm to calculate the profile of probability distribution of charge carriers. Our analysis shows that in the presence of external electric and magnetic fields, bound state properties of carriers are sensitive functions of an asymmetric parameter $a=\frac{W_{x}}{W_{y}}$ which measures the relative width of the well in two directions. We also study many body effect of bandgap renormalization in this quasi one dimensional system within dynamical random phase approximation.