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

TL;DR

This study numerically investigates bound states, wave functions, and many-body effects in H-shaped quantum wires under external fields, highlighting the influence of geometric asymmetry and electron interactions.

Contribution

It introduces a numerical method for analyzing bound states and charge distribution in asymmetric H-shaped quantum wires considering external fields and many-body effects.

Findings

Bound state energies are sensitive to the asymmetry parameter $a$.

External electric and magnetic fields significantly affect carrier properties.

Bandgap renormalization due to many-body effects is analyzed within RPA.

Abstract

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.