Local Density of States around an Impurity in a Strong Magnetic Field. I. a Two-Dimensional System with Parabolic Dispersion

TL;DR

This paper investigates the bound states around an impurity in a two-dimensional electron system under a strong magnetic field, using numerical solutions of the Schrödinger equation to compare theoretical LDOS with experimental observations.

Contribution

It provides a numerical analysis of impurity-bound states and their local density of states in a 2D system with parabolic dispersion under strong magnetic fields, aligning theory with experiment.

Findings

Theoretical LDOS matches experimental data reasonably well.

Bound states are effectively characterized by numerical solutions.

Impurity effects are significant in the local density of states in 2D systems.

Abstract

Bound states around an impurity are investigated for a two dimensional electron system in a strong magnetic field. Long-range Coulomb potential and related potentials are considered. Schr\"odinger equation is solved numerically to obtain the bound states. The energy and wave function of these bound states are indirectly observed by the scanning tunneling spectroscopy as local density of states (LDOS). Theoretically obtained LDOS is compared with experiment. Reasonable agreement is obtained.