Magnetic von-Neumann lattice for two-dimensional electrons in the magnetic field

TL;DR

This paper introduces a magnetic von-Neumann lattice approach to analyze two-dimensional electrons in strong magnetic fields, revealing dualities and providing a useful framework for understanding their quantum states.

Contribution

It develops a novel von-Neumann lattice method to solve for electron states in magnetic fields with various potentials, highlighting duality and computational advantages.

Findings

Eigenstates and eigenvalues are obtained for different impurity and potential configurations.

A duality between cosine potential and lattice kinetic term is demonstrated.

The von-Neumann lattice representation simplifies the analysis of electron dynamics.

Abstract

One-particle eigenstates and eigenvalues of two-dimensional electrons in the strong magnetic field with short range impurity and impurities, cosine potential, boundary potential, and periodic array of short range potentials are obtained by magnetic von-Neumann lattice in which Landau level wave functions have minimum spatial extensions. We find that there is a dual correspondence between cosine potential and lattice kinetic term and that the representation based on the von-Neumann lattice is quite useful for solving the system's dynamics.