Electron States in a Staircase Infinitely Deep Well in a Magnetic Field

TL;DR

This paper analyzes electron states in a coated semiconductor wire under a magnetic field, deriving wave functions, energy levels, and impurity binding energies, revealing how magnetic fields influence electronic properties.

Contribution

It provides a detailed analytical and variational study of electron states and impurity energies in a coated semiconductor wire in a magnetic field, which was not previously explored.

Findings

Electron energy levels depend on magnetic field and wire parameters.

Binding energy of impurity increases with magnetic field strength.

Wave functions are explicitly derived for the system.

Abstract

The electron states in a size-quantaized coated semiconductor wire in a uniform magnetic field applied parallel to the wire axis is considered. The wave functions are found and the equation for determination of energy eigenvalues depending both on magnetic field and parameters of the wire and the coating is obtained. The binding energy of a hydrogen-like impurity located on the wire axis is computed by the use of the variational method, and it is shown that this energy increases with the increase of the magnetic field.