Stationary states of an electron in periodic structures in a constant uniform electrical field

TL;DR

This paper develops an analytical transfer matrix method to study stationary electron states in one-dimensional periodic structures under a uniform electric field, revealing continuous spectra and current-carrying wave functions.

Contribution

It introduces a symmetry-based analytical approach for electron states in periodic structures with an external electric field, highlighting new spectral and wave function properties.

Findings

Electron spectrum is continuous for infinite structures.

Stationary states are current-carrying.

Wave functions do not satisfy the symmetry condition.

Abstract

On the basis of the transfer matrix technique an analytical method to investigate the stationary states, for an electron in one-dimensional periodic structures in an external electrical field, displaying the symmetry of the problem is developed. These solutions are shown to be current-carrying. It is also shown that the electron spectrum for infinite structures is continuous, and the corresponding wave functions do not satisfy the symmetry condition of the problem.