Density of electron states in a rectangular lattice under uniaxial stress

TL;DR

This paper derives an analytical expression for the electron density of states in a rectangular lattice under uniaxial stress, revealing how lattice deformation affects electronic properties and anisotropy.

Contribution

It provides a new analytical formula for the density of states in a deformed lattice considering anisotropic transfer integrals due to uniaxial stress.

Findings

Analytical expression involves complete elliptic integrals.

Uniaxial stress modifies transfer integrals and symmetry.

Density of states decouples based on lattice deformation.

Abstract

The closed analytical expression for the electron density of states function in a rectangular lattice is derived in an elementary way in terms of complete elliptic integrals of the first kind. The lattice can be treated as a deformed square lattice under uniform uniaxial stress (or strain). In contrast to hydrostatic case the uniaxial pressure, say along axis y, modifies a length of the y-bonds while the x-bonds remain intact. It also alters the corresponding tight-binding transfer integral gamma_2 between two y-nearest-neighbours leaving unchanged the gamma_1 for x-nn interactions. Due to stress-induced lowering symmetry of this simple model one can get an insight into the decoupling of its density of states on dependence of the lattice deformation or transfer integrals anisotropy.