Electronic states in nanowires with hexagonal cross-section

TL;DR

This paper calculates the electronic states in nanowires with hexagonal cross-sections using a numerical diagonalization approach, offering advantages over traditional mesh methods and allowing for extensions to complex Hamiltonians and external fields.

Contribution

It introduces a numerical scheme for calculating electron spectra in hexagonal nanowires that avoids non-physical solutions and can be extended to multi-band Hamiltonians and external field effects.

Findings

Calculated wave-functions of low-lying states visualized

Method avoids non-physical solutions common in mesh schemes

Approach adaptable to multi-band Hamiltonians and external fields

Abstract

The electron spectrum in a uniform nanowire with a hexagonal cross-section is calculated by means of a numerical diagonalization of the effective-mass Hamiltonian. Two basis sets are utilized. The wave-functions of low-lying states are calculated and visualized. The approach has an advantage over mesh methods based on finite-differences (or finite-elements) schemes: non-physical solutions do not arise. Our scheme can be easily generalized to the case of multi-band (Luttinger or Kane) ${\bf k}\cdot{\bf p}$ Hamiltonians. The external fields (electrical, magnetic or strain) can be consistently introduced into the problem as well.