Exact wave functions for an electron on a graphene triangular quantum dot

TL;DR

This paper analytically derives exact wave functions, eigenenergies, and quantization conditions for an electron in a triangular graphene quantum dot with armchair edges, including effects of edge bond distortions.

Contribution

It provides the first analytical solutions for the quantum states of electrons in triangular graphene quantum dots with edge distortions.

Findings

Analytical wave functions and eigenenergies are obtained.

Edge bond distortions cause measurable energy level shifts.

Quantization conditions are explicitly derived.

Abstract

We generalize the known solution of the Schr\"odinger equation, describing a particle confined to a triangular area, for a triangular graphene quantum dot with armchair-type boundaries. The quantization conditions, wave functions, and the eigenenergies are determined analytically. As an application, we calculate the corrections to the quantum dot's energy levels due to distortions of the carbon-carbon bonds at the edges of the quantum dot.