Density of States Analysis of Electrostatic Confinement in Gapped Graphene

TL;DR

This paper analyzes how electrostatic confinement in gapped graphene quantum dots influences the density of states, revealing oscillatory behavior and resonances controlled by the energy gap, with implications for quantum device design.

Contribution

It provides an explicit analytical solution for the energy spectrum and density of states in gapped graphene quantum dots under electrostatic confinement and magnetic flux.

Findings

Density of states exhibits oscillations with resonant peaks.

Energy gap controls resonance amplitude, width, and position.

Analytical methods using Hankel functions are employed.

Abstract

We investigate the electrostatic confinement of charge carriers in a gapped graphene quantum dot in the presence of a magnetic flux. The circular quantum dot is defined by an electrostatic gate potential delimited in an infinite graphene sheet which is then connected to a two terminal setup. Considering different regions composing our system, we explicitly determine the solutions of the energy spectrum in terms of Hankel functions. Using the scattering matrix together with the asymptotic behavior of the Hankel functions for large arguments, we calculate the density of states and show that it has an oscillatory behavior with the appearance of resonant peaks. It is found that the energy gap can controls the amplitude and width of these resonances and affect their location in the density of states profile.