Quasiparticles for quantum dot array in graphene and the associated Magnetoplasmons

TL;DR

This paper investigates the low-frequency magnetoplasmon excitations in a square array of quantum dots on graphene, revealing conditions under which collective plasma modes emerge based on lattice period and electronic transitions.

Contribution

It introduces a theoretical framework for calculating magnetoplasmon spectra in quantum dot arrays on graphene, incorporating inter-dot coupling and effective magnetic field mappings.

Findings

Plasmons occur when lattice period d is less than approximately 100 Å.

The dispersion relations depend on magnetic field, wave vector, and confinement parameters.

Collective plasma excitations are identified for specific array configurations.

Abstract

We calculate the low-frequency magnetoplasmon excitation spectrum for a square array of quantum dots on a two-dimensional (2D) graphene layer. The confining potential is linear in the distance from the center of the quantum dot. The electron eigenstates in a magnetic field and confining potential are mapped onto a 2D plane of electron-hole pairs in an effective magnetic field without any confinement. The tight-binding model for the array of quantum dots leads to a wavefunction with inter-dot mixing of the quantum numbers associated with an isolated quantum dot. For chosen confinement, magnetic field, wave vector and frequency, we plot the dispersion equation as a function of the period $d$ of the lattice. We obtain those values of $d$ which yield collective plasma excitations. For the allowed transitions between the valence and conduction bands in our calculations, we obtain plasmons when $d \lesssim 100 {\AA}$.