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 wave function with interdot 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 $d\ensuremath{\lesssim}100\text{ }\text{\AA{}}$.
Highlights
A two-dimensional2Dhoneycomb lattice of carbon atoms that form the basic planar structure in graphitegraphenehas recently been produced.[1,2] Unusual manybody effects in graphene have been attributed to low-lying excitations in the vicinity of the Fermi level.[3,4,5,6] The influence of an external magnetic field on the many-electron properties of graphene results in an unusual quantum Hall effect
II, we introduce the quasiparticle electron-hole representation for the eigenvalue problem for an electron in a single graphene quantum dot in magnetic field
The eigenvalue problem of an electron in a linear confining potential can be mapped onto one for a noninteracting electron-hole pair in an effective magnetic fieldBeff under conditions we introduce below
Summary
A two-dimensional2Dhoneycomb lattice of carbon atoms that form the basic planar structure in graphitegraphenehas recently been produced.[1,2] Unusual manybody effects in graphene have been attributed to low-lying excitations in the vicinity of the Fermi level.[3,4,5,6] The influence of an external magnetic field on the many-electron properties of graphene results in an unusual quantum Hall effect. Several works were reported for quantum dots in graphene.[18,19,20] The transport characteristics of quantum dot devices etched entirely in graphene have been studied experimentally.[21] According to Ref. 21, these quantum dots at large sizes behave as conventional singleelectron transistors This is just one of the areas of research in the fast-growing field of the electronic transport, thermal, and optical properties of graphene which may have important device applications because of its high mobility.[22] The single-particle states and collective modes in semiconductor quantum dots have long been a subject of interest to both theoreticians and experimentalists.[23,24,25] The spectrum of collective plasma modes in a 2D array of quantum dots in semiconductors has been calculated.[26].
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