Energy spectrum and density of states for a graphene quantum dot in a magnetic field

• Published in: Journal of physics. Condensed matter Vol. 22; no. 2; pp. 025502 - 025502 (5)
• Main Authors: Morgenstern Horing, Norman J, Liu, S Y
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 20.01.2010; Institute of Physics
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Electron states and collective excitations in thin films, multilayers, quantum wells, mesoscopic and nanoscale systems; Electronic structure and electrical properties of surfaces, interfaces, thin films and low-dimensional structures; Exact sciences and technology; Physics; Quantum dots; Quantum magnetic field; Graphene; Quantum dots; Hamiltonians; Potential well; Magnetic field effects; Boundary conditions; Eigenfunctions; Subband; Landau levels; Electronic density of states; Green's function methods
• ISSN: 0953-8984; 1361-648X; 1361-648X
• DOI: 10.1088/0953-8984/22/2/025502

In this paper, we determine the spectrum and density of states of a graphene quantum dot in a normal quantizing magnetic field. To accomplish this, we employ the retarded Green function for a magnetized, infinite-sheet graphene layer to describe the dynamics of a tightly confined graphene quantum dot subject to Landau quantization. Considering a δ((2))(r) potential well that supports just one subband state in the well in the absence of a magnetic field, the effect of Landau quantization is to 'splinter' this single energy level into a proliferation of many Landau-quantized states within the well. Treating the graphene sheet and dot as a closed system subject to a fully Hermitian Hamiltonian (including boundary conditions), there is no indication of decay of the Landau-quantized graphene dot states into the quantized states of the host graphene sheet for 'tight' confinement by the δ((2))(r) potential well, notwithstanding extension of the dot Green function (and eigenfunctions) outside the δ((2))(r) potential well.