States near Dirac points of rectangular graphene dot in a magnetic field

Abstract

In neutral graphene dots the Fermi level coincides with the Dirac points. We have investigated in the presence of a magnetic field several unusual properties of single electron states near the Fermi level of such a rectangular-shaped graphene dot with two zigzag and two armchair edges. We find that a quasi-degenerate level forms near zero energy and the number of states in this level can be tuned by the magnetic field. The wavefunctions of states in this level are all peaked on the zigzag edges with or without some weight inside the dot. Some of these states are magnetic field-independent surface states while the others are field-dependent. We have found a scaling result from which the number of magnetic field-dependent states of large dots can be inferred from those of smaller dots.

Physical review B in press

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• Soliton fractional charges in graphene nanoribbon and polyacetylene: similarities and differences
• Unique nature of the lowest Landau level in finite graphene samples with zigzag edges: Dirac electrons with mixed bulk-edge character
• Self-Adjointness of Dirac Operators with Infinite Mass Boundary Conditions in Sectors
• Electronic properties of a graphene antidot in magnetic fields
• Snake states in graphene quantum dots in the presence of a p-n junction
• Topologically ordered zigzag nanoribbon: $e/2$ fractional edge charge, spin-charge separation, and ground state degeneracy
• Spintronic properties of one-dimensional electron gas in graphene armchair ribbons
• Topological end states and Zak phase of rectangular armchair ribbon
• Gap states and edge properties of rectangular graphene quantum dot in staggered potential