Hamiltonian decomposition for bulk and surface states

Abstract

We demonstrate that a tight-binding Hamiltonian with nearest- and next-nearest-neighbor hopping integrals can be decomposed into bulk and boundary parts in a general lattice system. The Hamiltonian decomposition reveals that next nearest-neighbor hopping causes sizable changes in the energy spectrum of surface states even if the correction to the energy spectrum of bulk states is negligible. By applying the Hamiltonian decomposition to edge states in graphene systems, we show that the next nearest-neighbor hopping stabilizes the edge states.

5 pages, 4 figures

References in corpus (7)

• Observation of zigzag and armchair edges of graphite using scanning tunneling microscopy and spectroscopy
• Scanning tunneling microscopy and spectroscopy studies of graphite edges
• Stabilization mechanism of edge states in graphene
• Theory of superconductivity of carbon nanotubes and graphene
• Local density of states at zigzag edge of carbon nanotubes and graphene
• Controlling edge states of zigzag carbon nanotubes by the Aharonov-Bohm flux
• Magnetism as a mass term of the edge states in graphene

Cited by in corpus (9)

• Electronic properties of mesoscopic graphene structures: charge confinement and control of spin and charge transport
• Robustness of edge states in graphene quantum dots
• Edge effects in graphene nanostructures: I. From multiple reflection expansion to density of states
• Dirac boundary condition at the reconstructed zigzag edge of graphene
• Electron Wave Function in Armchair Graphene Nanoribbons
• Edge States of Monolayer and Bilayer Graphene Nanoribbons
• Chiral Gauge Theory for Graphene Edge
• Tuning edge state localization in graphene nanoribbons by in-plane bending
• Graphene zigzag ribbons, square lattice models and quantum spin chains