Effective Hamiltonian for protected edge states in graphene

Abstract

Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta $\Lambda$ in the Brillouin zone (BZ) with protected degeneracies at $\Lambda$. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant $M$ point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for both zigzag and armchair ribbons though the concept of a BZ is not part of such an effective model. We show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select $\Lambda$ for the edge states without affecting the bulk spectrum.

6 pages, 6 figures

References in corpus (6)

• The electronic properties of graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Electronic States of Graphene Nanoribbons
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• Finite size effects of helical edge states in HgTe/CdTe quantum wells

Cited by in corpus (7)

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• Topological edge states on time-periodically strained armchair graphene nanoribbons
• Universality and stability of the edge states of chiral-symmetric topological semimetals and surface states of the Luttinger semimetal
• Topological phase-diagram of time-periodically rippled zigzag graphene nanoribbons
• Dirac electrons in quantum rings
• Boundary obstructed topological superconductor in buckled honeycomb lattice under perpendicular electric field