Marginality of bulk-edge correspondence for single-valley Hamiltonians
arXiv:1011.0654 · doi:10.1103/PhysRevB.82.245404
Abstract
We study the correspondence between the non-trivial topological properties associated with the individual valleys of gapped bilayer graphene (BLG), as a prototypical multi-valley system, and the gapless modes at its edges and other interfaces. We find that the exact connection between the valley-specific Hall conductivity and the number of gapless edge modes does not hold in general, but is dependent on the boundary conditions, even in the absence of intervalley coupling. This non-universality is attributed to the absence of a well-defined topological invariant within a given valley of BLG; yet, a more general topological invariant may be defined in certain cases, which explains the distinction between the BLG-vacuum and BLG-BLG interfaces.
7 pages, 4 figures
References in corpus (9)
- Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
- Biased bilayer graphene: semiconductor with a gap tunable by electric field effect
- Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
- Gate-induced insulating state in bilayer graphene devices
- Electronic States of Graphene Nanoribbons
- Topological confinement in bilayer graphene
- Edge states in Graphene: from gapped flat band to gapless chiral modes
- A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
- Localized states at zigzag edges of bilayer graphene
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- Distinct quasiparticle interference patterns for surface impurity scattering on various Weyl semimetals
- A Quantized Interband Topological Index in Two-Dimensional Systems
- Edge dependece of nonlocal transport in gapped bilayer graphene
- Robustness of topologically protected transport in graphene-boron nitride lateral heterostructures
- Electrostatic tuning of bilayer graphene edge modes