Marginal topological properties of graphene: a comparison with topological insulators

Abstract

The electronic structures of graphene systems and topological insulators have closely-related features, such as quantized Berry phase and zero-energy edge states. The reason for these analogies is that in both systems there are two relevant orbital bands, which generate the pseudo-spin degree of freedom, and, less obviously, there is a correspondence between the valley degree of freedom in graphene and electron spin in topological insulators. Despite the similarities, there are also several important distinctions, both for the bulk topological properties and for their implications for the edge states -- primarily due to the fundamental difference between valley and spin. In view of their peculiar band structure features, gapped graphene systems should be properly characterized as marginal topological insulators, distinct from either the trivial insulators or the true topological insulators.

This manuscript will be published on the Proceedings of the 2010 Nobel Symposium on Graphene and Quantum Matter

References in corpus (19)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State 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
• Nonlocal edge state transport in the quantum spin Hall state
• Quantum-limited shot noise in graphene
• Topological Defects and Gapless Modes in Insulators and Superconductors
• The Quantum Spin Hall Effect: Theory and Experiment
• Topological confinement in bilayer graphene
• Spontaneous Quantum Hall States in Chirally-stacked Few-Layer Graphene Systems
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Edge states in Graphene: from gapped flat band to gapless chiral modes
• Coulomb-driven broken-symmetry states in doubly gated suspended bilayer graphene
• A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
• Valley-Hall Kink and Edge States in Multilayer Graphene
• Localized states at zigzag edges of bilayer graphene
• Marginality of bulk-edge correspondence for single-valley Hamiltonians

Cited by in corpus (11)

• Valley Topological Phases in Bilayer Sonic Crystals
• Theory of strain in single-layer transition metal dichalcogenides
• Magnon valley Hall effect in CrI3-based vdW heterostructures
• Kagome Lattice from Exciton-Polariton Perspective
• Crafting zero-bias one-way transport of charge and spin
• Band gap and broken chirality in single-layer and bilayer graphene
• Current partition at zero-line intersection of quantum anomalous Hall topologies
• Zero-line modes at stacking faulted domain walls in multilayer graphene
• Proximity induced topological state in graphene
• Evidence of Lifshitz transition in thermoelectric power of ultrahigh mobility bilayer graphene
• Vortex Solutions and a Novel Role for R-parity in an N=2-Supersymmetric Model for Graphene