title: Edge states in graphene: from gapped flat-band to gapless chiral modes.
abstract: We study edge states in graphene systems where a bulk energy gap is opened by inversion symmetry breaking. We find that the edge bands dispersion can be controlled by potentials applied on the boundary with unit cell length scale. Under certain boundary potentials, gapless edge states with valley-dependent velocity are found, exactly analogous to the spin-dependent gapless chiral edge states in quantum spin Hall systems. The connection of the edge states to bulk topological properties is revealed.
authors.affiliation: Department of Physics, The University of Texas, Austin, Texas 78712-0264, USA.
authors.forename: Wang
authors.initials: W
authors.lastname: Yao
authors.forename: Shengyuan A
authors.initials: SA
authors.lastname: Yang
authors.forename: Qian
authors.initials: Q
authors.lastname: Niu