Absence of Edge States in The Valley Chern Insulator in Moiré Graphene

Abstract

We study the edge spectrum of twisted sheets of single layer and bilayer graphene in cases where the continuum model predicts a valley Chern insulator -- an insulating state in which the occupied moiré mini-bands from each valley have a net Chern number, but both valleys together have no net Chern number, as required by time reversal symmetry. In a simple picture, such a state might be expected to have chiral valley polarized counter-propagating edge states. We present results from exact diagonalization of the tight-binding model of commensurate structures in the ribbon geometry. We find that for both the single-layer and bilayer moiré ribbons robust edge modes are generically absent. We attribute this lack of edge modes to the fact that the edge induces valley mixing. Further, even in the bulk, a sharp distinction between the valley Chern insulator and a trivial insulator requires an exact $C_3$ symmetry.

References in corpus (17)

• The electronic properties of graphene
• Flat Bands in Slightly Twisted Bilayer Graphene
• Lattice relaxation and energy band modulation in twisted bilayer graphenes
• Origin of band gaps in graphene on hexagonal boron nitride
• Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
• Tunable correlation-driven symmetry breaking in twisted double bilayer graphene
• Flatbands in twisted double bilayer graphene
• Band structure and topological property of twisted double bilayer graphenes
• The crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the "magic angle" $\theta \sim 1.08^{\circ }$
• Continuum models for twisted bilayer graphene: the effects of lattice deformation and hopping parameter
• Collective Excitations of Quantum Anomalous Hall Ferromagnets in Twisted Bilayer Graphene
• Continuum model for relaxed twisted bilayer graphenes and moiré electron-phonon interaction
• Moiré band model and band gaps of graphene on hexagonal boron nitride
• Bulk and Edge Properties of Twisted Double-Bilayer Graphene
• Current-induced reversal of anomalous Hall conductance in twisted bilayer graphene
• Moiré edge states in twisted bilayer graphene and their topological relation to quantum pumping
• Phase diagram and orbital Chern insulator in twisted double bilayer graphene

Cited by in corpus (3)

• Tunable moiré materials for probing Berry physics and topology
• Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
• Magic-angle twisted bilayer graphene under orthogonal and in-plane magnetic fields