TY - JOUR T1 - Topological Invariants of Eigenvalue Intersections and Decrease of Wannier Functions in Graphene JF - J. Stat. Phys 155 (2014) 1027-1071 Y1 - 2014 A1 - Domenico Monaco A1 - Gianluca Panati KW - Wannier functions, Bloch bundles, conical intersections, eigenspace vorticity, pseudospin winding number, graphene AB -

We investigate the asymptotic decrease of the Wannier functions for the valence and conduction band of graphene, both in the monolayer and the multilayer case. Since the decrease of the Wannier functions is characterised by the structure of the Bloch eigenspaces around the Dirac points, we introduce a geometric invariant of the family of eigenspaces, baptised eigenspace vorticity. We compare it with the pseudospin winding number. For every value n∈Z of the eigenspace vorticity, we exhibit a canonical model for the local topology of the eigenspaces. With the help of these canonical models, we show that the single band Wannier function w satisfies |w(x)|≤const |x|^{−2} as |x|→∞, both in monolayer and bilayer graphene.

PB - Journal of Statistical Physics U1 - 7368 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER -