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 -