Topological invariants of edge states for periodic two-dimensional models

Journal article
(Original article)


Publication Details

Author(s): Avila JC, Schulz-Baldes H, Villegas-Blas C
Journal: Mathematical Physics Analysis and Geometry
Publisher: Springer Verlag (Germany)
Publication year: 2013
Volume: 16
Pages range: 136-170
ISSN: 1385-0172


Abstract


Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define topological invariants by considering the associated Bott-Maslov indices which can be easily calculated numerically. For time-reversal symmetric systems in the symplectic universality class this leads to a ℤ2-invariant for the edge states. It is shown that the edge state invariants are related to Chern numbers of the bulk systems and also to (spin) edge currents, in the spirit of the theory of topological insulators. © 2012 Springer Science+Business Media Dordrecht.



FAU Authors / FAU Editors

Schulz-Baldes, Hermann Prof. Dr.
Professur für Mathematik


External institutions
Instituto Nacional de Tecnología Agropecuaria (INTA)
National Autonomous University of Mexico / Universidad Nacional Autónoma de México (UNAM)


How to cite

APA:
Avila, J.C., Schulz-Baldes, H., & Villegas-Blas, C. (2013). Topological invariants of edge states for periodic two-dimensional models. Mathematical Physics Analysis and Geometry, 16, 136-170. https://dx.doi.org/10.1007/s11040-012-9123-9

MLA:
Avila, Julio Cesar, Hermann Schulz-Baldes, and Carlos Villegas-Blas. "Topological invariants of edge states for periodic two-dimensional models." Mathematical Physics Analysis and Geometry 16 (2013): 136-170.

BibTeX: 

Last updated on 2018-09-08 at 16:38