Topological invariants of edge states for periodic two-dimensional models

Avila JC, Schulz-Baldes H, Villegas-Blas C (2013)


Publication Type: Journal article, Original article

Publication year: 2013

Journal

Publisher: Springer Verlag (Germany)

Book Volume: 16

Pages Range: 136-170

URI: http://de.arxiv.org/abs/1202.0537

DOI: 10.1007/s11040-012-9123-9

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.

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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.

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