Eur. Phys. J. B (2012) 85: 94
https://doi.org/10.1140/epjb/e2012-21057-8

Regular Article

Local topological phase transitions in periodic condensed matter systems

Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany

^a e-mail: jbudich@physik.uni-wuerzburg.de

Received: 20 December 2011
Published online: 14 March 2012

Abstract

Topological properties of a periodic condensed matter system are global features of its Brillouin zone (BZ). In contrast, the validity of effective low energy theories is usually limited to the vicinity of a high symmetry point in the BZ. We derive a general criterion under which the control parameter of a topological phase transition localizes the topological defect in an arbitrarily small neighbourhood of a single point in k-space upon approaching its critical value. Such a local phase transition is associated with a Dirac-like gap closing point, whereas a flat band transition is not localized in k-space. This mechanism and its limitations are illustrated with the help of experimentally relevant examples such as HgTe/CdTe quantum wells and bilayer graphene nanostructures.