2011/02/28 by Jan Carl Budich, J. C. Budich, Björn Trauzettel +1 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Brillouin zone #Critical point (mathematics) #Graphene research and applications #Phase (matter) #Phase transition #Quantum many-body systems #Quantum phase transition #Quantum phases #Symmetry (geometry) #Topological Materials and Phenomena #Topological order #Topology (electrical circuits) #cond-mat.mes-hall #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1140/epjb/e2012-21057-8
published as Eur. Phys. J. B 85 (3) 94 (2012)
arxiv created 2012/01/16 · openalex publication_date 2012/03/01 · arxiv updated 2012/03/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.