Elements of Topological Band Theory in Condensed Matter Physics

Milan Damnjanović, Ivanka Milošević

Band theory of crystals, essentially Bloch theory of periodic systems combined with single-particle approximation, is a scene of detailed and essential analysis of the band topology by means of application of full crystal group symmetry and combinatorial graph theoretical methods, eventually yielding topological classification of gapped band structures. Here we give an introduction to the field by summarizing the symmetry based techniques used in the band topology considerations.