Topology of bands

Since the 2000s multiple interrelations of crystal symmetry and band topology have been realized. Recently, various groups made breakthroughs and explained and classified the basic types of the 3D crystal bands in terms of the compatibility relations of the neighboring strata, with many interesting results. As for low-dimensional, line and layer groups there are no systematic results. While it is commonly addopted that for the layer groups the classification of the elementary band representations (EBRs) including the topological differences can be obtained from those for 3D crystals, for line groups it is not possible.

NanoLab is going to perform the task for all line and layer groups in the forthcoming period. The interest for this activity is initiated by I. Milosevic and S. Dmitrovic. During 2019 spring term S. Dmitrovic has delivered a series of seminars, being one of the most important events for the NanoLab, as it strongly impacted afterward research. Soon after, POLSym code new extensions (M. Damnjanovic) enabled combinatorial calculation of line and layer groups' EBRs; the algorithm for Wilson operator calculation, elaborated and implemented in POLSym by Z. Popovic is crucial breakthrough providing physically sound insight into the band topology. In this way the goal of the whole team to expand the expertise to topological insulators has been achieved.

EBRs of the line groups Typical EBRs of the layer group 58