Robust level coincidences in the subband structure of quasi-2D systems

Recently, level crossings in the energy bands of crystals have been identified as a key signature for topological phase transitions. Using realistic models we show that the parameter space controlling the occurrence of level coincidences in energy bands has a much richer structure than anticipated previously. In particular, we identify robust level coincidences that cannot be removed by a small perturbation of the Hamiltonian compatible with the crystal symmetry. Different topological phases that are insulating in the bulk are then separated by a gapless (metallic) phase. We consider HgTe/CdTe quantum wells as a specific example.