Abstract | Recently, level crossings in the energy bands of crystals have been identified as a key signature for topological phase transitions. I will discuss the criteria that need to be met for level crossings or anticrosssings to occur in quantum systems. In general, three independent parameters must be tuned appropriately to bring two quantum levels into degeneracy. Small perturbations thus easily destroy a level degeneracy. For Bloch electrons in a crystal the
situation is qualitatively different due to crystal symmetries giving rise to rich phase diagrams for the occurrence of level crossings and anticrossings. In particular, we show that topologically distinct insulating phases are, in general, separated by a novel metallic phase, where a level degeneracy is induced
between the conduction and valence band states that cannot be destroyed by a small perturbation of the system. We consider HgTe/CdTe quantum wells as a specific example. Recently, these were the first systems for which the topological phase transition to a quantum spin Hall state was observed experimentally. |
