Z/2 invariants of topological insulators as geometric obstructions

par Domenico Fiorenza (Università di Roma "La Sapienza")

vendredi 13 mai 2016, 14:00 → 15:00 Europe/Paris

salle Fokko du Cloux (Institut Camille Jordan)

We consider a gapped periodic quantum system with time-reversal symmetry of odd type, i.e. such that the time-reversal operator squares to -1. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2d, the obstruction to the existence of such a frame is shown to be encoded in a Z/2-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3d, instead, four Z/2 invariants emerge from the construction, again related to the Fu-Kane-Mele indices. Joint work with Domenico Monaco and Gianluca Panati.