01400nas a2200169   4500008004100000022001400041245007000055210006900125260000800194300001600202490000800218520089300226100002301119700002101142700002101163856004601184       2016                        eng d  a1432-091600aZ2 Invariants of Topological Insulators as Geometric Obstructions0 aZ2 Invariants of Topological Insulators as Geometric Obstruction  cMay  a1115–11570 v3433 a<p>We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to $-\mathbb{1}$. 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 $\mathbb{Z}_2$-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 $\mathbb{Z}_2$ invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones.</p>1 aFiorenza, Domenico1 aMonaco, Domenico1 aPanati, Gianluca  uhttps://doi.org/10.1007/s00220-015-2552-0