Graduate Lunch Talk: Judith Hoeller, Yale Physics, “Topological invariance in crystalline topological insulators”

Why are condensed matter scientists so excited about topology? The integer quantum hall conductivity, which advanced the theory of topological phases of matter, is a topological invariant, meaning that it is a ‘robust’ to local changes of the system like small deformation of the shape of a sample and therefore can be measured to very high accuracy. One of the most intuitive explanations for topological invariance is given by Laughlin’s flux tube argument to describe twisted boundary conditions in translation invariant systems. I give an intuitive picture how to go from translation invariance to twisted boundary conditions to fiber bundles to holonomies and to the classification of topological phases, called Kitaev’s periodic table. The classification scheme disregards spatial symmetries and I will introduce a way how topological invariance can arise because of spatial symmetries in insulators.