ICTS

Our understanding of topological systems is based on an underlying lattice where the local electronic degrees of freedom at different sites interact with each other in ways that produce nontrivial band topology. Indeed, the search for material systems to realize such phases have been strongly influenced by this. In this talk, I will present a recent work where we show that topological insulating phases do not need a lattice.  We explicitly construct topological Hamiltonians on a set of randomly distributed sites and demonstrate their topological character by studying quantized conductances and Bott indices. We show this physics in all topologically non-trivial symmetry classes in two dimensions and also for a three dimensional topological insulator. Time permitting, I will also narrate another work where an interacting quantum impurity was studied in a spin-orbit coupled system. Interestingly, these quantum impurities can host fractional spins and realize a novel kind of Kondo effect.