Hosted by: Robert Konik

I will discuss two very recent results relating to the properties of electrons in two spatial dimensions (2D), subject to the effects of quenched disorder (impurities) and quantum interference [Anderson (de)localization]. In both cases, the key physics is tied to classical geometric critical phenomena in 2D. I will first present numerical evidence that strongly suggests the equivalence of disordered surface states of topological superconductors and geometric percolation. Percolation is known to play a role in quantum Hall systems with magnetic fields. Our unexpected result implies that percolation applies to topological superconductor surface states in the absence of time-reversal symmetry breaking. Moreover, the usual "even-odd" effect that occurs in such a system (as identified by Pruisken in the integer quantum Hall effect and by Haldane for spin chains) is found to be absent. Second, I will discuss a "toy model" for the ergodic to many-body localized phase transition in 2D, and relate it to an effective self-interacting walk. I will present analytical results of a controlled expansion which suggest that the transition can be viewed as a "dephasing catastrophe."