Kibble-Zurek Behavior in Disordered Chern Insulators.

Even though no local order parameter in the sense of the Landau theory exists for topological quantum phase transitions in Chern insulators, the highly nonlocal Berry curvature exhibits critical behavior near a quantum critical point. We investigate the critical properties of its real space analog, the local Chern marker, in weakly disordered Chern insulators. Because of disorder, inhomogeneities appear in the spatial distribution of the local Chern marker.

On the resilience of magic number theory for conductance ratios of aromatic molecules.

If simple guidelines could be established for understanding how quantum interference (QI) can be exploited to control the flow of electricity through single molecules, then new functional molecules, which exploit room-temperature QI could be rapidly identified and subsequently screened. Recently it was demonstrated that conductance ratios of molecules with aromatic cores, with different connectivities to electrodes, can be predicted using a simple and easy-to-use "magic number theory." In contrast with counting rules and "curly-arrow" descriptions of destructive QI, magic number theory captures the many forms of constructive QI, which can occur in molecular cores.

Linear Conductances of Gated Graphene Structures with Selected Connectivity.

The ratio of conductances through carbon-ring based molecules are calculated for various positions of source-drain electrode leads on the molecule. These ratios are usually integers the so-called magic numbers. We find that deviations of the magic number ratios are either zero or quadratic in ratios of tight-binding model parameters.