Static and Dynamic Disorder in Topological Systems: Localized, Critical and Extended States.

Topological properties may be induced or changed by the action of disorder. We investigate two examples of this scenario: in the first, by showing that either trivial or topological two-dimensional superconductors, as a result of a static random distribution of magnetic impurities, display topological phases. The second one involves using timedependent perturbations, which also have the general effect of inducing topology and, under appropriate conditions, the appearance of topological properties is shown. In this case, we consider the effect on the topology of onedimensional systems, of time periodic or aperiodic perturbations consisting of kicks of spatially non-homogeneous potentials. One finds different regimes characterized by localized, critical, or extended non-equilibrium states, as a result of the time dependent perturbation. We further carry out the existence and characterization of the topological edge states that occur both in the case of a static and dynamic perturbations. In the case of the static disorder, the topological phases are characterized calculating the real space Chern number and various regimes for the low energy density of states are identified and explained in the context of general properties of the symmetry classes D and C. In the case of a time periodic perturbation (the Floquet regime) we contrast the dynamical localization, and its properties, when using kicks either in the quasiperiodic spatially inhomogeneous potentials of the Aubry-André type or in the case of kicks on the pairing amplitude in the presence of static Aubry-André quasi-disorder. In both, we make use of lattice sizes drawn from the Fibonacci sequence. We also show that aperiodicity in the sequence of time perturbations leads in general to delocalization, a regime characterized by a fully random matrix Hamiltonian with the appropriate symmetry. [ABSTRACT FROM AUTHOR]