Mobility edges and multifractal properties in a one-dimensional system with three incommensurate frequencies

Phase diagram of the incommensurate off-diagonal Aubry-André model with p-wave pairing

Using exact numerical methods, we study the interplay between p-wave superconductivity and off-diagonal modulation in the incommensurate off-diagonal Aubry-André model with p-wave pairing. When chemical potential is zero, the modulation not only leads to an Anderson-like localization with all bulk states changing into critical ones, but also induces a topological phase transition accompanying the disappearing of exponentially localized zero-energy edge Majorana fermions. These two transitions happen at different places and true Anderson localization is absent. With a finite chemical potential, the quasi-periodicity of the modulation causes band splitting and drives the system into a band insulator phase. It has a fixed incommensurate particle density which is determined by the modulation frequency. Phase diagrams are identified, and can be tested with existing proposals for experimental realizations of the effective off-diagonal disorder and the p-wave pairing.

Metal-insulator transition in an aperiodic ladder network: an exact result

We prove that a tight-binding ladder network composed of atomic sites with on-site potentials distributed according to the quasiperiodic Aubry model can exhibit a metal-insulator transition at multiple values of the Fermi energy. For specific values of the first and second neighbor electron hopping, the result is obtained exactly. With a more general model, we numerically calculate the two-terminal conductance. The numerical results corroborate the analytical findings.