Inducing transitions and quantum transport in topological meta-materials

Official URL: http://risc01.sabanciuniv.edu/record=b2058056 (Table of Contents)

In this Thesis, we propose a novel method that changes the topological order in superconductor wires. We first consider the case of disorder in one dimensional topological superconductors and show how disorder can destroy or create topological order leading to reentrant topological phases. We then consider the effects of a superlattice potential, a zero-average piecewise continuous weak electrostatic potential, on p-wave and s-wave topological superconductor wires. We call such stacked wires leading to weak periodic potential modulation, meta-topological superconductor wires. Topological superconducting wires in their nontrivial phases exhibit Majorana modes as their edge states. We show that by stacking topologically trivial pieces of superconductors, it is possible to induce a topological phase which feature Majorana states at the edges of the superlattice: the meta-topological superconductor. The presence of an electrostatic superlattice allows us to control the topological phase space via the geometry of the electrostatic superlattice. We consider strictly one dimensional meta-topological superconductor wires as well as their quasi-one dimensional multichannel counterparts and show that reentrant topological phases in multichannel meta-topological superconductors occur. Finally, we consider the analogous case of a meta-topological insulator, a quantum anomalous Hall insulator featuring a weak superlattice of magnetic modulation, and show that the transmission can be topologically controlled as a function of energy. The topological protection leads to binary transmission (either transmit or reflect) through the meta-topological quantum anomalous Hall insulator, details of which can be controlled by tuning the properties of the weak superlattice.