QDev Seminar: Cristina Bena

Majorana and Andreev bound states in topological wires in the proximity of superconductors

We study one-dimensional topological SN and SNS long junctions obtained by placing a topological insulating nanowire in the proximity of either one or two SC finite-size leads. Using the Majorana Polarization order parameter we find that for a finite-size SN junction the ABS spectrum exhibits a zero-energy extended state which carries a full Majorana fermion, while the ABS of long SNS junctions with a phase difference of pi transform into two zero-energy states carrying two Majorana fermions with the same MP. We also study the effects of finite SC penetration depths in such junctions, as well as the effects of uniform phase gradients. Last but not least we analyze a more realistic model for the coupling between a superconducting substrate and a topological wire, the resulting proximity effect, and the role played by the Andreev bound states in the topological wire in such a setup.