Andreev reflection and bound states in topological insulator based planar and step Josephson junctions

A superconductor-topological insulator-superconductor (S/TI/S) junction having normal region at angle θ is studied theoretically to investigate the junction angle dependency of the Andreev reflection and the formation of the Andreev bound states in the step and planar S/TI/S structures. It is found that the Andreev reflection becomes θ dependent only in the presence of the potential barrier at the TI/S interface. In particular, the step and planar TI/S junction have totally different conductive behavior with bias voltage and potential barrier in the regime of retro and specular Andreev reflection. Interestingly, we find that the elliptical cross section of Dirac cone, an important feature of topological insulator with step surface defect, affects the Fabry-Perot resonance of the Andreev reflection induced Andreev bound states (which become Majorana zero energy states at low chemical potential) in the step S/TI/S structure. Unlike the usual planar S/TI/S structures, we find these ellipticity affected Andreev bound states lead to non-monotonic Josephson super-current in the step S/TI/S structure whose non-monotonicity can be controlled with the use of the potential barrier, which may find applications in nanoelectronics.