Majorana fermions in topological superconductors

Abstract

This thesis is divided into two parts. In the rst part we show that a quasi-one-dimensional d_x2_-y2-wave superconductor with Rashba spin-orbit coupling is a DIII class, time-reversal invariant, topological superconductor (TS) which supports a Majorana Kramers Doublet (MKD) at each end of the TS. A MKD is a pair of Majorana end states (MESs) protected by time-reversal symmetry (TRS). An external magnetic field breaks TRS and drives the system from DIII to D class in which case a single MES appears at each end of the TS. We show that a MKD induces resonant Andreev reflection with zero bias conductance peak of 4e²/h. Experimental realizations of the proposed model are discussed. In the second part we show that an in-plane magnetic field can drive a fully gapped p ± ip topological superconductor into a gapless phase which supports Majorana flat bands (MFBs). Unlike previous examples, the MFBs in the gapless regime are protected from disorder by a chiral symmetry. We show that the Majorana fermions associated with the MFBs induce nearly quantized zero bias conductance peak in tunnelling experiments. The consequences of broken chiral symmetry are discussed.

Date of Award	2013
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology