Majorana modes and transport across junctions of superconductors and normal metals

Manisha Thakurathi, Oindrila Deb, Diptiman Sen

Published 2014-11-29Version 1

We study Majorana modes and transport in some one-dimensional systems with junctions of $p$-wave superconductors and normal metal leads. For a system with a superconductor lying between two normal metal leads, it is known that there is a Majorana mode at the junction between the superconductor and each normal metal. If a strong impurity is present or the $p$-wave pairing amplitude changes sign at some point in the superconductor, two additional Majorana modes appear near that point. We study the effects of all these modes on the sub-gap charge conductances between the leads and the superconductor. The main effect is to shift the conductance peaks away from zero bias due to hybridization between the Majoranas; the shift oscillates and also decays exponentially as the length of the superconductor is increased. Using bosonization and the renormalization group method, we study the effect of interactions between the electrons on the Majorana modes and on the conductances. We discuss experimental realizations of these systems.