Possibility of adiabatic transport of a Majorana edge state through an extended gapless region

TL;DR

This paper demonstrates that, contrary to previous beliefs, a Majorana edge state can be adiabatically transported across a gapless region in a modified p-wave superconducting chain, given an optimal slow quench and finite system size.

Contribution

It shows that Majorana edge states can be adiabatically transferred through a gapless region by breaking time-reversal symmetry, which was previously thought impossible.

Findings

Adiabatic transport is possible with an optimal quench time.

Transport probability increases with system size and diverges in the thermodynamic limit.

Majorana states couple with low-lying bulk states during transport.

Abstract

In the context of slow quenching dynamics of a $p$-wave superconducting chain, it has been shown that a Majorana edge state can not be adiabatically transported from one topological phase to the other separated by a quantum critical line. On the other hand, the inclusion of a phase factor in the hopping term, that breaks the extended time reversal invariance, results in an extended gapless region between two topological phases. We show that for a finite chain with an open boundary condition there exists a non-zero probability that an edge Majorana can be adiabatically transported from one topological phase to the other across this gapless region following a slow quench of the superconducting term; this happens for an optimum transit time, that is proportional to the system size and diverges for a thermodynamically large chain. We attribute this phenomenon to the mixing of the Majorana only with low-lying inverted bulk states.