Reentrant topological transitions with Majorana end states in 1D superconductors by lattice modulation

TL;DR

This paper investigates how periodic lattice modulation in 1D superconductors influences Majorana end states, revealing reentrant topological phases and robustness of topological states despite phase jumps.

Contribution

It demonstrates the emergence of multiple topological phases due to lattice modulation and analyzes the stability of Majorana states against phase jumps and hopping modulation.

Findings

Multiple topological phases appear with lattice modulation.

Topological states are robust against phase jumps.

Spatial modulation affects the phase diagram and Majorana states.

Abstract

The possibility to observe and manipulate Majorana fermions as end states of one-dimensional topological superconductors has been actively discussed recently. In a quantum wire with strong spin-orbit coupling placed in proximity to a bulk superconductor, a topological superconductor has been expected to be realized when the band energy is split by the application of a magnetic field. When a periodic lattice modulation is applied multiple topological superconductor phases appear in the phase diagram. Some of them occur for higher filling factors compared to the case without the modulation. We study the effects of phase jumps and argue that the topologically nontrivial state of the whole system is retained even if they are present. We also study the effect of the spatial modulation in the hopping parameter.