Interaction between spin and Abrikosov vortices in doped topological insulators

TL;DR

This paper investigates the interaction between Abrikosov and spin vortices in doped topological superconductors, revealing their attractive interaction and common core, with implications for experimental detection and Majorana fermion localization.

Contribution

It derives the free energy for vortex interactions in topological superconductors and shows the attraction and combined core of Abrikosov and spin vortices using Ginzburg-Landau theory.

Findings

Abrikosov and spin vortices attract and form a common core.

No zero-energy Majorana states are localized at the combined vortex core.

Critical strain for spin vortex formation is calculated.

Abstract

In the topological superconductor with the nematic superconductivity in $E_u$ representation, it is possible to have different types of vortices. One is associated with the vorticity in the particle-hole space and corresponds to the Abrikosov vortex. Another type corresponds to the vorticity in the spin space and is called spin vortex. We study the interaction of the Abrikosov vortex with the spin vortices. We derive the free energy of the sample with the Abrikosov and the strain-induced spin vortices using the Ginzburg-Landau approach for the two-component superconducting order parameter. We calculate the critical strain at which the spin vortex is formed. We show that the spin vortex and the Abrikosov vortex attract to each other and, as a result, they have a common core. We show that there are no zero-energy states (Majorana fermions) localized near the common vortex core of the Abrikosov vortex and the spin vortex of any type. Possible experimental realization is discussed.