Robust zero-energy bound states around a pair-density-wave vortex core in locally noncentrosymmetric superconductors

TL;DR

This study numerically explores vortex core electronic structures in bilayer superconductors with PDW and BCS phases, revealing magnetic field-induced changes in vortex states and potential experimental signatures.

Contribution

It uncovers how vortex bound states and core structures evolve across BCS-PDW transition, highlighting the role of spin-orbit coupling in high magnetic fields.

Findings

Vortex core shrinks and zero-energy states emerge at BCS-PDW transition.

PDW state and vortex states are protected by spin-orbit coupling.

Distinct vortex core behaviors can be detected via scanning tunneling microscopy.

Abstract

We numerically investigate the electronic structures around a vortex core in a bilayer superconducting system, with s-wave pairing, Rashba spin-orbit coupling and Zeeman magnetic field, with use of the quasiclassical Green's function method. The Bardeen-Cooper-Schrieffer (BCS) phase and the so-called pair-density wave (PDW) phase appear in the temperature-magnetic-field phase diagram in a bulk uniform system [Phys. Rev. B 86, 134514 (2012)]. In the low magnetic field perpendicular to the layers, the zero-energy vortex bound states in the BCS phase are split by the Zeeman magnetic field. On the other hand, the PDW state appears in the high magnetic field, and sign of the order parameter is opposite between the layers. We find that the vortex core suddenly shrinks and the zero-energy bound states appear by increasing the magnetic field through the BCS-PDW transition. We discuss the origin of the change in vortex core structure between the BCS and PDW states by clarifying the relation between the vortex bound states and the bulk energy spectra. In the high magnetic field region, the PDW state and vortex bound states are protected by the spin-orbit coupling. These characteristic behaviors in the PDW state can be observed by scanning tunneling microscopy/spectroscopy.