Robust zero-energy bound states around a pair-density-wave vortex core in locally noncentrosymmetric superconductors
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 the use of the quasiclassical Green's function method. The BCS phase and the so-called pair-density-wave (PDW) phase appear in the temperature-magnetic-field phase diagram in a bulk uniform system [T. Yoshida et al., Phys. Rev. B 86, 134514 (2012), 10.1103/PhysRevB.86.134514]. 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 the 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 the 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.