Excitation spectra and wave functions of quasiparticle bound states in bilayer Rashba superconductors

•We focus on the pair-density wave state in bilayer Rashba superconductors.•The zero energy Bogoliubov wave functions are localized at the edge and vortex core.•We investigate the excitation spectra of edge and vortex bound states.

We study the excitation spectra and the wave functions of quasiparticle bound states at a vortex and an edge in bilayer Rashba superconductors under a magnetic field. In particular, we focus on the quasiparticle states at the zero energy in the pair-density wave state in a topologically non-trivial phase. We numerically demonstrate that the quasiparticle wave functions with zero energy are localized at both the edge and the vortex core if the magnetic field exceeds the critical value.