Active research on superconductivity in locally noncentrosymmetric systems has continued over the last decade. In these systems, exotic superconducting (SC) phases are predicted to stabilize in magnetic fields [1, 2] due to spatially inhomogeneous antisymmetric spin-orbit coupling (ASOC) caused by local spatial asymmetry and paramagnetic pair-breaking effects. The vortex state is of interest because exotic SC phases stabilize in a magnetic field. We are particularly interested in quasiparticle (QP) states. A previous study in the Pauli limit [2], neglecting vortices, reported the formation of the QP spectral gap at the central conduction layer in the pair density wave (PDW) state (π-phase difference between layers without local inversion symmetry). This phenomenon occurs due to the QP transitions from the outer conduction layers and the magnetic field induced shift of the density of states, despite the disappearance of the SC order parameter in the central layer. The QP states in the vortex core in the central layer could also be affected by perturbations due to QP transitions from the outer layers. We reported numerical results based on the quasiclassical method for the BCS state (0-phase difference), which is the low-field phase of a trilayer Rashba system [4]. The structure of the local density of states around the vortex core differs significantly from layer to layer, reflecting the inhomogeneous ASOC. In the PDW state, however, we failed to obtain the QP spectral gap at the central layer, in contrast to the result in Ref. [2], and instead used the Bogoliubov-de Gennes equation to calculate the QP states in the trilayer Rashba system to report the spectral gap in the excitation energy spectra in the PDW state [4]. In this study, we report the local QP density of states layer by layer in depth.

[1]  D. Maruyama et al.,  J. Phys. Soc. Jpn. 81, 034702 (2012).
[2]  T. Yoshida et al., Phys. Rev. B 86, 134514 (2012).
[3]  Y. Higashi et al., Phys. Rev. B 93, 104529 (2016).
[4]  Y. Higashi, Meeting Abstracts of the Physical Society of Japan 76.2 (2021).