Strong anomalous proximity effect from spin-singlet superconductors

Anomalous proximity effect is a remarkable phenomenon which arises due to the cooperative interplay oftopologically-protected quasiparticles at zero-energy and odd-frequency Cooper pairs. So far, a spin-triplet superconductor, which is difficult to find in nature, has been supposed to be essential for the anomalous proximity effect, and therefore the experimental observation of this effect has been considered to be a challenging issue. In this paper, we demonstrate that the anomalous proximity effect also occurs in a semiconductor/high-$T_c$ cuprate superconductor hybrid devices in which two potentials coexist: a spin-singlet $d$-wave pair potential and a spin-orbit coupling potential sustaining persistent spin-helix. By utilizing the spin-singlet superconductors, we propose an alternative and promising route to observe the anomalous proximity effect.