Zi-Ting Sun, Xilin Feng, Ying-Ming Xie, Benjamin T. Zhou, Jin-Xin Hu, K. T. Law
Unconventional magnetic orders usually interplay with superconductivity in intriguing ways. Here, we propose that a conventional superconductor in proximity to a compensated $p$-wave magnet exhibits behaviors analogous to those of Ising superconductivity found in transition-metal dichalcogenides, which we refer to as pseudo-Ising superconductivity. The pseudo-Ising superconductivity is characterized by several distinctive features: (i) it stays much more robust under strong $p$-wave magnetism than usual ferromagnetism or $d$-wave altermagnetism, owing to the apparent time-reversal symmetry in $p$-wave spin splitting; (ii) in the low-temperature regime, a second-order superconducting phase transition occurs at a significantly enhanced in-plane upper critical magnetic field ${B}_{c2}$; (iii) the supercurrent-carrying state establishes nonvanishing out-of-plane spin magnetization, which is forbidden by symmetry in Rashba and Ising superconductors. We further propose a spin-orbit-free scheme to realize Majorana zero modes by placing superconducting quantum wires on a $p$-wave magnet. Our work establishes another form of unconventional superconductivity generated by $p$-wave magnetism.