We study the surface density of states in $p$-wave unconventional magnet-spin-singlet $s$-wave superconductor hybrid systems ($p$-wave unconventional magnetic superconductors), by using the effective $p$-wave unconventional magnet model [B. Brekke, et al., Phys. Rev. Lett. 133, 236703 (2024)]. Owing to the noncollinear spin structure along the $x$-direction, the quasiparticle energy dispersion has the spin-triplet $p_x$-wave energy gap structure, and then zero-energy flat bands emerge at the [100] edge. Analyzing the pair amplitude at the [100] edge, odd-frequency spin-triplet even-parity pairing is induced in the presence of zero-energy flat bands, while even-frequency spin-singlet even-parity remains. We also demonstrate the Josephson current in superconducting junctions with $p$-wave unconventional magnet-conventional $s$-wave superconductor hybrid systems. By the cooperation of spin-singlet $s$-wave pair potential and the $p$-wave unconventional magnetic order, the current phase relation shows the $\varphi$-junction in the high-transparency but also the temperature dependence of the Josephson current caused by the coupling of the spin-singlet even-parity pairings in the low-transparency limit, even though $p$-wave superconductivity is mainly realized both in the bulk and at the edge. Our calculations provide the possible superconducting phenomena and transport properties in $p$-wave unconventional magnet-$s$-wave superconductor hybrid systems.
Categories: cond-mat.supr-con cond-mat.mes-hall