Topological insulators and superconductors based on $p$-wave magnets,electrical control and detection of a domain wall

Altermagnets are time-reversal broken antiferromagnets, where the $z$ component of the N\'{e}el vector is detectable by anomalous Hall effects. On the other hand, recently proposed $p$-wave magnets are time-reversal preserved antiferromagnets, and it is a highly nontrivial problem how to detect and control a domain wall. We study a one-dimensional hybrid system made of a $p$-wave magnet and a metal possessing the orbital degree of freedom. The hybrid system is a topological insulator without the spin-orbit interaction. There emerge two edge states per one edge, because the system is mapped to a set of two copies of a topological insulator. Each copy resembles the long-range Su-Schrieffer-Heeger model but it is topologically different. Topological interface states emerge at a domain wall in the $p$-wave magnet, which are charged due to the Jackiw-Rebbi mechanism. Consequently, a domain wall in the $p$-wave magnet will be controllable and detectable purely by electrical means. We also study Majorana fermions induced by proximity coupling of $s$-wave superconductivity and $p$-wave magnet.