Topological insulators and superconductors based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-wave magnets: Electrical control and detection of a domain wall

Recently proposed $p$-wave magnets are time-reversal preserved antiferromagnets, where the detection and control of a domain wall is a highly nontrivial problem. 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 boundary states per one boundary, 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 their topological phase diagrams are different. A topological interface state emerges at a domain wall in the $p$-wave magnet, which is 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 a $p$-wave magnet.