Topological Ising superconductivity in two-dimensional p-wave magnet
Fermi-surface spin splitting generated by non-relativistic exchange fields provides a new route to topological superconductivity without relying on strong spin-orbit coupling. Here, we study superconducting instabilities of a square-lattice $p$-wave magnet with onsite and nearest-neighbour attractive interactions. The odd-parity exchange field removes inversion symmetry in the spin-split electronic structure, mixing singlet and triplet order parameters within a single symmetry channel. The leading instability is a mixed-parity A$_1$ Ising state, in which singlet components coexist with the $p_x$-wave triplet component, whose $d$-vector is locked along the exchange-field axis. As the nearest-neighbour attraction grows, this Ising state undergoes a transition into a nodal topological superconducting phase with Majorana edge modes protected by momentum-resolved winding numbers. These modes extend over finite momentum intervals bounded by the surface projections of bulk point nodes. We further show that a Zeeman field perpendicular to the exchange field can induce a $\mathbb{Z}_2$ topological superconducting phase. Our results identify $p$-wave magnets as a versatile testbed for topological superconductivity driven by non-relativistic spin splitting.