Realizing tunable higher-order topological superconductors with altermagnets

We propose a method for realizing tunable higher -order topological superconductors (TSCs) by coupling class DIII TSCs with recently discovered altermagnets exhibiting nonrelativistic spin splitting. We exemplify our approach using d -wave spin splitting and demonstrate the emergence of inversion -protected Majorana zero modes (MZMs) localized at the corner of the system, i.e., Majorana corner modes. Critically, we show that manipulating the N & eacute;el vector of the altermagnets enables control over the MZM distribution. This constitutes a crucial step towards achieving non -Abelian braiding of MZMs, a key ingredient for fault -tolerant topological quantum computation. Finally, we discuss a physical system that implements our proposal.