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 Néel 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.