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\'eel 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.