Topological superconductivity in layered d-wave altermagnetic metals

We investigate multilayer d-wave altermagnetic metals with odd-parity helical p-wave pairing. In the minimal bilayer system, interlayer tunneling reconstructs the spin-split Fermi surfaces and generates two layer-hybridized sectors with distinct effective chemical potentials. Without Rashba spin-orbit coupling (RSOC), the emergent mirror symmetry and subsystem chiral symmetry stabilize phases with different numbers of helical Majorana edge-mode pairs and additional counterpropagating pairs, jointly characterized by the mirror Chern number and the winding numbers defined along high-symmetry lines. The combination of RSOC and the altermagnetic exchange field gaps out the helical Majorana pairs while, in a certain parameter regime, leaving another pair of counterpropagating Majorana edge modes gapless, giving rise to second-order topological phases with isolated or twofold Majorana corner modes, as well as a hybrid-order phase in which gapless Majorana edge modes coexist with Majorana corner modes. We identify a layer symmetry that elucidates the physical origin of these phases. For an arbitrary N-layer system, such a symmetry naturally arises from the interlayer-coupling matrix, allowing N-fold Majorana corner modes to emerge when all layer-hybridized sectors enter the nontrivial second-order regime. Our results establish the interplay among the layer degree of freedom, odd-parity pairing, and Fermi-surface configurations as a controllable route to engineering topological superconductivity in layered altermagnetic systems.