Double-peak Majorana bound states in altermagnet--superconductor heterostructures

We study Majorana bound states in a planar Josephson junction in which the middle channel is a $d$-wave altermagnetic metal deposited on a proximitized two-dimensional electron gas. In the topological regime, the near-zero-energy states reveals a characteristic double-peak spatial profile, with the Majorana wavefunction localized near the altermagnet--superconductor interfaces. Using simplified theoretical models, we show that anisotropic hopping intrinsic to altermagnetism naturally generates interface-localized low-energy states, providing the natural explanation for the double-peak structure. In a nanowire geometry with extended normal metallic regions, the same feature persists but the Majorana bound states become more sensitive to the chemical potential compared to the case in planar Josephson junction. In a T-shaped Josephson junction, multiple near-zero-energy states appear, and the Majorana bound state expected at the crossing point is found to be localized near the interfaces, demonstrating that the localization of the Majorana bound states is primarily governed by interface boundaries rather than by the junction geometry. These results show that anisotropic hopping and interface structure play a central role in altermagnet-based topological superconductors and provide a promising route toward a network of controllable Majorana bound states without external magnetic fields.