Majorana corner modes and tunable patterns in an altermagnet heterostructure

The mutual competition and synergy of magnetism and superconductivity provide us with a very valuable opportunity to access topological superconductivity and Majorana fermions. Here, we devise a heterostructure consisting of an $s$-wave superconductor, a two-dimensional topological insulator, and an altermagnet, which is classified as the third magnet and featured by zero magnetization but spin polarization in both real and reciprocal spaces. We find that the altermagnet can induce mass terms at the edges that compete with electron pairing, and mass domains are formed at the corners of the sample, resulting in zero-energy Majorana corner modes (MCMs). The presence or absence of MCMs can be engineered by only changing the direction of the N\'eel vector. Moreover, uniaxial strain can effectively manipulate the patterns of the MCMs, such as moving and interchanging MCMs. Experimental realization, remarkable advantages of our proposal, and possible braiding are discussed.