Proximity-induced superconductivity and emerging topological phases in altermagnet-based heterostructures

Abstract

We present a theoretical framework for investigating superconducting proximity effect in altermagnet (AM)-superconductor (SC) heterostructures. In general, AMs, characterized by vanishing net magnetization but spin-split electronic spectra, provide a promising platform for realizing unconventional magnetic phases. We consider a two-dimensional $d$-wave AM proximity coupled to a three dimensional ordinary $s$-wave SC. By integrating out the superconducting degrees of freedom, we derive an effective Hamiltonian that describes the proximity-induced modifications in the AM layer in the form of a self-energy. We then derive an effective Green's function to obtain the proximity-induced pairing amplitudes in the AM layer and classify the induced pairing amplitudes according to their parity, frequency, and spin. We find the presence of even-parity singlet and triplet pairing amplitudes in the AM layer. To achieve the odd-parity triplet components, important to realize topological superconductivity, we introduce a layer of Rashba spin-orbit coupling (RSOC) in the heterostructure. We analyse the band topology of this proximity-induced AM-RSOC layer and demonstrate the emergence of both weak and strong topological superconducting phases with edge-localized modes, characterized by winding number and Chern number. These findings highlight the role of AM-SC hybrid setup as a versatile platform for realizing odd-parity triplet pairings and engineering topological superconductivity in two-dimension.