Interplay between altermagnetism and superconductivity in two dimensions: intertwined symmetries and singlet-triplet mixing

We study the interplay between altermagnetism and unconventional superconductivity for two-dimensional square- and triangular-lattice systems. Our approach is based on an effective single particle Hamiltonian which mimics the alternating spin splitting of the d - wave and i - wave altermagnetic state. By supplementing the model with intersite pairing term we characterize the principal features of the coexistent altermagnetic-superconducting state as well as the possibility of inducing the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. Our calculations show that the subtle interplay between the symmetries of the superconducting and altermagnetic order parameters as well as the shape/size of the Fermi surface lead to various types of anisotropic behaviors of the resultant non-zero momentum pairing, which has not been possible in the originally proposed FFLO state. Moreover, additional pairing symmetries appear leading to multi-component order parameter with singlet-triplet mixing. We discuss our result in the context of possible applications like, e.g., the superconducting diode.