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

TL;DR

This paper investigates how altermagnetism influences unconventional superconductivity in two-dimensional lattice systems, revealing complex anisotropic pairing behaviors, multi-component order parameters, and potential applications like superconducting diodes.

Contribution

It introduces a model capturing the interplay between altermagnetism and superconductivity, highlighting the emergence of anisotropic pairing and singlet-triplet mixing in 2D systems.

Findings

Anisotropic non-zero momentum pairing behaviors are identified.

Exotic multi-component order parameters with singlet-triplet mixing are observed.

Potential for inducing FFLO phases in altermagnetic-superconducting systems.

Abstract

We study the interplay between altermagnetism and unconventional superconductivity for the case of two-dimensional square- and triangular-lattice systems. Our approach is based on an effective single particle Hamiltonian which mimics the alternating spin splitting characteristic for 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, in the considered systems additional pairing symmetries appear leading to an exotic multi-component order parameter with singlet-triplet mixing. To interpret the obtained data we analyze the Cooper pair density in the momentum space and the corresponding Fermi wave vector mismatch resulting from the altermagnetic spin splitting. We discuss our result in the context of possible applications like, e.g., the superconducting diode.