Energy dispersion, superconductivity, and magnetic fluctuations in stacked altermagnetic materials

Recently, altermagnetism (AM) has emerged as a new category of magnetism, alongside conventional antiferromagnetism (AFM) and ferromagnetism. In an AM, superconductivity (SC) is faced with a dilemma that the spin-polarized bands, induced by the broken time reversal ($\mathcal{T}$) symmetry, dominantly support spin-triplet pairing. In contrast, AM spin fluctuations routinely facilitate spin-singlet pairing as in AFM. Consequently, unconventional SC is either absent or weak in AM materials. Here, we propose that stacking two-dimensional (2D) AM materials could resolve this dilemma. Stacked 2D materials have yielded a variety of new electronic properties by altering the symmetries inherent in the monolayer. In a 2D anisotropic Hubbard model, we investigate the general energy dispersions of both single-layer and stacked AM materials. We demonstrate that AM sheet stacking can alter the original symmetries, consequently affecting the energy dispersion. The interlayer magnetic coupling enhances the low $\mathbf{q}$ magnetic fluctuations. $\mathcal{T}$ symmetry is restored in the AA stacking with an antiferromagnetic interlayer coupling and then both the energy dispersion and pairing interaction are in favor of spin-singlet SC. The ferromagnetic interlayer coupling in the AB stacking not only recovers $\mathcal{T}$ symmetry but also supports spin-triplet pairing. It is further anticipated that twisted bilayer AM sheets could exhibit additional novel electronic properties, including topology, flat bands, and collective excitations. Our work illustrates that stacking sheets of AM materials could open up a unique research domain in exploring novel quantum phenomena and offer a fertile ground for potential electronic applications.