Crossed surface flat bands in three-dimensional superconducting altermagnets

Abstract: Superconducting altermagnets have proven to be a promising ground for emergent phenomena but their study has involved two dimensional systems. In this work, we investigate three-dimensional $d$- and $g$-wave altermagnets with chiral $d$-wave superconductivity and show the formation of crossed surface flat bands due to the underlying symmetries. We find that these crossed flat bands appear at zero energy in the surface along $z$ due to the superconducting nodal lines in the $xy$-plane, while the number of corners is determined by the crystal symmetry of altermagnets. We also show that the superconducting nodal lines give rise to Bogoliubov-Fermi surfaces, which then affect the appearance of zero-energy arcs in the surface along $x$. Moreover, we demonstrate that the crossed surface flat bands, surface arcs, and Bogoliubov-Fermi surfaces give rise to distinct signals in charge conductance, hence offering a solid way for their detection and paving the way for realizing higher dimensional topological phases using altermagnets.