Time-reversal symmetric topological superconductivity in Machida-Shibata lattices

Recent experiments engineered special spin-degenerate Andreev states in atomic cages of adatoms on superconductors, the Machida-Shibata states, revealing a promising building block for quantum matter. Here, we investigate the formation of time-reversal symmetric bands by hybridizing multiple such states and analyzing their electronic topological properties. The low-energy theory shows that competing emerging singlet and triplet superconducting pairings drive the formation of topologically non-trivial phases in symmetry class DIII. Therefore, Kramers pairs of Majorana zero modes appear at the ends of Machida-Shibata chains, while two-dimensional lattices host helical Majorana edge modes. Additionally, we discover extended regions in the Brillouin zone with vanishing superconducting pairings, which can be lifted by repulsive electron interactions. Our findings offer new perspectives for manipulating topological superconductivity and pairings in non-magnetic adatom systems.