van Hove, Rashba, and Hubbard meet to form first-order and higher-order topological superconductors

We investigate topological superconductivity in the Rashba-Hubbard model, describing heavy-atom superlattice and van der Waals materials with broken inversion. We focus in particular on fillings close to the van Hove singularities, where a large density of states enhances the superconducting transition temperature. To determine the topology of the superconducting gaps and to analyze the stability of their surface states in the presence of disorder and residual interactions, we develop an fRG+MFT approach, which combines the unbiased functional renormalization group (fRG) with a real-space mean-field theory (MFT). Our approach uncovers a cascade of topological superconducting states, including A1 and B1 pairings, whose wave functions are of dominant p- and d-wave character, respectively, as well as a time-reversal breaking A1+iB1 pairing. While the A1 and B1 states have first order topology with helical and flat-band Majorana states, respectively, the A1+iB1 pairing exhibits second-order topology with Majorana corner modes.