Title:Probing ground-state degeneracies of a strongly interacting Fermi-Hubbard model with superconducting correlations

Abstract:The Fermi-Hubbard model and its rich phase diagram naturally emerges as a description for a wide range of electronic systems. Recent advances in semiconductor-superconductor hybrid quantum dot arrays have allowed to realize degenerate quantum systems in a controllable way, e.g., allowing to observe robust zero-bias peaks in Kitaev chains, indicative for Majorana bound states. In this work, we connect these two domains. Noting the strong on-site Coulomb repulsion within quantum dots, we study small arrays of spinful hybrid quantum dots implemented in a two-dimensional electron gas. This system constitutes a Fermi-Hubbard model with inter-site superconducting correlations. For two electronic sites, we find robust zero-bias peaks indicative of a strongly degenerate spectrum hosting emergent Majorana Kramers pairs or $\mathbb{Z}_3$-parafermions. Extending to three sites, we find that these spinful systems scale very differently compared to spinless Kitaev chains. When the sweet-spot conditions are satisfied pairwise, we find that the ground state degeneracy of the full three-site system is lifted. This degeneracy can be restored by tuning the superconducting phase difference between the hybrid segments. However, these states are not robust to quantum dot detuning. Our observations are a first step towards studying degeneracies in strongly interacting Fermi-Hubbard systems with superconducting correlations.