Intertwined Orders, Skyrmion Mediated Superconductivity and Exotic Quantum Criticality in Tunable Topological Flat Bands

The study of interacting topological bands with a tunable bandwidth offers a unique platform to study the interplay of intertwined orders and emergent non-electronic excitations (e.g. skyrmions). Here we design a time-reversal symmetric and sign-problem-free electronic model with tunable Chern bands carrying valley-contrasting Chern number, interacting via competing (anti-)ferromagnetic interactions. Using numerically exact quantum Monte-Carlo computations, we analyze the many-body phase-diagram as a function of temperature and band filling fractions over a wide range of electronic bandwidth, interaction anisotropy, and an Ising spin-orbit coupling. At a commensurate filling of the Chern bands, the ground state hosts intra-valley ferromagnetic coherence and inter-valley antiferomagnetism, thus realizing an insulating Chern antiferromagnet (CAF). Upon doping, the ground-state develops superconductivity, but where the low-energy charged quasiparticles are composite objects — electrons dressed by multiple spin-flip excitations. These spin-polaron (or skyrmion) excitations persist in the presence of a weak spin-orbit coupling. We also present quantum Monte-Carlo results and a complementary field-theoretical analysis for the quantum phase transition(s) that arise between the intertwined phases as a function of two distinct tuning parameters. Our numerical results are consistent with a single continuous quantum phase transition between a CAF insulator and a fully gapped superconductor, with an emergent SO(5) symmetry at the putative critical point, highly suggestive of deconfined quantum (pseudo-)criticality. We end by providing a general outlook towards building microscopic connections with models of interacting moire materials, where many of the ingredients considered here are naturally present.