Multi-component Chiral Topological Superconductors in 2D Superlattices

The advent of superlattices in recent years has made possible the realization of two-dimensional lattices with large magnetic fluxes per unit cell when in the presence of an external magnetic field. The interplay of lattice effects and magnetic field creates a scenario of multiple Fermi surfaces related by magnetic translation symmetry. I will discuss the onset of time-reversal symmetry breaking superconductivity in such systems, and demonstrate the existence of mean-field superconductors characterized by multi-component triplet order parameters, which are greatly constrained by the action of the magnetic translation group. An outstanding property of these large flux superconductors is that Cooper pairs have finite momentum, and bulk state is characterized by higher Chern numbers, signaling the presence of many chiral Majorana edge modes. I will discuss their bulk properties as well as multi-stage phase transitions that change the bulk topology and the nature of the chiral edge Majorana fermions.