Jose Torres Lopez Qualifying Exam

Abstract: Two-dimensional moiré materials are characterized by their ample tunability, large periodicity lengths, and strong electronic interactions. In particular, electrons and holes can easily be doped and coupled in these systems, leading to interesting charge excitations such as excitons, which are bound states of electrons and holes. When the bound electrons carry a minority spin relative to the background, the resulting exciton is called a spin-polaron. In this talk, I will present two exact diagonalization studies involving excitons and polarons in moiré materials. The first is a generalization of the continuum moiré model, where we introduce independent moiré potentials that allow for relative polarization of the electron and hole. We apply this model to study polarization-induced trapping of the exciton at moiré domain boundaries, which lifts the degeneracy at zero momentum between the linear and quadratic valley modes induced by electron-hole exchange interaction. Second, we study pairing of spin-polarons that are known to be the preferred charge excitation, for suitable parameter regimes, in moiré transition-metal-dichalcogenide bilayers described by the Hubbard model. We stack two such moiré-Hubbard lattices, coupling them via interlayer tunnel, and identify a range of experimentally realistic parameters where the system forms a layer antiferromagnet that gives rise to the formation of charge 2e bipolarons upon hole doping. We investigate the resulting superconductivity emerging from bipolaron condensation, as well as the stability of the bipolaron against different perturbations and larger polarons.