Dirac Superconductors: Superconductivity in Artificial Graphene

Abstract

In this Master's thesis, I investigate the possibility to build a Dirac superconductor under supervision of Prof. Dr. Cristiane Morais Smith and Dr. Vladimir Juričić. By arranging nanocrystals that are known to be superconducting in honeycomb superlattices, we combine the physics of graphene with that of superconductivity. In this research, the focus is on CdSe nanocrystals in a honeycomb configuration. It is assumed there is one effective phonon per site that couples to on-site and nearest-neighbor electrons. Using a path-integral approach, the phonons are integrated out such that effective Hubbard U and V terms are derived. Order parameters for the on-site Cooper pairs and Cooper pairs of nearest-neighbor electrons were defined. For the latter, the competition between the hidden order, which renormalizes Fermi velocity instead of opening a gap, and the Kekule order, which opens a gap, is considered. Using the order parameters, the electron densities in the Hubbard terms are decoupled via mean-field theory. BCS theory is used to recover the gap equations and critical temperature. I find that the Kekule order is preferred over the hidden order provided nearest-neighbor coupling is favored over on-site coupling.