Nematic superconducting state promoted by electromagnetic gauge field fluctuations

Motivated by the recent observation of nematic superconductivity in twisted bilayer graphene (TBG), we present a theory for the pairing state symmetry of two-component p-wave and d-wave unconventional superconductors on the triangular lattice. Here, we show that electromagnetic (EM) fluctuations play a crucial role in selecting between chiral (p+ip and d+id) and nematic (p+p and d+d) solutions. Specifically, we derive an effective free energy for the two-component superconducting order parameter after integrating out the EM fluctuations just above the superconducting transition. The effects of such fluctuations are encoded in a non-analytic term that is cubic in the order parameter, and generally favors a nematic superconducting state being realized below T_c. The quartic terms of the free energy are little affected by the EM fluctuations, and continue to favor a chiral state. The competition between cubic and higher order terms leads to a phase diagram in which the nematic solution emerges over a wide parameter-space region where the chiral solution would be favored in the mean-field approach. We discuss the stability of the fluctuation-induced nematic phase and explain how our results may be applied to TBG and other nematic superconductors.