Interacting Random Dirac Fermions in Superconducting Cuprates

We study the effects of quasiparticle interactions on disorder-induced localization of Dirac-like nodal excitations in superconducting high- $T_c$ cuprates. As suggested by the experimental angle-resolved photoemission spectroscopy and terahertz conductivity data in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$, we focus on the interactions mediated by the order parameter fluctuations near an incipient second pairing transition $d\to d+is\left({\mathrm{id}}^{\prime }\right)$. We find interaction corrections to the density of states, specific heat, and conductivity as well as phase and energy relaxation rates and assess the applicability of the recent localization scenarios for noninteracting random Dirac fermions to the cuprates.