Interacting random Dirac fermions in superconducting cuprates

We study interaction effects in disorder-induced localization of Dirac-like low-energy quasiparticles in superconducting high-$T_c$ cuprates. As suggested by the experimental ARPES and terahertz conductivity data in $Bi_2Sr_2CaCu_2O_{8+\delta}$, we focus on the quasiparticle interaction mediated by the order parameter fluctuations near an incipient second pairing transition $d\to d+is (id^\prime)$. We find interaction corrections to the density of states, specific heat, and conductiity as well as phase and energy relaxation rates and assess the applicability of the non-interacting localization scenarios to the cuprates.