Phase stiffness in flat-band superconductors with nodal pairing

We study Bogoliubov quasiparticle spectrum in a two-band system with momentum-dependent hybridization between a dispersive band and a flat band. The interplay between the interband mixing and intraband Cooper pairing may give rise to a parabolic node in the spectrum of flat band quasiparticles, resulting in a quadratic temperature dependence of the superconducting phase stiffness at low temperatures. We also comment that nonmagnetic disorder induces Machida-Shibata deep subgap resonances suggesting the sensitivity of flat-band superconductivity to disorder.