Shear viscosity to entropy density ratio in an electron-boson superconductor

Shear viscosity quantifies the diffusion of momentum and is connected to the energy-momentum tensor of a system. Within the two-dimensional Yukawa-SYK (Y-SYK) model of an electron with spatially random coupling to a quantum-critical scalar, we study the shear viscosity to entropy density ratio, focusing on the regimes where there are no well-defined quasi-particles. We investigate the crossover from the marginal Fermi-liquid to incoherent metal regime of the Y-SYK model, finding the shear viscosity to entropy density ratio approaches the Kovtun-Son-Starinets (KSS) bound in the Mott-Ioffe-Regel limit, and strongly violates the KSS bound in the small bandwidth limit at intermediate temperatures.