Critical non-Fermi-liquid metal in overdoped random t-J model

It is often assumed that the high-doping (overdoped) region of high-Tc cuprates is a Fermi-liquid metal. However, careful experiments have reported significant deviations from it. We will discuss a candidate non-Fermi-liquid phase using a Sachdev-Ye-Kitaev type random model of electrons. The solutions of this model will be discussed in the large-M limit, where SU(2) symmetry is generalized to SU(M). At large hole dopings we will establish the presence of a critical non-Fermi- liquid metal, which has doping- dependent exponents, a linear-in-temperature resistivity, and a strong particle-hole asymmetry. These features have been reported in recent experiments. I will also show that this critical metal has an instability to a low-doping spin-glass phase and discuss its spectral functions.