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Non-Fermi liquid regime of a doped Mott insulator

We study the doping of a Mott insulator in the presence of quenched frustrating disorder in the magnetic exchange. A low doping regime $δ<J/t$ is found, in which the quasiparticle coherent scale is low : $ε_F^* = J (δ/δ^*)^2$ with $δ^*=J/t$ (the ratio of typical exchange to hopping). In the ``quantum critical regime'' $ε_F^*<T<J$, several physical quantities display Marginal Fermi Liquid behaviour : NMR relaxation time $1/T_1\sim const.$, resistivity $ρ_{dc}(T) \propto T$, optical lifetime $τ_{opt}^{-1}\propto ω/\ln(ω/\epstar)$ and response functions obey $ω/T$ scaling, e.g. $J\sum_q χ''(q,ω) \propto \tanh (ω/2T)$. In contrast, single-electron properties display stronger deviations from Fermi liquid theory in this regime with a $\sqrtω$ dependence of the inverse single-particle lifetime and a $1/\sqrtω$ decay of the photoemission intensity. On the basis of this model and of various experimental evidence, it is argued that the proximity of a quantum critical point separating a glassy Mott-Anderson insulator from a metallic ground-state is an important ingredient in the physics of the normal state of cuprate superconductors (particularly the Zn-doped materials). In this picture the corresponding quantum critical regime is a ``slushy'' state of spins and holes with slow spin and charge dynamics responsible for the anomalous properties of the normal state.