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 magnitude and sign of the magnetic exchange. Two quite different doping regimes $\delta <{\delta }^{*}$ and $\delta >{\delta }^{*}$ are found, with ${\delta }^{*}\simeq J/t\hspace{0.5em}(J$ is the characteristic magnitude of the exchange, and t the hopping amplitude). In the high-doping regime, a (Brinkman-Rice) Fermi-liquid description applies with a coherence scale of order $\delta t.\mathrm{}$ In the low-doping regime, local magnetic correlations strongly affect the formation of quasiparticles, resulting in a very low coherence scale ${\epsilon }_F^{*}\simeq J(\delta /{\delta }^{*}{)}^2.$ Fermi-liquid behavior does apply below ${\epsilon }_F^{*},$ but a “quantum-critical regime” ${\epsilon }_F^{*}<T<J$ holds, in which marginal Fermi-liquid behavior of several physical properties is found: NMR relaxation time ${1/T}_1\sim \mathrm{const},$ resistivity ${\rho }_{\mathrm{dc}}\mathrm{}\left(T\right)\mathrm{}\propto T,$ optical lifetime ${\tau }_{\mathrm{opt}}^{-1}\propto \omega /\ln (\omega /{\epsilon }_F^{*})$ together with $\omega /T$ scaling of response functions, e.g., $J{\sum }_{\overrightarrow{q}}{\chi }^{″}(\overrightarrow{q},\omega )\propto \tanh (\omega /2T).\mathrm{}$ In contrast, single-electron properties display stronger deviations from Fermi-liquid theory in this regime with a $\sqrt{\omega }$ dependence of the inverse single-particle lifetime and a $1/\sqrt{\omega }$ decay of the photoemission intensity. On the basis of this model and of various experimental results, 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. In this picture the corresponding quantum critical regime is a spin liquid with incoherent holes and a slow state of spins and holes with slow spin and charge dynamics responsible for the anomalous properties of the normal state. This picture may be particularly relevant to Zn-doped materials.