Non-Fermi-liquid regime of a doped Mott insulator

Abstract

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 $\ensuremath{\delta}<{\ensuremath{\delta}}^{*}$ and $\ensuremath{\delta}>{\ensuremath{\delta}}^{*}$ are found, with ${\ensuremath{\delta}}^{*}\ensuremath{\simeq}J/t (J$ 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 $\ensuremath{\delta}t.$ In the low-doping regime, local magnetic correlations strongly affect the formation of quasiparticles, resulting in a very low coherence scale ${\ensuremath{\epsilon}}_{F}^{*}\ensuremath{\simeq}J(\ensuremath{\delta}/{\ensuremath{\delta}}^{*}{)}^{2}.$ Fermi-liquid behavior does apply below ${\ensuremath{\epsilon}}_{F}^{*},$ but a ``quantum-critical regime'' ${\ensuremath{\epsilon}}_{F}^{*}<T<J$ holds, in which marginal Fermi-liquid behavior of several physical properties is found: NMR relaxation time ${1/T}_{1}\ensuremath{\sim}\mathrm{const},$ resistivity ${\ensuremath{\rho}}_{\mathrm{dc}}(T)\ensuremath{\propto}T,$ optical lifetime ${\ensuremath{\tau}}_{\mathrm{opt}}^{\ensuremath{-}1}\ensuremath{\propto}\ensuremath{\omega}/\mathrm{ln}(\ensuremath{\omega}/{\ensuremath{\epsilon}}_{F}^{*})$ together with $\ensuremath{\omega}/T$ scaling of response functions, e.g., $J{\ensuremath{\sum}}_{\stackrel{\ensuremath{\rightarrow}}{q}}{\ensuremath{\chi}}^{\ensuremath{''}}(\stackrel{\ensuremath{\rightarrow}}{q},\ensuremath{\omega})\ensuremath{\propto}\mathrm{tanh}(\ensuremath{\omega}/2T).$ In contrast, single-electron properties display stronger deviations from Fermi-liquid theory in this regime with a $\sqrt{\ensuremath{\omega}}$ dependence of the inverse single-particle lifetime and a $1/\sqrt{\ensuremath{\omega}}$ 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.