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