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* similar or equal to 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 delta t. In the low-doping regime, local magnetic correlations strongly affect the formation of quasiparticles, resulting in a very low coherence scale epsilon(F)(*) similar or equal to 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 similar to const, resistivity p(dc)(T)proportional to T, optical lifetime 7(opt)(-1)proportional to omega/1n(omega/epsilon(F)(*)) together with omega/T scaling of response functions, e.g., J Sigma (q) over right arrow chi"(q,omega) proportional to tanh(omega/2T). in contrast, single-electron properties display stronger deviations from Fermi-liquid theory in this regime with a root omega dependence of the inverse single-particle lifetime and a 1/root 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.