Non-Fermi liquid regime of a doped Mott insulator

TL;DR

This work develops a solvable doped Mott-insulator model with quenched frustrated magnetic exchange by extending the Sachdev-Ye spin-liquid to a disordered SU(M) t-J framework and solving it in the large-M limit. It reveals a low-doping regime where a markedly reduced coherence scale $ε_F^*$ emerges, leading to a quantum-critical regime ($ε_F^* < T < J$) with Marginal Fermi Liquid–like spin dynamics and ω/T scaling, while single-particle properties exhibit stronger non-Fermi-liquid behavior (√ω self-energy). The results yield a consistent picture of incoherent transport and a broad set of experimental signatures, including linear-in-T resistivity and slow spin dynamics, relevant to cuprates near a Mott transition. The study also discusses potential instabilities and caveats, and outlines how the proposed slushy state may underpin the normal-state anomalies of cuprate superconductors, especially under Zn-doping.

Abstract

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.

Figures (13)

• Figure 1: Crossover diagram as a function of temperature and doping. The coherence scale $\epsilon_F^{*}$ is indicated by a dashed line and is given by $\epsilon_F^{*} \simeq J (\delta /\delta^{*})^{2}$ for $\delta <\delta^{*}$, $\epsilon_F^{*} \simeq \delta t$ for $\delta > \delta^{*}$, with $\delta^{*} = J/t$. Below $\epsilon_F^{*}$, Fermi liquid behaviour holds. For $\delta <\delta^{*}$, an intermediate "quantum critical" regime is found in the range $\epsilon_F^{*} <T <J$, in which charge transport is incoherent and spins have a marginal Fermi liquid dynamics.
• Figure 2: Local dynamical susceptibility $\chi_{\hbox{\tiny loc}}"(\omega,T=0 )$ of the undoped spin liquid. Inset : spectral function.
• Figure 3: The spectral function of the auxiliary fermion as a function of frequency for a doping $\delta=0.1$ and three values of $J=0.01,0.3,1$
• Figure 4: $T=0$ scaling function associated with the spectral density $\rho_{f}(\omega ) = \frac{1}{t\delta } \phi_{f}(\omega /\epsilon_F^{*})$ in the low-doping regime.
• Figure 5: Physical electron quasi-particle residue $Z_{c}$ vs. doping for $J=0.3,1,2.5$ (the proportionality factor $2/M$ has been set equal to $1$)