A simple model for strange metallic behavior
Résumé
A refined semi-holographic non-Fermi liquid model with features of Mottness has been proposed recently in which carrier electrons hybridize with a fermionic operator of a holographic quantum critical sector while interacting with conventional quasi-particles of other filled lattice bands. The Wilsonian RG analysis shows that the model has only two leading effective dimensionless couplings on the Fermi surface in the large $N$ limit. We establish that this model has an emergent universal spectral function near the Fermi surface at an optimal ratio of the two effective couplings when the critical exponent $\nu$ lies between $0.66$ and $0.95$. This ratio is naturally related to the strength of the doping. The universal regime extends to temperatures as low as $0.01 E_F$ at higher $\nu$. Our spectral function fits well with experimental ARPES data of copper oxide samples for under/optimal/over-doping with a fixed exponent over a range of temperatures, validating universality at optimal doping. We show that the universal spectral function leads to linear-in-T dc resistivity (as seen earlier) and (for spherical Fermi surface) a $T^{-2}$ behavior for Hall conductivity at small magnetic fields for a very wide range of temperatures. We obtain a refined Planckian dissipation picture where the scattering time $\tau \approx f\cdot \hbar/(k_B T)$ with $f$ almost independent of all model parameters except for the overall strength of the two couplings when their ratio is optimal. We find $f \approx 1$ when the couplings take maximal value for which strange metallic behavior is exhibited. However, $f\approx \mathcal{O}(10)$ when the couplings are smaller. Although not derivable from quasi-particles, our results at optimal doping fit a Drude-type phenomenology with Planckian scattering time, and an almost model-independent $n/m$, which is about $2\pi$ times the Fermi liquid value at same $E_F$.