An effective framework for strange metallic transport

Abstract

Semi-holography, originally proposed as a model for conducting lattice electrons coupled to a holographic critical sector, leads to an effective theory of non-Fermi liquids with only a few relevant interactions on the Fermi surface in the large $N$ limit. A refined version of such theories has only two effective couplings which give holographic and Fermi-liquid-like contributions to the self-energy, respectively. We show that a low co-dimension sub-manifold exists in the space of refined semi-holographic theories in which strange metallic behavior is manifested, and which can be obtained just by tuning the ratio of the two couplings. On this sub-manifold, the product of the spectral function and the temperature is approximately independent of the critical exponent, the Fermi energy, and the temperature at all frequencies and near the Fermi surface when expressed in terms of suitably scaled momentum and frequency variables. This quasi-universal behavior leads to linear-in-$T$ dc resistivity and Planckian dissipation over a large range of temperatures, and we also obtain $T^{-3}$ scaling of the Hall conductivity at higher temperatures. The quasi-universal spectral function also fits well with photoemission spectroscopic data without varying the critical exponent with the doping. Combining with the results for optical conductivity, we construct a generalized version of Drude phenomenology for strange-metallic behavior which satisfies non-trivial consistency tests. Finally, we discuss a possible dynamical mechanism for the fine-tuning of the ratio of the two couplings necessary to realize the strange metallic behavior in a typical state.