Linear-in-T resistivity from semi-holographic non-Fermi liquid models

We construct a semi-holographic effective theory in which the electron of a two-dimensional band hybridizes with a fermionic operator of a critical holographic sector, while also interacting with other bands that preserve quasiparticle characteristics. Besides the scaling dimension $ u$ of the fermionic operator in the holographic sector, the effective theory has two {dimensionless} couplings $alpha$ and $gamma$ determining the holographic and Fermi-liquid-type contributions to the self-energy respectively. We find that irrespective of the choice of the holographic critical sector, there exists a ratio of the effective couplings for which we obtain linear-in-T resistivity for a wide range of temperatures. This scaling persists to arbitrarily low temperatures when $ u$ approaches unity in which limit we obtain a marginal Fermi liquid with a specific temperature dependence of the self-energy.