Plasmons in a layered strange metal using the gauge-gravity duality

In an attempt to understand the density-density response of the cuprate superconductors, we study plasmons in a layered strange metal using the Gubser-Rocha model. The latter is a well-known bottom-up holographic model for a strange metal that is used here to describe the strongly repulsive on-site interactions between the electrons in each copper-oxide (CuO$_2$) layer, whereas the long-range Coulomb interactions are incorporated by a so-called double-trace deformation. To be able to model the bilayer cuprates more realistically, we consider in particular the case of two closely-spaced CuO$_2$ layers per unit cell. In the response we then obtain for vanishing out-of-plane momentum both an optical and an acoustic plasmon, whereas for nonvanishing out-of-plane momentum there are two acoustic plasmon modes. We present the full density-density spectral functions with parameters typical for cuprates and discuss both the dispersion and the lifetime of these plasmon excitations. Moreover, we compute the conductivity after introducing disorder into the system. Finally, we also compute the loss function to facilitate a comparison with experimental results from electron energy loss spectroscopy.