The disordered Bose condensate in two dimensions: application to high-Tc superconductors

We calculate the dynamical conductivity for a weakly disordered Bose condensate in two dimensions. The disorders is due to neutral impurities. We compare the asymptotic laws (for small and large frequencies) for neutral impurities with the ones for charged impurities. Universal functions for the dynamical transport properties are derived. The plasmon density of states shows a linear increase with energy for intermediate energies and a peak structure at larger energies. Our theoretical results are compared with experimental results (far-infrared, electron-energy-loss and Raman spectroscopy) found in the high-T_c superconductor YBa₂Cu₃O_7−δ. The occurrence of a quasi-gap in a disordered Bose condensate is described and discussed in connection with experiments on high-T_c superconductors.