Long-wavelength collective excitations of charge carriers in high-Tcsuperconductors

The long-wavelength dispersion of the charge-carrier plasmon in ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$ for wave vectors parallel to the ${\mathrm{CuO}}_2$ planes has been investigated by transmission-electron-energy-loss spectroscopy. For the [100] and the [110] directions the size of the quadratic plasmon dispersion differs by a factor of about 2. This strong in-plane anisotropy can be explained by a calculation in the framework of the random-phase approximation using a simple tight-binding ansatz for the CuO band having a quadratic Fermi surface. However, a different Fermi surface at a lower-energy scale cannot be excluded.