  The origin of high-temperature superconductivity has been widely debated
since its discovery. Here, we propose a model to reveal the mechanism based on
the interaction between carrier and local potential. In this model, the
potential that is analogous to the lattice point is composed of localized
charges and its vibration mediates the coupling of mobile carriers. A
Hamiltonian that describes the vibration, coupling, and various interactions
among the ordered potentials and carriers is established. By analyzing the
Hamiltonian, we find that the vibration of local potential and the
interactions, which are determined by the carrier density, control the
transition temperature. We show that the transition temperature is high if the
local potential is composed of electrons and the mobile carrier is hole because
of the strong coupling between them. By replacing the local potential with
lattice point, our model is equivalent to the BCS theory. Therefore, our model
may provide a general theoretical description on the superconductivity.
