  The effect of the lattice periodic potential on superconductivity which was
ignored by BCS theory has been investigated. According to the effective mass
approximation of band theory, the effect of lattice periodic potential can be
embodied in the effective mass of the Ginzburg-Landau (GL) equations. The
effective mass has s special property. It can be negative. Negative effective
mass leads to many unusual phenomena. The superconducting order parameter shows
the period distribution. Its modulate wavevector is proportional to the
condensed carrier density, which explains the linear relation between the
magnetic peaks displacement epsilon and x for La2-xSrxCuO4. The superconducting
phase is always local and separated originally and evolves into global
superconducting phase at the certain pairs concentration, which explains why
the cuprate superconductors must be insulator at low doped. The doped
concentrations of insulator to superconductor transition for La2-xSrxCuO4 is
consistent with the experiment results. The relation of the superconducting gap
(SG) and the pseudogap (PG) was discussed. Spin density wave state is obtained
when the order parameter is homogenous distribution.
