Charging effects on the critical temperature of the Josephson-coupled layered superconductors

Effects of quantum phase fluctuations on the critical temperature T_c of Josephson-coupled layered superconductors are considered. T_c is shown to decrease nonlinearly with increasing charge fluctuations. The results obtained for the critical temperature by applying the self-consistent mean field method reveal no phase transition from superconducting state to normal metal for a finite value of charging energy. The destruction of the long range phase coherence appeared to occur at asymptotically large values of self-capacitance charging. For the weak quantum phase fluctuations limit, T_c is obtained to be vary in the interval of T_c* < T_c < T⁽²⁾_c, where T⁽²⁾_c is the critical temperature for a single superconducting layer evaluated by the mean field theory, and T_c* is the temperature when the phase coherence between the nearest neighboring layers is lost. Since T_c approaches T_c* with vanishing interlay er tunneling integral J_⊥. Calculation of the dependence of the transverse stiffness on the charging energy is carried out at T=0. The reentrance found can in principle occur at a sufficiently large value of the interlayer tunneling integral J_⊥ > J^cr_⊥ = kT⁽²⁾_c, where J^cr_⊥≈ kT⁽²⁾_c is the value of J_⊥ when the superconductor normal metal phase transition takes place. However, the condition J_⊥≥ kT⁽²⁾_c contradicts to the existence of the Josephson coupling between superconducting layers.