We generalize the analytical investigation on the properties of s-wave holographic superconductors in the presence of Born-Infeld nonlinear electrodynamics by taking the backreaction into account. We find that in the presence of nonlinear gauge field, one can still employ the analytical method when the backreaction is turned on. Our calculation is based on the Sturm-Liouville eigenvalue problem, which is a variational method. For the system under consideration, we obtain the relation between the critical temperature and the charge density. We find that both backreaction and Born-Infeld parameters decrease the critical temperature of the superconductor and make the condensation harder. At the ned of paper, we calculate the critical exponent associated with the condensation near the critical temperature and find that it has the universal value 1/2 of the mean field theory.

No abstract

We analytically study the properties of a (2 + 1)-dimensional s-wave holographic superconductor in the presence of exponential nonlinear electrodynamics. We consider the case in which the scalar and gauge fields back react on the background metric. Employing the analytical Sturm-Liouville method, we find that in the black hole background, the nonlinear electrodynamics correction will affect the properties of the holographic superconductors. We find that with increasing both backreaction and nonlinear parameters, the scalar hair condensation on the boundary will develop more difficult. We obtain the relation connecting the critical temperature with the charge density. Our analytical results support that, even in the presence of the nonlinear electrodynamics and backreaction, the phase transition for the holographic superconductor still belongs to the second order and the critical exponent of the system always takes the mean-field value 1/2.

No abstract

Based on the Sturm–Liouville eigenvalue problem, we analytically study several properties of holographic s-wave superconductors with exponential nonlinear (EN) electrodynamics in the background of Schwarzschild anti-de Sitter black holes. We assume the probe limit in which the scalar and gauge fields do not back react on the background metric. We show that for this system, one can still obtain an analytical relation between the critical temperature and the charge density. Interestingly enough, we find that EN electrodynamics decreases the critical temperature, Tc, of the holographic superconductors compared to the linear Maxwell field. This implies that the nonlinear electrodynamics make the condensation harder. The analytical results obtained in this paper are in good agreement with the existing numerical results. We also compute the critical exponent near the critical temperature and find out that it is still 1/2, which seems to be a universal value in mean field theory.