Exponential nonlinear electrodynamics and backreaction effects on holographic superconductor in the Lifshitz black hole background

We analytically describe the properties of the s-wave holographic superconductor with the exponential nonlinear electrodynamics in the Lifshitz black hole background in four-dimensions. Employing an assumption the scalar and gauge fields backreact on the background geometry, we calculate the critical temperature as well as the condensation operator. Based on Sturm–Liouville method, we show that the critical temperature decreases with increasing exponential nonlinear electrodynamics and Lifshitz dynamical exponent, [Formula: see text], indicating that condensation becomes difficult. Also we find that the effects of backreaction has a more important role on the critical temperature and condensation operator in small values of Lifshitz dynamical exponent, while [Formula: see text] is around one. In addition, the properties of the upper critical magnetic field in Lifshitz black hole background using Sturm–Liouville approach is investigated to describe the phase diagram of the corresponding holographic superconductor in the probe limit. We observe that the critical magnetic field decreases with increasing Lifshitz dynamical exponent, [Formula: see text], and it goes to zero at critical temperature, independent of the Lifshitz dynamical exponent, [Formula: see text].

Effects of backreaction and exponential nonlinear electrodynamics on the holographic superconductors

We analytically study the properties of a [Formula: see text]-dimensional [Formula: see text]-wave holographic superconductor in the presence of exponential nonlinear (EN) 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 [Formula: see text].