Abstract
We analytically and numerically investigate the properties of s-wave holographic superconductors by considering the effects of scalar and gauge fields on the background geometry in five dimensional Einstein-Gauss-Bonnet gravity. We assume the gauge field to be in the form of the Power-Maxwell nonlinear electrodynamics. We employ the Sturm-Liouville eigenvalue problem for analytical calculation of the critical temperature and the shooting method for the numerical investigation. Our numerical and analytical results indicate that higher curvature corrections affect condensation of the holographic superconductors with backreaction. We observe that the backreaction can decrease the critical temperature of the holographic superconductors, while the Power-Maxwell electrodynamics and Gauss-Bonnet coefficient term may increase the critical temperature of the holographic superconductors. We find that the critical exponent has the mean-field value $\beta=1/2$, regardless of the values of Gauss-Bonnet coefficient, backreaction and Power-Maxwell parameters.
Highlights
In 2008, Hartnol et al, put forwarded a new step on the application of the gauge/gravity duality in condensedmatter physics [1,2]
The wellknown duality between anti-de Sitter (AdS) spacetime and the conformal field theories (CFT) [3,4,5] implies that there is a correspondence between the gravity in the d-dimensional spacetime and the gauge field theory livening on its (d − 1)dimensional boundary
We have considered the case in which the gauge and scalar fields back react on the background geometry
Summary
In 2008, Hartnol et al, put forwarded a new step on the application of the gauge/gravity duality in condensedmatter physics [1,2]. Taking the backreaction of the gauge and scalar field on the background geometry into account, a numerical as well as an analytical study of the holographic superconductors in five-dimensional Einstein–Gauss–Bonnet gravity were carried out in [20]. It is interesting to investigate the effects of the nonlinear corrections to the gauge field on the condensation and the critical temperature of the holographic superconductors. When the gauge field is in the form of Born–Infeld nonlinear electrodynamics, an analytical study, based on the Sturm–Liouville eigenvalue problem, of holographic superconductors in Einstein [28,29,30,31,32,33] and Gauss–Bonnet gravity [34,35,36,37] has been carried out.
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