Gauss–Bonnet holographic superconductors in exponential nonlinear electrodynamics

Abstract

The low-energy limits of the string theory lead to the higher-order curvature corrections for Einstein gravity. Also, they give the higher-order derivative corrections for the Maxwell or linear electrodynamics, which suggests the nonlinear electrodynamics. Inspired by this, in this paper we investigate d-dimensional holographic superconductors in the probe limit in the framework of Einstein-Gauss-Bonnet gravity and exponential nonlinear electrodynamics.Based on the Sturm-Liouville eigenvalue method, we compute the critical temperature, the condensation value, and the critical exponent. It is observed that the critical temperature decreases when the Gauss-Bonnet (GB) parameter or the nonlinear parameter increases, but it increases with the higher dimension of the spacetime at the efficiently low charge density. In addition, we found that the condensation value becomes larger as increasing the GB parameter, the nonlinear parameter as well as the spacetime dimension. Finally, we calculate the optical conductivity and study the effects of the GB term and exponential nonlinear electrodynamics on superconducting energy gap. I. INTRODUCTIONThe BCS theory provides a microscopic description with great accuracy for conventional or low temperature superconductors [1]. Here, the occurrence of the superconducting state is a result of the spontaneously broken U(1) symmetry due to the condensation of Cooper pairs which are formed by the attractive interaction coming from the virtual exchange of the phonons. However, the BCS theory fails in explaining of the pairing mechanism in the high temperature superconductors in which the system is strongly coupled. Since, understanding the mechanism of the high temperature superconductors has been one of the most important problems in condensed-matter physics and it requires new theoretical approaches.The AdS/CFT correspondence, proposed firstly by Maldacena, indicates a correspondence between a weakly coupled garvity theory in a d-dimensional anti-de Sitter (AdS) spacetime and a * Electronic address: hncao@yonsei.ac.kr 1 The GB term appears in the heterotic string theory at which α is regarded as the inverse string tension [54,56].Thus, in this paper only the case α ≥ 0 is considered.

Holographic superconductors in 4D Einstein-Gauss-Bonnet gravity

“…All the studies mentioned above concerning the holographic dual models with the curvature correction are based on the Einstein-Gauss-Bonnet gravity in dimensions D ≥ 5, where we find that the higher curvature corrections make it harder for the scalar [14,[16][17][18][19][20][21][22][23][24][25][26][27][28][29] or vector [30][31][32][33][34][35][36] hair to form. As pointed out by Gregory et al in [14], one can expect this tendency to be the same even in (2 + 1)-dimensions, however, it remains obscure to what extent this suppression affects the physics of holographic superconductors in (2 + 1)dimensions.…”

“…Other generalized investigations based on the effects of the curvature correction on the holographic dual models can be found, for example, in refs. [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”

Thermodynamic stability and P–V criticality of nonsingular-AdS black holes endowed with clouds of strings

“…Figure 6 shows the plot of the Gibbs free energy vs temperature. For the values of pressure below the critical pressure Pc , the G − T diagram exhibits a swallowtail structure [57] where the Gibbs free energy of the black hole intersects with itself which is indicative of first-order phase transition between SBH and LBH (cf. Fig.…”

“…The exponents α and β determine the behaviour of specific heat at constant volume [21] and behaviour of the order parameter η which is the difference between the volume of the gas phase and the volume of the liquid phase respectively. γ explains the behaviour of isothermal compressibility κ T and δ governs the behaviour of the critical isotherm P − Pc [57]. The critical exponents can be calculated by using following relations [35,36]…”

Analytical study of holographic p-wave superfluid models in Gauss–Bonnet gravity

“…In this direction, lots of work studying various holographic superconductors in Einstein-Gauss-Bonnet gravity have been performed and the effects of the GB correction on the phase transition have been discovered [26][27][28][29][30][31][32][33][34][35]. Recently, Nam studied d-dimensional holographic superconductors in the probe limit in the framework of Einstein-Gauss-Bonnet gravity as well as exponential nonlinear electrodynamics, and found that the GB correction makes the formation of condensation harder, and the superconducting energy gap becomes larger when increasing GB parameter [36]. Ref.…”