Holographic Superconductors with Logarithmic Nonlinear Electrodynamics in an External Magnetic Field

Abstract

Based on the matching method, we explore the effects of adding an external magnetic field on the s-wave holographic superconductor when the gauge field is in the form of the logarithmic nonlinear source. First, we obtain the critical temperature as well as the condensation operator in the presence of logarithmic nonlinear electrodynamics and understand that they depend on the nonlinear parameter b. We show that the critical temperature decreases with increasing b, which implies that the nonlinear gauge field makes the condensation harder. Then, we turn on the magnetic field in the bulk and find the critical magnetic field, B c , in terms of the temperature, which also depends on the nonlinear parameter b. We observe that for temperature smaller than the critical temperature, T < T c , the critical magnetic field increases with increasing b and goes to zero as T → T c , independent of the nonlinear parameter b. In the limiting case where b → 0, all results restore those of the holographic superconductor with magnetic field in Maxwell theory.

Conductivity of higher dimensional holographic superconductors with nonlinear electrodynamics

“…So the condensation gets harder as the nonlinear parameter becomes larger. This result is consistent with the earlier findings [26,28,34,37]. Fig.…”

“…The investigation was also generalized to nonlinear gauge fields such as Born-Infeld, Exponential, Logarithmic and Power-Maxwell electrodynamics. Applying the analytical method including the Sturm-Liouville eigenvalue problem [26,27,28,29,30,31,32], or matching method which is based on the match of the solutions near the boundary and on the horizon at some intermediate point [33,34], or using the numerical method [35,36,37], the relation between critical temperature and charge density of the s-wave holographic superconductors have been investigated. It was argued that the nonlinear electrodynamics will affect the formation of the scalar hair, the phase transition point, and the gap frequency.…”

Effects of backreaction on power-Maxwell holographic superconductors in Gauss–Bonnet gravity

“…(15) with φ(z) and f (z) given in Eqs. (27) and (28). Then we find the critical charge density ρ which satisfy the boundary condition ψ − = 0 in z → 0.…”

“…(4), (12), (27), and using definition of ζ , we obtain the following expression for the critical temperature:…”

“…In particular, 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. It was argued that in the Schwarzschild AdS black hole background, the higher nonlinear electrodynamics corrections make the condensation harder [24][25][26][27]. 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.…”