Conductivity of higher dimensional holographic superconductors with nonlinear electrodynamics

Abstract

We investigate analytically as well as numerically the properties of s-wave holographic superconductors in d-dimensional spacetime and in the presence of Logarithmic nonlinear electrodynamics. We study three aspects of this kind of superconductors. First, we obtain, by employing analytical Sturm-Liouville method as well as numerical shooting method, the relation between critical temperature and charge density, ρ, and disclose the effects of both nonlinear parameter b and the dimensions of spacetime, d, on the critical temperature T c . We find that in each dimension, T c /ρ 1/(d−2) decreases with increasing the nonlinear parameter b while it increases with increasing the dimension of spacetime for a fixed value of b. Then, we calculate the condensation value and critical exponent of the system analytically and numerically and observe that in each dimension, the dimensionless condensation get larger with increasing the nonlinear parameter b. Besides, for a fixed value of b, it increases with increasing the spacetime dimension. We confirm that the results obtained from our analytical method are in agreement with the results obtained from numerical shooting method. This fact further supports the correctness of our analytical method. Finally, we explore the holographic conductivity of this system and find out that the superconducting gap increases with increasing either the nonlinear parameter or the spacetime dimension. * asheykhi@shirazu.ac.ir

Conductivity of the holographic p-wave superconductors with higher order corrections

“…which is in complete agreement with the σ xx obtained in [26]. This shows that the calculation of σ yy in holographic p-wave superconductor is the same as σ xx in holographic s-wave superconductor [52].…”

“…by considering A (0) and A (1) as constant parameters, we have the following solution for A y asymptotically where Λ is an arbitrary constant. Equations (16) and (17) are the same as corresponding equations in s-wave case [26]. According to the AdS/CFT correspondence, the electrical current based on on-shell bulk action S o.s and the Lagrangian of the matter field L m is defined by…”

“…So, the bigger values of ω g leads to harder formation of fermion pairs which hinders the conductor/superconductor phase transition [52]. At large frequencies, the behavior of conductivity can be indicated to have a power law behavior as Re[σ] = ω (d−4) similar to s-wave case [26]. In addition, based on the BCS theory ω g ≈ 3.5T c while in holographic setup the ratio of gap frequency over critical temperature is found to be the universal value around 8 which hints to the fact that in BCS theory the pairs couple to each other weakly with no interaction.…”

Analytical and numerical study of backreacting one-dimensional holographic superconductors in the presence of Born–Infeld electrodynamics

“…While the solution depends on the spacetime dimensions. This is due to the fact that equation for the ψ given in (10) is independent on the type of electrodynamics but depends on the spacetime dimensions and the mass parameter m [29,48,62]. The next step is to solve the coupled nonlinear field equations (10)- (13) simultaneously and obtain the behavior of model functions.…”

“…During the past decade, the investigation on the holographic superconductor has got a lot of attentions * Electronic address: asheykhi@shirazu.ac.ir † Electronic address: mkzangeneh@scu.ac.ir (see e.g. [6][7][8][9][10][11][12][13][14][15][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]).…”