The Studies Of Holographic Superconductor And Superfluidity In Gravitational Background

As an important breakthrough in physics,Anti-de Sitter/Conformal field theory(AdS/CFT)correspondence reveals the equivalence relation between the higher dimensional gravity theory and the low dimensional quantum field theory,and provides a new approach to investigate the various properties of the strongly coupled quantum field theory.In this paper,we apply this dual relation to study strongly coupled superconductor and superfluid phase transition which capture great interest in condensed matter physics.Based on the variational method for the Sturm-Liouville eigenvalue problem,we analytically investigate the holographic s-wave model of superconductor with Born-Infeld electrodynamics in the background of the d + 1 dimensional Schwarzchild AdS black hole.By introducing an iterative procedure in the perturbative approach proposed by Banerjee et al.,we further improve the analytical results and the consistency with the numerical findings for the 2 + 1 dimensional superconductor model with Born-Infeld electrodynamics,and can easily extend the analytical study to the higher-dimensional superconductor with Born-Infeld electrodynamics.The study shows that the higher Born-Infeld corrections make it harder for the condensation to form but do not affect the critical phenomena of the system.Our analytical results can be used to back up the numerical computations for the holographic superconductors with various condensates in Born-Infeld electrodynamics.We analytically study the holographic superfluid phase transition in the five dimensional Schwarzchild AdS soliton background by using the Sturm-Liouvillevariational method.By investigating the holographic s-wave and p-wave superfluid models in the probe limit,we observe that the spatial component of the gauge field will hinder the phase transition.Moreover,we note that,different from the AdS black hole spacetime,in the AdS soliton background the holographic superfluid phase transition always belongs to the second order and the critical exponent of the system takes the mean-field value 1/2 in both s-wave and p-wave models.Our analytical results are found to be in good agreement with the numerical findings.In the Gauss-Bonnet gravitational background,in order to explore the influence of the higher curvature correction on the holographic superfluid phase transition,we analytically investigate the p-wave superfluid model in five dimensional AdS soliton and AdS black hole.Our results have shown that: for the case in AdS soliton,the critical chemical potential of the system increases with the increase of the Gauss-Bonnet parameter,while for the case in AdS black hole the critical temperature reduces with the larger Gauss-Bonnet factor if the phase transition of the system is of second-order.Both of the observations dig out the fact that the higher curvature correction hinder the formation of the condensation of the vector operator,and the critical exponent of the system takes the mean field value 1/2,which is independent of the Gauss-Bonnet parameter and the spatial component of the gauge field.