Coherence length and magnetic penetration depth of the s-wave holographic superconductor model in Lifshitz spacetime

Abstract

The AdS/CFT duality provides us a powerful guidance to study the strong-coupled conformal field theory by using its dual weak-coupled gravity. One of the interesting applications of the duality is to study high temperature superconductors, which are supposed to be a strongly coupled system. According to Ginzburg-Landau theory, a superconductor can be characterized by only two parameters, coherence length and the magnetic penetration length ; therefore, it is important to determine the two parameters. In this paper in the D=d+2-dimensional Lifshitz black hole, we analytically study the static fluctuation of the scalar field with nonzero spatial momentum along one spatial coordinate of the boundary, and investigate the perturbation of the gravitational system near the critical temperature Tc. Working in the probe limit (the gauge field and scalar field do not backreact on the original metric), we obtain the superconducting coherence length via AdS/CFT (anti-de Sitter/conformal field theory) correspondence, which is (1/Tc)(1-(T/Tc)-1/2. Moreover, in the probe limit (the magnetic field does not backreact to the background spacetime), we have calculated the diamagnetic current induced by a homogeneous external magnetic field perpendicular to the surface of the superconductor. Then, we obtain the magnetic penetration depth (Tc-T)-1/2, which agrees with the result in Ginzburg-Landau theory. And these results strongly support the idea that a superconductor can be described by a charged scalar field on the Lifshitz black hole via AdS/CFT (anti-de Sitter/conformal field theory) duality.