Higher derivatives driven symmetry breaking in holographic superconductors
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Regular Article - Theoretical Physics
Higher derivatives driven symmetry breaking in holographic superconductors Hai-Li Li1, Guoyang Fu2 , Yan Liu1, Jian-Pin Wu2,a , Xin Zhang1,3,4,b 1
Department of Physics, College of Sciences, Northeastern University, Shenyang 110819, China Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China 3 Ministry of Education’s Key Laboratory of Data Analytics and Optimization for Smart Industry, Northeastern University, Shenyang 110819, China 4 Center for High Energy Physics, Peking University, Beijing 100080, China
2
Received: 16 October 2019 / Accepted: 22 January 2020 © The Author(s) 2020
Abstract In this paper, we construct a novel holographic superconductor from higher derivative (HD) gravity involving a coupling between the complex scalar field and the Weyl tensor. This HD coupling term provides a near horizon effective mass squared, which can violates IR Breitenlohner– Freedman (BF) bound by tuning the HD coupling and induces the instability of black brane such that the superconducting phase transition happens. We also study the properties of the condensation and the conductivity in the probe limit. We find that a wider extension of the superconducting energy gap ranging from 4.6 to 10.5 may provide a novel platform to model and interpret the phenomena in the real materials of high temperature superconductor.
1 Introduction Based on AdS/CFT (Anti-de Sitter/Conformal Field theory) correspondence [1–5], a holographic superconductor model is suggested in [6]. In this model, a complex charged scalar field is introduced in Schwarzschild-AdS (SS-AdS) black brane to spontaneously break the U(1) symmetry and transform to a charged scalar hair black brane. The charged scalar field in the bulk is dual to the “Cooper pair” operator at the boundary and the vacuum expectation value is the order parameter. The symmetry breaking is introduced by a negative mass squared of the scalar field, which is allowed due to the Breitenlohner–Freedman (BF) bound in AdS spacetime [6,7]. In [8], a positive mass squared situation was studied. It was shown that as m 2 increase the phase space folds due to the non-linearity of the equations of motion, so the two nearby points in the phase space can represent symmetry breaking. a e-mail:
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And they show that for a small positive mass squared, the results is not much different from the negative case which has been studied in [9–13]. In [14], they discuss the superconductivity instability by studying the normalisable solution of equations of motion (EOMs) for the charged scalar field on top of RN-AdS black brane geometry. In essence, it is that the near horizon effective mass squared is below the AdS2 BF bound, which induces the instability. At the same time, we also require that the mass squared is above the boundary AdS4 BF bound, which guarantees the stability of scalar field at the boundary. In this paper
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