Holographic s -wave superconductors with Horndeski correction
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Regular Article - Theoretical Physics
Holographic s-wave superconductors with Horndeski correction Jun-Wang Lu1,a , Ya-Bo Wu2,b , Li-Gong Mi1, Hao Liao1, Bao-Ping Dong1 1 2
School of Physics and Electronics, Qiannan Normal University for Nationalities, Duyun 558000, People’s Republic of China Department of Physics, Liaoning Normal University, Dalian 116029, People’s Republic of China
Received: 4 March 2020 / Accepted: 20 June 2020 © The Author(s) 2020
Abstract Via both numerical and analytical methods, we build the holographic s-wave insulator/superconductor model in the five-dimensional AdS soliton with the Horndeski correction in the probe limit and study the effects of Horndeski parameter k on the superconductor model. For the fixed mass squared of the scalar field (m 2 ), the critical chemical potential μc increases with the larger Horndeski parameter k, which means that the increasing Horndeski correction hinders the superconductor phase transition. Meanwhile, above the critical chemical potential, the obvious pole arises in the low frequency of the imaginal part of conductivity, which signs the appearance of superconducting state. What is more, the energy of quasiparticle excitation decreases with the larger Horndeski correction. Furthermore, the critical exponent of the condensate (charge density) is 21 (1), which is independent of the Horndeski correction. In addition, the analytical results agree well with the numerical results. Subsequently, the conductor/superconductor model with Horndeski correction is analytically realized in the fourand five-dimensional AdS black holes. It is observed that the increasing Horndeski correction decreases the critical temperature and thus hinders the superconductor phase transition, which agrees with the numerical result in the previous works.
1 Introduction Due to the clear strong/weak dual dictionary, the AdS/CFT correspondence provides a powerful tool to study (d + 1) dimensional strongly coupled systems by means of its ddimensional weak AdS gravity [1,2]. In the recent years, the AdS/CFT correspondence and its generalized version (gauge/gravity duality) have been widely applied in many strong correlated systems [3–6], especially the holographic a e-mail:
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construction of the high critical temperature superconductor [7,8]. In contrast with the conventional superconductor, the high critical temperature superconductor is believed to involve strong interaction and thus its pair mechanism is one of the most challenges in condensed matter physics. The AdS/CFT correspondence obviously opens a new window to understand the properties of superconductors. In 2008, by using the Einstein-Abelian-Higgs system, the authors in Ref. [7] built numerically a holographic description of the s-wave conductor/superconductor model in the probe limit, and produced the main characters of the superconductor, such as the appearance of the scalar condensate accompanied by spontaneous breaking of
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