Holographic s -wave superconductors with conformal anomaly correction
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Holographic s-wave superconductors with conformal anomaly correction Jun-Wang Lu1,2,a
, Huai-Fan Li3,b , Ya-Bo Wu4,c
1 School of Physics and Electronics, Qiannan Normal University for Nationalities, Duyun 558000, People’s
Republic of China
2 CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences,
Beijing 100190, People’s Republic of China
3 Department of Physics, Shanxi Datong University, Datong 037009, People’s Republic of China 4 Department of Physics, Liaoning Normal University, Dalian 116029, People’s Republic of China
Received: 29 May 2020 / Accepted: 8 November 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We build a holographic s-wave conductor/superconductor model and an insulator/superconductor model in the four-dimensional conformal anomaly corrected (CAC) AdS gravity. The effects of CAC parameter α are studied using both numerical and analytical methods in the probe approximation. Concretely, when the CAC parameter increases, the critical temperature increases for the conductor/superconductor phase transition, while the critical chemical potential decreases for the insulator/superconductor case, which suggests that the increasing CAC parameter enhances both superconducting phase transitions. Meanwhile, below the critical temperature or beyond the critical chemical potential, the scalar hair begins to condense, and the condensed phases are found to be thermodynamically stable. The critical behaviors obtained from numerics are confirmed by our analytical analysis. In addition, the energy gap in the conductor/superconductor model decreases monotonically with the increasing CAC parameter.
1 Introduction The AdS/CFT correspondence provides a powerful tool to study d-dimensional strongly coupled systems from its (d + 1)-dimensional gravitational theory in AdS spacetime [1]. In the recent years, the correspondence and its generalized version (the so-called gauge/gravity duality) have been widely applied in various strongly correlated systems [2–7], especially the high temperature superconductor [8,9]. The high temperature superconductor (with the critical temperature usually larger than 39K ) is believed to involve strong interaction. To understand its properties and, in particular, the microscopic mechanism are still one of the biggest challenges in condensed matter physics. The AdS/CFT correspondence naturally opens a new window to study the properties of high temperature superconductors. By using the Einstein-Abelian-Higgs
a e-mail: [email protected] (corresponding author) b e-mail: [email protected] c e-mail: [email protected]
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system, the authors of Refs. [8,10] built a holographic description of the s-wave conductor/superconductor model, where the main characters of a superconductor were reproduced, such as the appearance of the condensate accompanied by spontaneously breaking of the U (1) symm
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