Excited states of holographic superconductors
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Springer
Received: November 15, Revised: April 6, Accepted: May 12, Published: June 1,
2019 2020 2020 2020
Yong-Qiang Wang,1 Tong-Tong Hu, Yu-Xiao Liu, Jie Yang and Li Zhao Institute of Theoretical Physics & Research Center of Gravitation, Lanzhou University, Lanzhou 730000, People’s Republic of China
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: In this paper we re-investigate the model of the anti-de Sitter gravity coupled to Maxwell and charged scalar fields, which has been studied as the gravitational dual to a superconductor for a long time since the famous work [Phys. Rev. Lett. 101 (2008) 031601]. By numerical method, we present a novel family of solutions of holographical superconductor with excited states, and find there exists a lower critical temperature in the corresponding excited state. Moreover, we study the condensate and conductivity in the excited states. It is very interesting that the conductivity σ of each excited state has an additional pole in Im[σ] and a delta function in Re[σ] arising at the low temperature inside the gap, which is just the evidence of the existence of excited states. Keywords: Holography and condensed matter physics (AdS/CMT), AdS-CFT Correspondence ArXiv ePrint: 1910.07734
1
Corresponding author.
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)013
JHEP06(2020)013
Excited states of holographic superconductors
Contents 1
2 Review of holographic superconductors
2
3 Numerical results 3.1 Condensates 3.2 Conductivity
4 5 7
4 Discussion
8
1
Introduction
In condensed matter physics, there is still no consensus on the mechanism of high temperature superconductivity. Over the past decade, the AdS/CFT correspondence [1–3] is one of the most important results from string theory, which establishes the relationship between the strongly correlated field on the boundary and a weak gravity theory in one higher-dimensional bulk spacetime. In the past ten years, the AdS/CFT correspondence has provided a novel way to study condensed matter theory, and received a great deal of attention. In the seminal papers [4–6], the authors investigated the model of a complex scalar field coupled to a U(1) gauge field in a (3 + 1)-dimensional Schwarzschild-AdS black hole and found that due to the U(1) symmetry breaking below the critical temperature Tc , the condensate of the scalar field could be interpreted as the Cooper pair-like superconductor condensate. Moreover, there exists a gap in the optical conductivity of the superconducting state, and the value of the gap is close to the value of a high temperature superconductor. Thus, this model can be regarded as the dual explanation to the high temperature superconductor. When replacing the scalar field with other matter fields, one can also obtain the condensate of matter fields corresponding to various kinds of holographic superconductors. For example, holographic d-wave model was constructed by introducing a symmetric, tr
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