Abstract
We analytically investigate the phase transition between the holographic insulator and superconductor with Weyl corrections by using the variational method for the Sturm–Liouville eigenvalue problem. We find that similar to the curvature corrections, in p-wave model, the higher Weyl couplings make the insulator/superconductor phase transition harder to occur. However, in s-wave case the Weyl corrections do not influence the critical chemical potential, which is in contrast to the effect caused by the curvature corrections. Moreover, we observe that the Weyl corrections will not affect the critical phenomena and the critical exponent of the system always takes the mean-field value in both models. Our analytic results are found to be in good agreement with the numerical findings.
Highlights
The anti-de Sitter/conformal field theory (AdS/CFT) correspondence [1], which relates a string theory in AdS spacetime to a conformal field theory living on its boundary, has motivated the development of dual gravity models to describe strongly correlated systems in condensed matter physics [2]
Using a five-dimensional AdS soliton background coupled to a Maxwell field and a scalar field, Nishioka et al first constructed a model describing an insulator/superconductor phase transition at zero temperature in the probe limit where the backreaction of matter fields on the spacetime metric is neglected [7]
It is found that when the chemical potential is sufficiently large beyond a critical value μc, the AdS soliton becomes unstable to form scalar hair and a second order phase transition can happen, which can be used to describe the transition between the insulator and superconductor
Summary
The anti-de Sitter/conformal field theory (AdS/CFT) correspondence [1], which relates a string theory in AdS spacetime to a conformal field theory living on its boundary, has motivated the development of dual gravity models to describe strongly correlated systems in condensed matter physics [2]. Considering the potential applications to the condensed matter physics, many authors have constructed various s-, p- and d-wave holographic superconductor models in the AdS black hole background, for reviews, see Ref. Using a five-dimensional AdS soliton background coupled to a Maxwell field and a scalar field, Nishioka et al first constructed a model describing an insulator/superconductor phase transition at zero temperature in the probe limit where the backreaction of matter fields on the spacetime metric is neglected [7]. We will generalize the S-L method to study holographic insulator/superconductor phase transition with Weyl corrections in the AdS soliton background. We will study the model of the p-wave insulator/superconductor phase transition with Weyl corrections in the five-dimensional AdS soliton spacetime by considering an SU (2) Yang-Mills action with Weyl corrections in the bulk theory [19].
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