Analytical holographic superconductors in $Ad{S}_N$ Lifshitz topological black holes

Abstract

We present the analytic Lifshitz solutions for a scalar field model minimally coupled with the abelian gauge field in $N$ dimensions. We also consider the presence of cosmological constant $\Lambda$. The Lifshitz parameter $z$ appearing in the solution plays the role of the Lorentz breaking parameter of the model. We investigate the thermodynamical properties of the solutions and discuss the energy issue. Furthermore, we study the hairy black hole solutions in which the abelian gauge field breaks the symmetry near the horizon. In the holographic picture, it is equivalent to a second order phase transition. Explicitly we show that there exists a critical temperature which is a function of the Lifshitz parameter $z$. The system below the critical temperature becomes superconductor, but the critical exponent of the model remains the same of the usual holographic superconductors without the higher order gravitational corrections, in agreement with Ginzburg-Landau theories.

27 pages, final version accepted in IJGMMP

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• Lifshitz effects on holographic $p$-wave superfluid
• Modelling of a compact anisotropic star as an anisotropic fluid sphere in $f(T)$ gravity
• Holographic Conductivity for Logarithmic Charged Dilaton-Lifshitz Solutions
• Thermodynamics and gauge/gravity duality for Lifshitz black holes in the presence of exponential electrodynamics
• Revisiting holographic superconductors with hyperscaling violation
• Fidelity susceptibility for Lifshitz geometries via Lifshitz Holography
• Thermodynamics and and phase transition of topological dilatonic Lifshitz-like black holes
• Optical properties of Born-Infeld-dilaton-Lifshitz holographic superconductors
• Magnetic Phenomena in Holographic Superconductivity with Lifshitz Scaling