Notes on analytical study of holographic superconductors with Lifshitz scaling in external magnetic field

Abstract

We employ the matching method to analytically investigate the holographic superconductors with Lifshitz scaling in an external magnetic field. We discuss systematically the restricted conditions for the matching method and find that this analytic method is not always powerful to explore the effect of external magnetic field on the holographic superconductors unless the matching point is chosen in an appropriate range and the dynamical exponent $z$ satisfies the relation $z=d-1$ or $z=d-2$. From the analytic treatment, we observe that Lifshitz scaling can hinder the condensation to be formed, which can be used to back up the numerical results. Moreover, we study the effect of Lifshitz scaling on the upper critical magnetic field and reproduce the well-known relation obtained from Ginzburg-Landau theory.

14 pages, 5 figures

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• Lectures on Holographic Superfluidity and Superconductivity
• A Holographic Superconductor in an External Magnetic Field
• AdS/CFT superconductors with Power Maxwell electrodynamics: reminiscent of the Meissner effect
• Holographic superconductors with $z=2$ Lifshitz scaling
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• Meissner-like effect and conductivity of power-Maxwell holographic superconductors
• Effects of massive gravity on $p$-wave holographic superconductor
• Vortex structure deformation of rotating Lifshitz Holographic Superconductors
• Magnetic Phenomena in Holographic Superconductivity with Lifshitz Scaling
• Excited states of holographic superconductors with hyperscaling violation
• New black holes with hyperscaling violation and transports of quantum critical points with magnetic impurity
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