Exploring the UV and IR of a type-II holographic superconductor using a dyonic black hole

Abstract

AbstractIn this study, we investigate a type-II holographic superconductor with a perturbative scalar field over a (3 + 1)-dimensional electric and magnetically charged planar AdS black hole. We review the thermodynamical properties of the background relevant for the dual description of the Ginzburg–Landau density of superconducting states, showing that the adoption of a London gauge allows a consistent description of the Abrikosov vortex lattices, typical of type-II superconductors. We further derive a new expression for the upper critical magnetic field as a function of temperature in the grand canonical ensemble, supplementary to the one previously obtained in the canonical ensemble setup. These results confirm that our perturbative scalar field model consistently reproduces the well-known temperature behavior of the upper critical magnetic field according to the Ginzburg–Landau theory and other Abelian–Higgs holographic developments for type-II superconductors. We then continue with an original analysis of the scalar field equation in terms of a Schrödinger potential that led to the observation of bound states, a signal for the condensation of Cooper pairs. These results provide robust evidence for the existence of an IR order parameter near extremality. In view of this, we performed a closer inspection of the IR effective scalar equation in which the geometry adopts a Schwarzschild $$\hbox {AdS}_{2}\times {\mathbb {R}}^{2}$$ AdS 2 × R 2 structure, finding novel condensed bound states in the IR regime.