Magnetic response of holographic Lifshitz superconductors: Vortex and Droplet solutions

In this paper a holographic model of s-wave superconductor with anisotropic Lifshitz scaling has been considered. In the presence of an external magnetic field our holographic model exhibits both vortex and droplet solutions. Based on analytic methods we have shown that the anisotropy has no effect on the vortex and droplet solutions whereas it may affect the condensation. Our vortex solution closely resembles the Ginzburg–Landau theory and a relation between the upper critical magnetic field and superconducting coherence length has been speculated from this comparison. Using Sturm–Liouville method, the effect of anisotropy on the critical parameters in insulator/superconductor phase transitions has been analyzed.