We study analytically the [Formula: see text]-wave holographic superconductors with Lifshitz scaling in the presence of external magnetic field. The vortex lattice solutions of the model have also been obtained with different Lifshitz scaling. Our results imply that holographic [Formula: see text]-wave superconductor is indeed a type II one even for different Lifshitz scaling. This is the same as the conventional [Formula: see text]-wave superconductors in the Ginzburg–Landau (GL) theory. Our results also indicates that the dynamical exponent [Formula: see text] cannot affect the droplet solutions, and the vortex lattice solutions receive its effects only in the radial part. This naively implies that it does not have direct influence on the shape of vortex lattice even after the higher-order corrections are taken into consideration (away from the phase transition point [Formula: see text]). However, it has effects on the upper critical magnetic field [Formula: see text] through the fact that a larger [Formula: see text] results in a smaller [Formula: see text] and therefore influences the size (characterized by [Formula: see text]) of the vortex lattices. Furthermore, close comparisons between our results and those of the GL theory reveal the fact that the upper critical magnetic field [Formula: see text] is inversely proportional to the square of the superconducting coherence length [Formula: see text], regardless of the anisotropy between space and time.
Analytical Calculation on Critical Magnetic Field in Holographic Superconductors with Backreaction
