Abstract
We investigate the effects of Lifshitz dynamical critical exponent z on a family of minimal D=4+1 holographic superconducting models, with a particular focus on magnetic phenomena. We see that it is possible to have a consistent Ginzburg–Landau approach to holographic superconductivity in a Lifshitz background. By following this phenomenological approach we are able to compute a wide array of physical quantities. We also calculate the Ginzburg–Landau parameter for different condensates, and conclude that in systems with higher dynamical critical exponent, vortex formation is more strongly unfavored energetically and exhibits a stronger Type I behavior. Finally, following the perturbative approach proposed by Maeda, Natsuume and Okamura, we calculate the critical magnetic field of our models for different values of z.
Highlights
The AdS/CFT correspondence [1] is one of the most important developments in theoretical physics in recent years
We investigate the effects of Lifshitz dynamical critical exponent z on a family of minimal D = 4 + 1 holographic superconducting models, with a particular focus on magnetic phenomena
Throughout this paper, for both brevity and simplicity, we will choose to work with the integer values z = 1, 2. This suits perfectly our primary objective, stated in the introduction, which is to have a general idea of how the dynamical critical exponent z affects our holographic superconductor with respect to its behavior in the usual (z = 1) isotropic realization of the gauge/gravity duality
Summary
The AdS/CFT correspondence [1] is one of the most important developments in theoretical physics in recent years. We will initially consider our minimal model in general dimensions, we will focus our attention on the D = 5 case The reason for this choice of dimension is that, as noted in [18, 19], dimensionality plays an important role in the way external magnetic fields act in the dual superconducting system. While high-Tc samples are typically composed of 2-dimensional CuO2 layers (cuprate superconductors), it is important to examine the effect of thickness when the system is probed by external magnetic fields In this respect, in this paper we see that it is possible to have a consistent GinzburgLandau phenomenological approach to holographic superconductivity [19] in a Lifshitz background.
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