Magnetic Phenomena in Holographic Superconductivity with Lifshitz Scaling

TL;DR

This paper explores how Lifshitz scaling affects magnetic phenomena in holographic superconductors, revealing that higher dynamical critical exponents favor Type I behavior and influence vortex formation and critical magnetic fields.

Contribution

It demonstrates the application of a Ginzburg-Landau framework to Lifshitz holographic superconductors and computes physical quantities, including the critical magnetic field, for various z values.

Findings

Higher z leads to stronger Type I behavior.

Vortex formation is energetically less favorable at higher z.

Critical magnetic fields vary with the Lifshitz exponent.

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 exhibit 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.