Holographic Lifshitz superconductors with six derivative correction

Abstract

We numerically realize the holographic s-wave conductor/superconductor model in the four-dimensional Lifshitz black hole with six derivative (SD) correction, and mainly study the influences of the Lifshitz parameter z as well as the SD parameter γ on the superconductor model. The results show that the increasing z inhibits the superconductor phase transition for large enough γ but enhances the phase transition for small enough γ. Meanwhile, the larger γ enhances the superconductor phase transition for small enough z (such as z=1,65), but inhibits the phase transition for large enough z, for example, z=85. Furthermore, for fixed γ, there exists a pronounced peak increasing with the improving z. However, for fixed z, the pronounced peak and the energy gap become weaker and weaker with the increasing γ. In addition, with the increasing z, the energy gap decreases for small enough γ but increases for large enough γ, which agrees well with the phase diagram of the critical temperature. Keywords: Holographic superconductor, Lifshitz gravity, High derivative correction