Optical properties of Born-Infeld-dilaton-Lifshitz holographic superconductors

In this letter, we first study the Lifshitz-dilaton holographic superconductors with nonlinear Born-Infeld (BI) gauge field and obtain the critical temperature of the system for different values of Lifshitz dynamical exponent, z, and nonlinear parameter b. We find that for fixed value of b, the critical temperature decreases with increasing z. This indicates that the increase of anisotropy between space and time (encoded in Lifshitz exponent z) prevents the phase transition. Also, for fixed value of z, the critical temperature decrease with increasing b. Then, we investigate the optical properties of (2+1) and (3+1)-dimensional BI-Lifshitz holographic superconductors in the presence of dilaton field. We explore the refractive index of the system. This is an important study, since it discloses the effects of anisotropy between space and time as well as nonlinearity of electrodynamics model and dimension on strange metamaterial behavior of the holographic superconductor. For z=1 and (2+1)-dimensional holographic superconductor, we observe negative real part for permittivity Re[ϵ] as frequency ω decreases. Thus, in low frequency region our superconductor exhibit metamaterial property. This behavior is independent of the nonlinear parameter and can be seen for either linear (b=0) and nonlinear (b≠0) electrodynamics. Interestingly, for (3+1)-dimensional Lifshitz-dilaton holographic superconductors, we observe metamaterial behavior neither in the presence of linear nor nonlinear electrodynamics.