Lifshitz scaling effects on the holographic p-wave superconductors coupled to nonlinear electrodynamics

We employ gauge/gravity duality to study the effects of Lifshitz scaling on the holographic p-wave superconductors in the presence of Born–Infeld nonlinear electrodynamics. By using the shooting method in the probe limit, we calculate the relation between critical temperature T${}_c$ and ρ${}^{z/d}$ numerically for different values of mass, nonlinear parameter b and Lifshitz critical exponent z in various dimensions. We observe that critical temperature decreases by increasing b, z or the mass parameter m which makes conductor/superconductor phase transition harder to form. In addition, we analyze the electrical conductivity and find the behavior of the real and the imaginary parts as a function of frequency, which depend on the model parameters. However, some universal behaviors are seen. For instance at low frequencies, the real part of conductivity shows a delta function behavior, while the imaginary part has a pole, which means that these two parts are connected to each other through the Kramers–Kronig relation. The behavior of the real part of the conductivity in the large frequency regime can be achieved by Re[σ]=ω${}^{D\text{â}\text{ˆ}\text{’}4}$. Furthermore, with increasing the Lifshitz scaling z, the energy gap and the minimum values of the real and imaginary parts become unclear.