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 Tc and rho 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[sigma]=omega D-4. Furthermore, with increasing the Lifshitz scaling z, the energy gap and the minimum values of the real and imaginary parts become unclear.