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 (BI) nonlinear electrodynamics. By using the shooting method in the probe limit, we calculate the relation between critical temperature $T_{c}$ 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 real and imaginary parts as a function of frequency which depend on the model parameters. However, some universal behaviors are seen. For instance at low frequencies, 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 Kramers-Kronig relation. The behavior of real part of 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.