We show a typical plot of the AC conductivity at
$\tfrac{T}{{T}_{{\rm{c}}}}\approx \tfrac{1}{5}$ for the fixed Weyl parameter
$\gamma =\tfrac{2}{50}$ (left) and the Lifshitz parameter
$z=\tfrac{5}{2}$(right), respectively, in figure
3. There are clear poles for the imaginary part of the conductivity Im[
σ] at the lower frequencies in all cases. From the Kramers-Kronig relation, these poles correspond to a delta function of the real part of the conductivity Re[
σ] at the vanishing frequency and thus indicate infinite DC conductivity. Moreover,
${\rm{Re}}[\sigma ]$ increases with frequency and diverges at large frequencies, which is also its universal character in five-dimensional spacetime [
11,
33,
42,
60]. Furthermore, in the case of
z = 1, there is a minimum for Im[
σ] in the intermediate frequency region, which corresponds to the energy gap of the superconductor
ωg. After the calculations, we find that the larger the Weyl correction, the smaller the value of
$\tfrac{{\omega }_{{\rm{g}}}}{{T}_{{\rm{c}}}}$; for instance,
$\tfrac{{\omega }_{{\rm{g}}}}{{T}_{{\rm{c}}}}=8.2821\left(\gamma =-\tfrac{3}{50}\right)$ ,
$8.1340\left(\gamma =-\tfrac{1}{50}\right),7.9200\left(\gamma =\tfrac{2}{50}\right)$. Meanwhile, the variation of
$\tfrac{{\omega }_{{\rm{g}}}}{{T}_{{\rm{c}}}}$ with respect to the Weyl parameter is very slow, which corresponds with the weak Weyl effects on the condensate. As we know, the location of the minimum of Im[
σ] corresponds to the frequency region where Re[
σ] increases quickly with frequency. As a result, for
z = 1, the phenomenon whereby the energy gap moves leftwards with increasing
γ corresponding to Re[
σ] increases more quickly with larger
γ. Interestingly, for a big enough Lifshitz parameter
z, such as
$z=\tfrac{5}{2}$ on the right-hand panel of figure
3, we find that Re[
σ] increases more and more slowly with increases in
γ. These different effects of the Lifshitz parameter
z on conductivity seem to be consistent with its effects on the condensate shown in figure
1. In addition, as displayed in the left-hand panel of figure
3, Re[
σ] is suppressed more and more obviously with an increase in the Lifshitz scaling, which is also observed in [
33,
42,
60]. In addition, we also calculated the conductivity for other cases with fixed
γ, for example,
$\gamma =-\tfrac{3}{50},\,0$ and qualitatively obtained the same results as the ones shown in the left-hand panel of figure
3.