  In this letter, we study the charge response from higher derivatives over the
background with homogeneous disorder introduced by axions. We first explore the
bounds on the higher derivatives coupling from DC conductivity and the
anomalies of causality and instabilities. Our results indicate no tighter
constraints on the coupling than that over Schwarzschild-AdS (SS-AdS)
background. And then we study the optical conductivity of our holographic
system. We find that for the case with $\gamma_1<0$ and the disorder strength
$\hat{\alpha}<2/\sqrt{3}$, there is a crossover from a coherent to incoherent
metallic phase as $\hat{\alpha}$ increases. When $\hat{\alpha}$ is beyond
$\hat{\alpha}=2/\sqrt{3}$ and further amplified, a peak exhibits again at low
frequency. But it cannot be well fitted by the standard Drude formula and new
formula for describing this behavior shall be called for. While for the
holographic system with the limit of $\gamma_1\rightarrow 1/48$, the disorder
effect drives the hard-gap-like at low frequency into the soft gap and
suppresses the pronounced peak at medium frequency.
