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We explore the response of the momentum dissipation introduced by spatial linear axionic fields in a holographic model without self-duality, which is broke by Weyl tensor coupling to Maxwell field. It is found that for the positive Weyl coupling parameter γ > 0, the momentum dissipation, characterized by parameterα, drives an incoherent metallic state with a peak at low frequency into another incoherent metallic phase with a dip. While for γ < 0, an oppositive scenario is observed. Another interesting feature in our model is that for some observables including the DC conductivity, diffusion constant and susceptibility, there exists a certain value ofα, for which these observables are independent of γ . Finally, the electromagnetic (EM) duality is also studied and there is also a specific value ofα, for which the particle-vortex duality related by the change of the sign of γ in the boundary theory holds better than for other values of α.

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.Comment: 15 pages,6 figure

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