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We construct a higher derivative theory involving an axionic field and theWeyl tensor in four dimensional spacetime. Up to the first order of thecoupling parameters, the charged black brane solution with momentum dissipationin a perturbative manner is constructed. Metal-insulator transitions areimplemented when varying the system parameters at zero temperature. Also, westudy the transports including DC conductivity and optical conductivity at zerocharge density. We observe the exact particle-vortex duality for some specificmomentum dissipation strength.

Transport phenomena and Weyl correction in effective holographic theory of momentum dissipation