  In this work a holographic model with the charge current dual to a general
nonlinear electrodynamics (NLED) is discussed in the framework of massive
gravity. Massive graviton can breaks the diffeomorphism invariance in the bulk
and generates momentum dissipation in the dual boundary theory. The expression
of DC conductivities in a finite magnetic field are obtained, with the
backreaction of NLED field on the background geometry. General transport
properties in various limits are presented, and then we turn to the three of
specific NLED models: the conventional Maxwell electrodynamics, the
Maxwell-Chern-Simons electrodynamics, and the Born-Infeld electrodynamics, to
study the parameter-dependence of in-plane resistivity. Two mechanisms leading
to the Mott-insulating behaviors and negative magneto-resistivity are revealed
at zero temperature, and the role played by the massive gravity coupling
parameters are discussed.

High Energy Physics - Theory;Strongly Correlated Electrons;General Relativity and Quantum Cosmology