  In this paper, we construct four-dimensional charged black branes of a
nonminimally coupled and self-interacting scalar field. In addition to the
scalar and Maxwell fields, the model involves two axionic fields homogeneously
distributed along the two-dimensional planar base manifold providing in turn a
simple mechanism of momentum dissipation. Interestingly enough, the horizon of
the solution can be set at two different positions, whose locations depend on
the axionic parameter, and in both cases there exists a wide range of values of
the nonminimal coupling parameter yielding physical acceptable solutions. For
one of our solutions, the allowed nonminimal coupling parameters take discrete
values and it turns out to be extremal since its has zero temperature. A
complete analysis of the thermodynamical features of the solutions is also
carried out. Finally, thanks to the mechanism of momentum dissipation, the
holographic DC conductivities of the solutions are computed in term of the
black hole horizon data, and we analyze the effects of the nonminimal coupling
parameter on these conductivities. For example, we notice that for the non
extremal solutions, there always exists a nonminimal coupling (which is greater
than the conformal one in four dimensions) yielding perfect conductivity in the
sense that the conductivity is infinite. Even more astonishing, the
conductivity matrix for the extremal solutions has a Hall effect-like behavior.
