  We present a class of holographic models that behave effectively as
prototypes of Mott insulators, materials where electron-electron interactions
dominate transport phenomena. The main ingredient in the gravity dual is that
the gauge-field dynamics contains self-interactions by way of a particular type
of non-linear electrodynamics. The electrical response in these models exhibits
typical features of Mott-like states: i) the low-temperature DC conductivity is
unboundedly low; ii) metal-insulator transitions appear by varying various
parameters; iii) for large enough self-interaction strength, the conductivity
can even decrease with increasing doping (density of carriers), which appears
as a sharp manifestation of `traffic-jam'-like behaviour; iv) the insulating
state becomes very unstable towards superconductivity at large enough doping.
We exhibit some of the properties of the resulting insulator-superconductor
transition, which is sensitive to the amount of disorder in a specific way.
These models imply a clear and generic correlation between Mott behaviour and
significant effects in the nonlinear electrical response. We compute the
nonlinear current-voltage curve in our model and find that indeed at large
voltage the conductivity is largely reduced.
