  The IR dynamics of effective holographic theories capturing the interplay
between charge density and the leading relevant scalar operator at strong
coupling are analyzed. Such theories are parameterized by two real exponents
$(\gamma,\delta)$ that control the IR dynamics. By studying the thermodynamics,
spectra and conductivities of several classes of charged dilatonic black hole
solutions that include the charge density back reaction fully, the landscape of
such theories in view of condensed matter applications is characterized.
Several regions of the $(\gamma,\delta)$ plane can be excluded as the extremal
solutions have unacceptable singularities. The classical solutions have
generically zero entropy at zero temperature, except when $\gamma=\delta$ where
the entropy at extremality is finite. The general scaling of DC resistivity
with temperature at low temperature, and AC conductivity at low frequency and
temperature across the whole $(\gamma,\delta)$ plane, is found. There is a
codimension-one region where the DC resistivity is linear in the temperature.
For massive carriers, it is shown that when the scalar operator is not the
dilaton, the DC resistivity scales as the heat capacity (and entropy) for
planar (3d) systems. Regions are identified where the theory at finite density
is a Mott-like insulator at T=0. We also find that at low enough temperatures
the entropy due to the charge carriers is generically larger than at zero
charge density.
