  We construct the gravity dual of $d=4$, $\mathcal{N}=4$, SU($N_\rm{c}$) super
Yang-Mills theory, coupled to $N_\rm{f}$ flavors of dynamical quarks, at
non-zero temperature $T$ and non-zero quark density $N_\rm{q}$. The
supergravity solutions possess a regular horizon if $T>0$ and include the
backreaction of $N_\rm{c}$ color D3-branes and $N_\rm{f}$ flavor D7-branes with
$N_\rm{q}$ units of electric flux on their worldvolume. At zero temperature the
solutions interpolate between a Landau pole singularity in the ultraviolet and
a Lifshitz geometry in the infrared. At high temperature the thermodynamics is
directly sensitive to the Landau pole, whereas at low temperature it is not, as
expected from effective field theory. At low temperature and sufficiently high
charge density we find thermodynamic and dynamic instabilities towards the
spontaneous breaking of translation invariance.
