  Flat electronic bands have recently attracted a great deal of attention since
they provide a platform hosting a plethora of interaction-driven quantum
phases, as, for instance, experimentally observed in twisted bilayer graphene.
Motivated by these developments, we here provide a holographic construction of
flat bands, by reproducing the symmetry breaking pattern of a rather simple
Dirac fermion model at zero chemical potential. In the bulk we explicitly
include the backreaction to the corresponding Lifshitz geometry and compute the
dynamical critical exponent. Most importantly, we find that such a geometry is
unstable towards a nematic phase, exhibiting an anomalous Hall effect and
featuring a Drude-like shift of its spectral weight. Our findings should
motivate further studies of the quantum phases emerging from holographic flat
bands.
