  We study lattice effects in strongly coupled systems of fermions at a finite
density described by a holographic dual consisting of fermions in
Anti-de-Sitter space in the presence of a Reissner-Nordstrom black hole. The
lattice effect is encoded by a periodic modulation of the chemical potential
with a wavelength of order of the intrinsic length scales of the system. This
corresponds with a highly complicated "band structure" problem in AdS, which we
only manage to solve in the weak potential limit. The "domain wall" fermions in
AdS encoding for the Fermi surfaces in the boundary field theory diffract as
usually against the periodic lattice, giving rise to band gaps. However, the
deep infrared of the field theory as encoded by the near horizon AdS2 geometry
in the bulk reacts in a surprising way to the weak potential. The hybridization
of the fermions bulk dualizes into a linear combination of CFT1 "local quantum
critical" propagators in the bulk, characterized by momentum dependent
exponents displaced by lattice Umklapp vectors. This has the consequence that
the metals showing quasi-Fermi surfaces cannot be localized in band insulators.
In the AdS2 metal regime, where the conformal dimension of the fermionic
operator is large and no Fermi surfaces are present at low T/\mu, the lattice
gives rise to a characteristic dependence of the energy scaling as a function
of momentum. We predict crossovers from a high energy standard momentum AdS2
scaling to a low energy regime where exponents found associated with momenta
"backscattered" to a lower Brillioun zone in the extended zone scheme. We
comment on how these findings can be used as a unique fingerprint for the
detection of AdS2 like "pseudogap metals" in the laboratory.
