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We study lattice effects in strongly coupled systems of fermions at a finitedensity described by a holographic dual consisting of fermions inAnti-de-Sitter space in the presence of a Reissner-Nordstrom black hole. Thelattice effect is encoded by a periodic modulation of the chemical potentialwith a wavelength of order of the intrinsic length scales of the system. Thiscorresponds with a highly complicated "band structure" problem in AdS, which weonly manage to solve in the weak potential limit. The "domain wall" fermions inAdS encoding for the Fermi surfaces in the boundary field theory diffract asusually against the periodic lattice, giving rise to band gaps. However, thedeep infrared of the field theory as encoded by the near horizon AdS2 geometryin the bulk reacts in a surprising way to the weak potential. The hybridizationof the fermions bulk dualizes into a linear combination of CFT1 "local quantumcritical" propagators in the bulk, characterized by momentum dependentexponents displaced by lattice Umklapp vectors. This has the consequence thatthe metals showing quasi-Fermi surfaces cannot be localized in band insulators.In the AdS2 metal regime, where the conformal dimension of the fermionicoperator is large and no Fermi surfaces are present at low T/\mu, the latticegives rise to a characteristic dependence of the energy scaling as a functionof momentum. We predict crossovers from a high energy standard momentum AdS2scaling to a low energy regime where exponents found associated with momenta"backscattered" to a lower Brillioun zone in the extended zone scheme. Wecomment on how these findings can be used as a unique fingerprint for thedetection of AdS2 like "pseudogap metals" in the laboratory.

Lattice potentials and fermions in holographic non Fermi-liquids: hybridizing local quantum criticality