Commensurability effects in holographic homogeneous lattices

An interesting application of the gauge/gravity duality to condensed matter physics is the description of a lattice via breaking translational invariance on the gravity side. by making use of global symmetries, it is possible to do so without scarifying homogeneity of the pertinent bulk solutions, which we thus term as “homogeneous holographic lattices.” due to their technical simplicity, these configurations have received a great deal of attention in the last few years and have been shown to correctly describe momentum relaxation and hence (finite) dc conductivities. however, it is not clear whether they are able to capture other lattice effects which are of interest in condensed matter. in this paper we investigate this question focusing our attention on the phenomenon of commensurability, which arises when the lattice scale is tuned to be equal to (an integer multiple of) another momentum scale in the system. we do so by studying the formation of spatially modulated phases in various models of homogeneous holographic lattices. our results indicate that the onset of the instability is controlled by the near horizon geometry, which for insulating solutions does carry information about the lattice. however, we observe no sharp connection between the characteristic momentum of the broken phase and the lattice pitch, which calls into question the applicability of these models to the physics of commensurability.