Crystalline geometries from fermionic vortex lattice with hyperscaling violation

Abstract: We analytically consider the spontaneous formation of a fermionic crystalline geometry in a gravity background with Lifshitz scaling and/or hyperscaling violation. Fermionic vortex lattice solution sourced by the lowest Laundau level has been obtained. Thermodynamic analysis shows that the fermionic vortex lattice favors a triangular configuration, regardless of the values of the Lifshitz scaling $z$ and the hyperscaling violation exponent $\theta$. Our results also show that the larger $z$ or lower $\theta$ leads to more stable lattices thermodynamically.