Crystalline geometries from fermionic vortex lattice with hyperscaling violation

TL;DR

This paper analytically explores the formation of fermionic crystalline geometries in gravity backgrounds with Lifshitz scaling and hyperscaling violation, revealing stable vortex lattice configurations and their dependence on scaling parameters.

Contribution

It introduces an analytical fermionic vortex lattice solution in gravity backgrounds with Lifshitz and hyperscaling violation, analyzing stability and geometric preferences.

Findings

Fermionic vortex lattice favors a triangular configuration.

Larger Lifshitz scaling $z$ enhances lattice stability.

Lower hyperscaling violation exponent $ heta$ leads to more stable lattices.

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.