Crystalline Geometries from Fermionic Vortex Lattice

TL;DR

This paper investigates how charged fermions in an AdS$_2\times R^2$ background with magnetic field can spontaneously form vortex lattices, inducing electric fields and affecting thermodynamics, revealing new insights into holographic fermionic phases.

Contribution

It demonstrates the spontaneous formation of vortex lattices from fermions in a holographic setting and analyzes their impact on electric fields and thermodynamics.

Findings

Vortex lattice formation leads to an emergent electric field.

The lattice induces a finite charge density at the boundary.

Thermodynamic functions are corrected by lattice effects.

Abstract

We study charged Dirac fermions on an AdS$_2\times R^2$ background with a non-zero magnetic field. Under certain boundary conditions, we show that the charged fermion can make the background unstable, resulting in spontaneously formation of a vortex lattice. We observe that an electric field emerges in the back-reacted solution due to the vortex lattice constructed from spin polarized fermions. This electric field may be extended to the UV boundary which leads to a finite charge density. We also discuss corrections to the thermodynamic functions due to the lattice formation.