Two-dimensional chiral crystals in the NJL model

TL;DR

This paper explores the phase structure of the NJL model, revealing that two-dimensional chiral crystals can be favored over homogeneous phases in certain regimes, with lattice structures becoming dominant at higher chemical potentials.

Contribution

It introduces the analysis of two-dimensional chiral crystal structures within the NJL model, highlighting their energetic favorability over homogeneous phases in specific parameter regions.

Findings

Two-dimensional chiral crystals are favored over homogeneous phases in certain regimes.

One-dimensional modulations are preferred over two-dimensional crystals in some regions.

Square and hexagonal lattices become favored at higher chemical potentials.

Abstract

We investigate the phase structure of the Nambu--Jona-Lasinio model at zero temperature, allowing for a two-dimensional spatial dependence of the chiral condensate. Applying the mean-field approximation, we consider various periodic structures with rectangular and hexagonal geometries, and minimize the corresponding free energy. We find that these two-dimensional chiral crystals are favored over homogeneous phases in a certain window in the region where the phase transition would take place when the analysis was restricted to homogeneous condensates. It turns out, however, that in this regime they are disfavored against a phase with a one-dimensional modulation of the chiral condensate. On the other hand, we find that square and hexagonal lattices eventually get favored at higher chemical potentials. Although stretching the limits of the model to some extent, this would support predictions from quarkyonic-matter studies.