Gauged Lifshitz model with Chern-Simons term

TL;DR

This paper introduces a gauged Lifshitz model with a Chern-Simons term, exploring classical solutions and revealing oscillatory behaviors similar to modulated phases, depending on parameter choices.

Contribution

It presents a novel Lifshitz scalar field model with Chern-Simons coupling, analyzing its classical solutions and identifying conditions for oscillatory and vortex behaviors.

Findings

Positive beta ensures energy positivity.

Parameter domains influence field behavior significantly.

Oscillatory solutions resemble modulated phases in Lifshitz systems.

Abstract

We present a gauged Lifshitz Lagrangian including second and forth order spatial derivatives of the scalar field and a Chern-Simons term, and study non-trivial solutions of the classical equations of motion. While the coefficient beta of the forth order term should be positive in order to guarantee positivity of the energy, the coefficient alpha of the quadratic one need not be. We investigate the parameter domains finding significant differences in the field behaviors. Apart from the usual vortex field behavior of the ordinary relativistic Chern-Simons-Higgs model, we find in certain parameter domains oscillatory solutions reminiscent of the modulated phases of Lifshitz systems.