# Chirality in the plane

## TL;DR

This paper introduces a method to construct three-dimensional chiral energy functions that induce two-dimensional chirality, using nonlinear rotational energy terms, and demonstrates explicit soliton solutions with chiral properties.

## Contribution

It presents a novel approach to achieve two-dimensional chirality directly from three-dimensional chiral models through nonlinear energy formulations.

## Key findings

- Explicit soliton solutions with two-dimensional chiral properties
- A new energy functional capturing three-dimensional to two-dimensional chirality transfer
- Demonstration of equations of motion for the proposed energy model

## Abstract

It is well-known that many three-dimensional chiral material models become non-chiral when reduced to two dimensions. Chiral properties of the two-dimensional model can then be restored by adding appropriate two-dimensional chiral terms. In this paper we show how to construct a three-dimensional chiral energy function which can achieve two-dimensional chirality induced already by a chiral three-dimensional model. The key ingredient to this approach is the consideration of a nonlinear chiral energy containing only rotational parts. After formulating an appropriate energy functional, we study the equations of motion and find explicit soliton solutions displaying two-dimensional chiral properties.