Chern-Simons Solitons in Quantum Potential

TL;DR

This paper explores self-dual Chern-Simons solitons influenced by quantum potential, revealing quantization conditions, a hierarchy of models, and discovering new localized solitons relevant to Bloch electrons near energy band boundaries.

Contribution

It introduces a hierarchy of Chern-Simons gauged nonlinear Schrödinger models with quantized parameters and identifies new exponentially localized solitons in this framework.

Findings

Quantization of Chern-Simons coupling constant and quantum potential strength.

Connection of the Jackiw-Pi model to the first hierarchy member.

Discovery of new localized Chern-Simons solitons near energy band boundaries.

Abstract

The self-dual Chern-Simons solitons under the influence of the quantum potential are considered. The single-valuedness condition for an arbitrary integer number $N \ge 0$ of solitons leads to quantization of Chern-Simons coupling constant $\kappa = m {e^{2} \over g}$, and the integer strength of quantum potential $s = 1 - m^{2}$. As we show, the Jackiw-Pi model corresponds to the first member (m = 1) of our hierarchy of the Chern-Simons gauged nonlinear Schr\"odinger models, admitting self-dual solitons. New type of exponentially localized Chern-Simons solitons for the Bloch electrons near the hyperbolic energy band boundary are found.