Edge States and Chiral Solitons in Topological Hall and Chern–Simons Fields

Agalar M Agalarov,Alexander A Potapov,Alexander E Rassadin,,Telman A Gadzhimuradov

doi:10.18255/1818-1015-2018-1-133-139

Abstract

The multi-component extension problem of the (2+1) D -gauge topological Jackiw–Pi model describing the nonlinear quantum dynamics of charged particles in multi-layer Hall systems is considered. By applying the dimensional reduction (2 + 1) D → (1 + 1) D to Lagrangians with the Chern–Simons topologic fields , multi-component nonlinear Schrodinger equations for particles are constructed with allowance for their interaction. With Hirota‘s method, an exact two-soliton solution is obtained, which is of interest in quantum information transmission systems due to the stability of their propagation. An asymptotic analysis t →±∞ of soliton-soliton interactions shows that there is no backscattering processes. We identify these solutions with the edge (topological protected) states – chiral solitons – in the multi-layer quantum Hall systems. By applying the Hirota bilinear operator algebra and a current theorem, it is shown that, in contrast to the usual vector solitons, the dynamics of new solutions (chiral vector solitons) has exclusively unidirectional motion. The article is published in the author’s wording.

Highlights

The (2+1)D matter particles interacting with gauge topological Chern–Simons fields support solitons solutions [1, 2, 3, 4, 5, 6]
One of most interesting combination of the quantum and nonlinear properties of solitons arises in the (2+1)D-nonlinear Schrodinger equation gauged by a Chern–Simons fields (Jackiw–Pi model) [4, 5]
The interesting pattern is follow from condition of (18): if λk > 0 with the gauge coupling constant fixed (g > 0), the soliton in all components moves in one direction (Vk < 0) – it is the chiral solitons

Summary

Introduction

The (2+1)D matter particles interacting with gauge topological Chern–Simons fields support solitons solutions [1, 2, 3, 4, 5, 6]. In context of the Landay–Ginzburg mean field theory the Langrange density of model (1) can be considered as the model to describe the edge states (chiral solitons) of the Integer Quantum Hall Effects in monolayer systems [6]. As well know [2, 6] in the multi-layer systems to take place the Fractional Quantum Hall Effect due to inter-layer correlations of interacting anyons – the planar particles with unconventional statistics It is interesting the extension of the theory (1) to the multi-component case of matter field: ψ → ψj, j = 1, 2, . A simple analysis allows us to describe an exact solution for system Eqs. (6)

Nonlinear Schrodinger equation and two-component chiral solitons

Conclusion