Bimerons in Double Layer Quantum Hall Systems

TL;DR

This paper numerically studies bimeron pseudospin textures in double layer quantum Hall systems, analyzing their energy contributions and dependence on system parameters, providing a detailed approach to understanding their structure and interactions.

Contribution

It introduces a numerical method to solve coupled nonlinear PDEs for bimerons, extending previous analytical work and examining their energy components and parameter dependencies.

Findings

Bimerons have energy contributions from pseudospin stiffness, capacitance, and Coulomb interactions.

The numerical approach validates the approximation of bimerons as pairs of rigid merons.

The study reveals how bimeron textures vary with inter-meron and inter-layer distances.

Abstract

In this paper we discuss bimeron pseudo spin textures for double layer quantum hall systems with filling factor $\nu =1$. Bimerons are excitations corresponding to bound pairs of merons and anti-merons. Bimeron solutions have already been studied at great length by other groups by minimising the microsopic Hamiltonian between microscopic trial wavefunctions. Here we calculate them by numerically solving coupled nonlinear partial differential equations arising from extremisation of the effective action for pseudospin textures. We also calculate the different contributions to the energy of our bimerons, coming from pseudospin stiffness, capacitance and coulomb interactions between the merons. Apart from augmenting earlier results, this allows us to check how good an approximation it is to think of the bimeron as a pair of rigid objects (merons) with logarithmically growing energy, and with electric charge ${1 \over 2}$. Our differential equation approach also allows us to study the dependence of the spin texture as a function of the distance between merons, and the inter layer distance. Lastly, the technical problem of solving coupled nonlinear partial differential equations, subject to the special boundary conditions of bimerons is interesting in its own right.