Bimerons in Double Layer Quantum Hall Systems

Abstract

In this paper we discuss bimeron pseudo spin textures for double layer quantum hall systems with filling factor $ν=1$. 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.