International Journal of Modern Physics B

A novel type of charged excitation, known as a Skyrmion, has recently been discovered in quantum Hall systems with filling factor near ν=1. A Skyrmion — which can be thought of as a topological twist in the spin density of the electron gas — has the same charge as an electron, but a much larger spin. In this review we present a detailed theoretical investigation of the optical properties of Skyrmions. Our results provide means for the optical detection of Skyrmions using photoluminescence (PL) spectroscopy. We first consider the optical properties of Skyrmions in disordered systems. A calculation of the luminescence energy reveals a special optical signature which allows us to distinguish between Skyrmions and ordinary electrons. Two experiments to measure the optical signature are proposed. We then turn to the optical properties of Skyrmions in pure systems. We show that, just like an ordinary electron, a Skyrmion may bind with a hole to form a Skyrmionic exciton. The Skyrmionic exciton can have a lower energy than the ordinary magnetoexciton. The optical signature of Skyrmions is found to be a robust feature of the PL spectrum in both disordered and pure systems.

In this paper we report calculations of some pseudospin textures for bilayer quantum hall systems with filling factor ν=1. The textures we study are isolated single meron solutions. Meron solutions have already been studied at great length by others by minimising the microscopic Hamiltonian between microscopic trial wavefunctions. Our approach is somewhat different. We calculate them by numerically solving the nonlinear integro-differential equations arising from extremisation of the effective action for pseudospin textures. Our results can be viewed as augmenting earlier results and providing a basis for comparison. Our differential equation approach also allow us to dilineate the impact of different physical effects like the pseudospin stiffness and the capacitance energy on the meron solution.

The Hierarchy of Fractional Quantum Hall (FQH) states have been studied here in the framework of chiral anomaly and Berry Phase. It is shown that the unambiguously observed FQH states with filling factor ν=p/q with p even or odd and q an odd integer can be considered from the viewpoint that the Berry phase associated with even number of vortices can be removed to the dynamical phase and the corresponding fermionic state attains a higher Landau level. This also leads to the fact that FQH states with even denominator filling factor can arise when we have pairs of degenerate electrons giving rise to the non-Abelian Berry phase which suggests that these FQH states correspond to non-Abelian Hall fluid. In this framework Integer Quantum Hall Effect (IQHE) as well as Fractional Quantum Hall Effect (FQHE) with filling factor ν=p/q with q odd or even can be studied in a unified way.

The effects of the sample's boundaries in the magnetic response of the charged anyon fluid at finite temperature are investigated. For the case of an infinite-strip sample it is shown that the Meissner effect takes place at temperatures lower than the fermion energy gap ω_c. The temperature dependence of the corresponding effective penetration depth is determined. At temperatures much larger than the scale ω_c, a different phase is found, in which the external magnetic field penetrates the fluid.

The two-dimensional Hubbard model is analyzed in the framework of the two-pole expansion. It is demonstrated that several theoretical approaches, when considered at their lowest level, are all equivalent and share the property of satisfying the conservation of the first four spectral momenta. It emerges that the various methods differ only in the way of fixing the internal parameters and that it exists a unique way to preserve simultaneously the Pauli principle and the particle–hole symmetry. A comprehensive comparison with respect to some general symmetry properties and the data from quantum Monte Carlo analysis shows the relevance of imposing the Pauli principle.

The Cooper pair (pairon) field operator ψ^†(r,t) changes, following Heisenberg's equation of motion. If the Hamiltonian ℋ contains pairon kinetic energies h₀, a condensation energy α(<0) and a repulsive point-like interpairon interaction βδ(r₁-r₂), β>0, the evolution equation for ψ is nonlinear, from which we obtain the Ginzburg–Landau (GL) equation: