Interaction and dynamical binding of spin waves or excitons in quantum Hall systems

Abstract

Interaction between spin waves (or excitons) moving in the lowest Landau level is studied using numerical diagonalization. Becuse of complicated statistics obeyed by these composite particles, their effective interaction is completely different from the dipole-dipole interaction predicted in the model of independent (bosonic) waves. In particular, spin waves moving in the same direction attract one another which leads to their dynamical binding. The interaction pseudopotentials V ↑↑ (k) and V ↑↓ (k) for two spin waves with equal wavevectors k and moving in the same or opposite directions have been calculated and shown to obey power laws V (k) ∝ k α at small k. A high value of α ↑↑ ≈ 4 explains the occurrence of linear bands in the spin excitation spectra of quantum Hall droplets.

Metastable Bound States of the Two-Dimensional Bimagnetoexcitons in the Lowest Landau Levels Approximation

“…The variational parameter  of these functions was determined so as to minimize the energy of the bound state. It is determined as the average value of the Hamiltonian (2) calculated with the wave functions (4) as follows (7) The obtained results and the electron structure of the bound states are described below. 7…”

“…4 The strong dependence between the relative electron-hole and the center-of-mass motions in the frame of the spin waves as well as in the case of the magnetoexcitons was underlined in the Ref. [5][6][7]. The difference between these two processes consists in the fact that the spin waves appear in the conditions of the completely filled lowest Landau levels, whereas the magnetoexcitons are described in the conditions of almost empty Landau levels.…”

“…The main formula of our paper (7) contains in the denominator the function 2 (1 ( )) L   (5), which at some values of  has the values lower than unity. It obliges us to calculate exactly the complicated integrals in the numerator containing one, two and three Bessel functions using the textbooks [10][11][12] so as to avoid the miscalculation of the fraction (7). The…”

Interaction of spin excitations in quantum Hall systems

“…The calculations were carried out for N 30 and 50, and the two curves are essentially indistinguishable. Other features of the numerical data are susceptible to simple physical interpretation and will be reported elsewhere [4].…”

“…In Fig.2 we show the results for the interaction energy of two SW's with wave number k R (and 1 2 N) traveling parallel to one another [4]. The interaction energy V is measured in the units of e 2 2πR, where R is the radius of the spherical surface, and the abscissa is kλ , where λ is the magnetic length.…”