## For a recent review on hyperfine interactions in QHE systems see: Vagner

- Physica B
- 1995

1 Excerpt

- Published 1997

– Two-dimensional electron gas (2DEG) under a strong perpendicular magnetic field in periodically modulated fields exhibits a peculiar discrete spectrum near the bottom of the spin-exciton band. The combined effect of the electrostatic modulation potential, and the e-h Coulomb attraction under the magnetic field, leads to nearly bound relative e-h oscillations perpendicular to the modulation axis, which have a characteristic Rydberg-like spectrum near the edge of the spin-exciton band. This low-lying, very narrow excitonic lines may significantly affect the spin and the charge transport in the thermally activated regime. The analysis of transport and relaxation phenomena in 2D electron systems (2DES) under strong magnetic fields near odd filling factors depends crucially on a clear physical understanding of the complicated electron spin-flip processes occuring within a Landau level, which are strongly modified by the electron correlations. The underlying elementary spin excitations are spin-excitons [1], [2], that are electron-hole pairs of opposite spins, having, due to the electron-electron interactions, a nonzero kinetic energy and strong k-dispersion. Spin-excitons constitute the building blocks, from which more complex spin textures can be formed. For example, at finite densities the spin-excitons “condense” [3] into skyrmionantiskyrmion pairs. These unusual topological excitations [4], [5] in the spin distribution of real 2D electron gas were observed, in NMR experiments, near the filling factor ν = 1 [6]. Further evidences for skyrmions in 2DES were found in transport and optical experiments [7], [8] At ν = 1 a macroscopically finite density of spin-excitons may appear when external potentials, like long-range impurities or the sample edge, diminish the Zeeman splitting. A () The Grenoble High Magnetic Field Laboratory is “Laboratoire conventionné à l’Université Joseph-Fourier de Grenoble”. c © Les Editions de Physique 558 EUROPHYSICS LETTERS detailed study of the spin-exciton energy spectrum in 2DES influenced by external potentials is, therefore, of crucial importance for understanding the physics of skyrmions in such systems and for analyzing the corresponding experimental results. In a recent paper [9] the general problem of a single spin-exciton in a 2DEG at filling factor ν = 1, subject to an external electrostatic potential, was exactly solved in the limit when the cyclotron energy, h̄ωc, is much larger than the effective Coulomb energy εc ≡ (e/κlB) √ (π/2) (κ is the dielectric constant of the 2DEG). A special case of a 1D periodic potential with period in the submicrometre range [10] was studied numerically there. In the present letter we reconsider the problem of spin-excitons at filling factor ν = 1 in the presence of a 1D periodic potential, focusing on spectral regions just below the continuum edge, where our numerical calculation, reported in [9], indicates the existence of discrete, or nearly discrete dispersion lines. Here we find, using a new analytical approach, that the corresponding low-lying excitations are electron-hole pairs, nearly localized in neighboring potential well and potential barrier along the modulation direction, while oscillating with respect to each other in the perpendicular direction. The corresponding 1D harmonic oscillator-like spectrum in the low-energy regime crossovers into a 1D Rydberg-like spectrum near the continuum edge. These low-lying excitations may significantly influence the spin and the charge transport in the thermally activated regime [11]. We shall express from now on all spatial variables in units of the magnetic length lB and all energies in units of the Coulomb energy εc. The general formalism developed in ref. [9] has shown that in the presence of an external electrostatic potential, U(r), the spin-exciton dispersion law can be obtained from a rather simple set of eigenvalue equations: [ε− ε ex(k )]f(k) = 2i ∑ q Ũ(q) sin([k× q] · n/2)f(k− q) , (1) where n ≡ B B , Ũ(q) ≡ U(q)e− 1 4 q 2 , and U(q) is the Fourier transform of the modulation potential with wave vector q. Here ε ex(k ) is the spin-exciton dispersion in a homogeneous sample [1], [2]: ε ex(k ) = εsp + εc[1− e 22BI0(k l B/4)] , (2) where I0 is a modified Bessel function, εsp ≡ gμBB, and g is the effective bare g-factor. A magnetoexciton with an electron-hole relative displacement (∆x,∆y) will move, due to the effect of the Coulomb attraction between the electron and the hole in a strong perpendicular magnetic field, with momentum, (kx, ky), proportional to the relative e-h coordinates rotated by 90◦, that is (kx, ky) ∝ (∆y,∆x). A 1D periodic potential, say along the x-axis, will therefore affect the transverse momentum (i.e. ky) dispersion of the exciton by influencing the longitudinal relative e-h coordinate (i.e. ∆x). For example, specifying the modulation potential: U(x) = V0 cos(2πx/a) , (3) eq. (1) reduces to [

@inproceedings{Bychkov1997NarrowresonanceSO,
title={Narrow-resonance states of 2D magnetic spin-exciton in periodically modulated fields},
author={Yu. A. Bychkov and Tsofar Maniv and I. D. Vagner and Peter Wyder},
year={1997}
}