Browsing by Subject "Landau levels"

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Open Access
Landau levels in lattices with long - range hopping
(American Physical Society, 2013) Atakişi, Hakan; Oktel, M. Özgür
Landau levels (LLs) are broadened in the presence of a periodic potential, forming a barrier for accurate simulation of the fractional quantum Hall effect using cold atoms in optical lattices. Recently, it has been shown that the degeneracy of the lowest Landau level (LLL) can be restored in a tight-binding lattice if a particular form of long-range hopping is introduced. In this paper, we investigate three problems related to such quantum Hall parent Hamiltonians in lattices. First, we show that there are infinitely many long-range hopping models in which a massively degenerate manifold is formed by lattice discretizations of wave functions in the continuum LLL. We then give a general method to construct such models, which is applicable to not only the LLL but also higher LLs. We use this method to give an analytic expression for the hoppings that restores the LLL, and an integral expression for the next LL. We also consider whether the space spanned by discretized LL wave functions is as large as the space spanned by continuum wave functions, and we find the constraints on the magnetic field for this condition to be satisfied. Finally, using these constraints and the first Chern numbers, we identify the bands of the Hofstadter butterfly that correspond to continuum LLs.
Open Access
Landau quantization of two-dimensional heavy holes, energy spectrum of magnetoexcitons and Auger-recombination lines
(2013) Podlesny I.V.; Moskalenko, S.A.; Hakioǧlu, T.; Kiselyov, A.A.; Gherciu L.
The Landau quantization of the two-dimensional (2D) heavy holes, its influence on the energy spectrum of 2D magnetoexcitons, as well as their optical orientation are studied. The Hamiltonian of the heavy holes is written in two-band model taking into account the Rashba spin-orbit coupling (RSOC) with two spin projections, but with nonparabolic dispersion law and third-order chirality terms. The most Landau levels, except three with m=0,1,2, are characterized by two quantum numbers m-3 and m for m≥3 for two spin projections correspondingly. The difference between them is determined by the third-order chirality. Four lowest Landau levels (LLLs) for heavy holes were combined with two LLLs for conduction electron, which were taken the same as they were deduced by Rashba in his theory of spin-orbit coupling (SOC) based on the initial parabolic dispersion law and first-order chirality terms. As a result of these combinations eight 2D magnetoexciton states were formed. Their energy spectrum and the selection rules for the quantum transitions from the ground state of the crystal to exciton states were determined. On this base such optical orientation effects as spin polarization and magnetoexciton alignment are discussed. The continuous transformation of the shake-up (SU) into the shake-down (SD) recombination lines is explained on the base of nonmonotonous dependence of the heavy hole Landau quantization levels as a function of applied magnetic field. © 2013 Elsevier B.V. All rights reserved.
Open Access
Optical properties of the two-dimensional magnetoexcitons under the influence of the Rashba spin-orbit coupling
(SPIE, 2011) Hakioglu, Tuğrul; Liberman, M.A.; Moskalenko, S.A.; Podlesny I.V.
The influence of the Rashba spin-orbit coupling on the two-dimensional (2D) electrons and holes in a strong perpendicular magnetic field leads to different results of the Landau quantization in different spin projections. In Landau gauge the unidimensional wave vector describing the free motion in one in-plane direction is the same for both spin projections, whereas the numbers of the Landau quantization levels are different. For electron in s-type conduction band they differ by one, as was established earlier by Rashba1, whereas for heavy holes in p-type valence band influenced by the 2D symmetry of the layer they differ by three. There are two lowest spin-splitted Landau levels for electrons as well as two lowest for holes. They give rise to four lowest energy levels of the 2D magnetoexcitons. It is shown that two of them are dipole-active in band-to-band quantum transitions, one is quadrupole-active and the fourth is forbidden. The optical orientation under the influence of the circularly polarized light leads to optical alignment of the magnetoexcitons with different orbital momentum projections on the direction of the external magnetic field. © 2011 SPIE.