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Anisotropic Fermi Contour of (001) GaAs Holes in Parallel Magnetic Fields

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 Added by Dobromir Kamburov
 Publication date 2012
  fields Physics
and research's language is English




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We report a severe, spin-dependent, Fermi contour anisotropy induced by parallel magnetic field in a high-mobility (001) GaAs two-dimensional hole system. Employing commensurability oscillations created by a unidirectional, surface-strain-induced, periodic potential modulation, we directly probe the anisotropy of the two spin subband Fermi contours. Their areas are obtained from the Fourier transform of the Shubnikov-de Haas oscillations. Our findings are in semi-quantitative agreement with the results of parameter-free calculations of the energy bands.



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We demonstrate tuning of the Fermi contour anisotropy of two-dimensional (2D) holes in a symmetric GaAs (001) quantum well via the application of in-plane strain. The ballistic transport of high-mobility hole carriers allows us to measure the Fermi wavevector of 2D holes via commensurability oscillations as a function of strain. Our results show that a small amount of in-plane strain, on the order of $10^{-4}$, can induce significant Fermi wavevector anisotropy as large as 3.3, equivalent to a mass anisotropy of 11 in a parabolic band. Our method to tune the anisotropy textit{in situ} provides a platform to study the role of anisotropy on phenomena such as the fractional quantum Hall effect and composite fermions in interacting 2D systems.
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There has been a surge of recent interest in the role of anisotropy in interaction-induced phenomena in two-dimensional (2D) charged carrier systems. A fundamental question is how an anisotropy in the energy-band structure of the carriers at zero magnetic field affects the properties of the interacting particles at high fields, in particular of the composite fermions (CFs) and the fractional quantum Hall states (FQHSs). We demonstrate here tunable anisotropy for holes and hole-flux CFs confined to GaAs quantum wells, via applying textit{in situ} in-plane strain and measuring their Fermi wavevector anisotropy through commensurability oscillations. For strains on the order of $10^{-4}$ we observe significant deformations of the shapes of the Fermi contours for both holes and CFs. The measured Fermi contour anisotropy for CFs at high magnetic field ($alpha_mathrm{CF}$) is less than the anisotropy of their low-field hole (fermion) counterparts ($alpha_mathrm{F}$), and closely follows the relation: $alpha_mathrm{CF} = sqrt{alpha_mathrm{F}}$. The energy gap measured for the $ u = 2/3$ FQHS, on the other hand, is nearly unaffected by the Fermi contour anisotropy up to $alpha_mathrm{F} sim 3.3$, the highest anisotropy achieved in our experiments.
In the present work, we were able to identify and characterize a new source of in-plane optical anisotropies (IOAs) occurring in asymmetric DQWs; namely a reduction of the symmetry from $D_{2d}$ to $C_{2v}$ as imposed by asymmetry along the growth direction. We report on reflectance anisotropy spectroscopy (RAS) of double GaAs quantum wells (DQWs) structures coupled by a thin ($<2$ nm) tunneling barrier. Two groups of DQWs systems were studied: one where both QWs have the same thickness (symmetric DQW) and another one where they have different thicknesses (asymmetric DQW). RAS measures the IOAs arising from the intermixing of the heavy- and light- holes in the valence band when the symmetry of the DQW system is lowered from $D_{2d}$ to $C_{2v}$. If the DQW is symmetric, residual IOAs stem from the asymmetry of the QW interfaces; for instance, associated to Ga segregation into the AlGaAs layer during the epitaxial growth process. In the case of an asymmetric DQW with QWs with different thicknesses, the AlGaAs layers (that are sources of anisotropies) are not distributed symmetrically at both sides of the tunneling barrier. Thus, the system losses its inversion symmetry yielding an increase of the RAS strength. The RAS line shapes were compared with reflectance spectra in order to assess the heavy- and light- hole mixing induced by the symmetry breakdown. The energies of the optical transitions were calculated by numerically solving the one-dimensional Schrodinger equation using a finite-differences method. Our results are useful for interpretation of the transitions occurring in both, symmetric and asymmetric DQWs.
The MBE-grown GaAs/AlGaAs superlattice with Si-doped barriers has been used to study a 3D-2D transition under the influence of the in-plane component of applied magnetic field. The longitudinal magnetoresistance data measured in tilted magnetic fields have been interpreted in terms of a simple tight-binding model. The data provide values of basic parameters of the model and make it possible to reconstruct the superlattice Fermi surface and to calculate the density of states for the lowest Landau subbands. Positions of van Hove singularities in the DOS agree excellently with magnetoresistance oscillations, confirming that the model describes adequately the magnetoresistance of strongly coupled semiconductor superlattices.
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