Anisotropic Quantum Hall Liquids at Intermediate Magnetic Fields
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Anisotropic Quantum Hall Liquids at Intermediate Magnetic Fields Orion Ciftja · Chidera Ozurumba · Francis Ujeyah
Received: 9 July 2012 / Accepted: 5 September 2012 / Published online: 15 September 2012 © Springer Science+Business Media, LLC 2012
Abstract The observation of significant magnetoresistance anisotropy of a twodimensional electronic system in very clean GaAs/AlGaAs heterostructure samples in presence of moderately large perpendicular magnetic fields is a striking example of novel anisotropic behavior in the quantum Hall regime. Anisotropy appears to be the strongest at quantum Hall even-denominator filled states for filling factors ν > 4 where several Landau levels are occupied. A possible explanation of these findings is due to the existence of charge density waves that are known to cause interesting phase transitions at high Landau levels. An alternative explanation of this phenomenon is to argue that the strongly correlated electronic system has stabilized in an orientationally ordered anisotropic quantum Hall liquid state. Quantum Monte Carlo calculations with a translationally invariant wave function in which rotation symmetry is broken indicate that this might be the case. Keywords Quantum Hall effect(s) · Two-dimensional electronic system · Strongly correlated electronic system · Landau levels 1 Introduction At low temperatures, a two-dimensional electron system (2DES) in a perpendicular magnetic field exhibits remarkable quantum phenomena such as the integer quantum Hall effect (IQHE) [1, 2] and the fractional quantum Hall effect (FQHE) [3]. A magnetic field applied perpendicularly to the 2DES sample leads to the creation of quantum states known as Landau levels (LLs). Such states have discrete energies, En = ωc (n + 1/2) where n = 0, 1, . . . is the quantum index, is Planck’s reduced constant and ωc is the cyclotron frequency. The LLs are hugely degenerate and their O. Ciftja () · C. Ozurumba · F. Ujeyah Department of Physics, Prairie View A&M University, Prairie View, TX 77446, USA e-mail: [email protected]
J Low Temp Phys (2013) 170:166–171
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degeneracy increases proportionally to the strength of the magnetic field. Thus, in presence of moderately large magnetic fields (but not very large) many LLs may be occupied with electrons. Laughlin [4] pioneered the use of microscopic wave functions to describe the novel nature of the principal FQHE liquid states in the lowest Landau level (LLL) at filling factors ν = 1/3 and 1/5. Other FQHE states at filling factors, ν = p/(2mp + 1) (p, m—integer) are now understood in terms of the composite fermion (CF) theory [5, 6]. The p → ∞ limit of the above sequence [7] results in even-denominator filled states which are believed to be compressible Fermi liquid phases [8]. In a very interesting experiment, Lilly et al. [9] studied high mobility molecular beam epitaxy (MBE) grown samples in the presence of moderately large magnetic fields (where LLs with indices n ≥ 2 were partially filled). They measured the magnetoresistance of the sample across two
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