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Register a new userEnhancement of the $ u = 5/2$ Fractional Quantum Hall State in a Small In-Plane Magnetic Field
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Guangtong Liu G. T. Liu
Publication date
2012
fields
Physics
and research's language is
English
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Using a 50-nm width, ultra-clean GaAs/AlGaAs quantum well, we have studied the Landau level filling factor $ u = 5/2$ fractional quantum Hall effect in a perpendicular magnetic field $B sim$ 1.7 T and determined its dependence on tilted magnetic fields. Contrary to all previous results, the 5/2 resistance minimum and the Hall plateau are found to strengthen continuously under an increasing tilt angle $0 < theta < 25^circ$ (corresponding to an in-plane magnetic field 0 $<$ $B_parallel$ $< 0.8$ T). In the same range of $theta$ the activation gaps of both the 7/3 and the 8/3 states are found to increase with tilt. The 5/2 state transforms into a compressible Fermi liquid upon tilt angle $theta > 60^circ$, and the composite fermion series [2+$p/(2ppm1)$], $p =$ 1, 2 can be identified. Based on our results, we discuss the relevance of a Skyrmion spin texture at $ u = 5/2$ associated with small Zeeman energy in wide quantum wells, as proposed by W$acute{text o}$js $et$ $al$., Phys. Rev. Lett. 104, 086801 (2010).
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We report quantitative measurements of the impact of alloy disorder on the $ u=5/2$ fractional quantum Hall state. Alloy disorder is controlled by the aluminum content $x$ in the Al$_x$Ga$_{1-x}$As channel of a quantum well. We find that the $ u=5/2$ state is suppressed with alloy scattering. To our surprise, in samples with alloy disorder the $ u=5/2$ state appears at significantly reduced mobilities when compared to samples in which alloy disorder is not the dominant scattering mechanism. Our results highlight the distinct roles of the different types of disorder present in these samples, such as the short-range alloy and the long-range Coulomb disorder.
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The evolution of the fractional quantum Hall state at filling 5/2 is studied in density tunable two-dimensional electron systems formed in wide wells in which it is possible to induce a transition from single to two subband occupancy. In 80 and 60 nm wells, the quantum Hall state at 5/2 filling of the lowest subband is observed even when the second subband is occupied. In a 50 nm well the 5/2 state vanishes upon second subband population. We attribute this distinct behavior to the width dependence of the capacitive energy for intersubband charge transfer and of the overlap of the subband probability densities.
We compare the energy gap of the u=5/2 fractional quantum Hall effect state obtained in conventional high mobility modulation doped quantum well samples with those obtained in high quality GaAs transistors (heterojunction insulated gate field-effect transistors). We are able to identify the different roles that long range and short range disorders play in the 5/2 state and observe that the long range potential fluctuations are more detrimental to the strength of the 5/2 state than short-range potential disorder.
We discuss the implications of approximate particle-hole symmetry in a half-filled Landau level in which a paired quantum Hall state forms. We note that the Pfaffian state is not particle-hole symmetric. Therefore, in the limit of vanishing Landau level mixing, in which particle-hole transformation is an exact symmetry, the Pfaffian spontaneously breaks this symmetry. There is a particle-hole conjugate state, which we call the anti-Pfaffian, which is degenerate with the Pfaffian in this limit. We observe that strong Landau level mixing should favor the Pfaffian, but it is an open problem which state is favored for the moderate Landau level mixing which is present in experiments. We discuss the bulk and edge physics of the anti-Pfaffian. We analyze a simplified model in which transitions between analogs of the two states can be studied in detail. Finally, we discuss experimental implications.
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