Measurements of quasiparticle tunneling in the υ= 5/2 fractional quantum Hall state

Physical review. B, Condensed matter (Impact Factor: 3.77). 04/2012; 85(16). DOI: 10.1103/PhysRevB.85.165321

ABSTRACT Some models of the 5/2 fractional quantum Hall state predict that the quasiparticles, which carry the charge, have non-Abelian statistics: exchange of two quasiparticles changes the wave function more dramatically than just the usual change of phase factor. Such non-Abelian statistics would make the system less sensitive to decoherence, making it a candidate for implementation of topological quantum computation. We measure quasiparticle tunneling as a function of temperature and dc bias between counterpropagating edge states. Fits to theory give e*, the quasiparticle effective charge, close to the expected value of e/4 and g, the strength of the interaction between quasiparticles, close to 3/8. Fits corresponding to the various proposed wave functions, along with qualitative features of the data, strongly favor the Abelian 331 state.

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    ABSTRACT: Two recent experiments [I. P. Radu et al., Science 320, 899 (2008) and X. Lin et al., Phys. Rev. B 85, 165321 (2012)] measured the temperature and voltage dependence of the quasiparticle tunneling through a quantum point contact in the \nu= 5/2 quantum Hall liquid. The results led to conflicting conclusions about the nature of the quantum Hall state. In this paper, we show that the conflict can be resolved by recognizing different geometries of the devices in the experiments. We argue that in some of those geometries there is significant unscreened electrostatic interaction between the segments of the quantum Hall edge on the opposite sides of the point contact. Coulomb interaction affects the tunneling current. We compare experimental results with theoretical predictions for the Pfaffian, SU(2)_2, 331 and K=8 states and their particle-hole conjugates. After Coulomb corrections are taken into account, measurements in all geometries agree with the spin-polarized and spin-unpolarized Halperin 331 states.
    Physical review. B, Condensed matter 06/2013; 88(8). · 3.77 Impact Factor
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    ABSTRACT: We discuss the orbital effect of a tilted magnetic field on the quantum Hall effect in parabolic quantum wells. Many-body states realized at the fractional 1/3 and 1/2 filling of the second electronic subband are studied using finite-size exact diagonalization. In both cases, we obtain the phase diagram consisting of a fractional quantum Hall fluid phase that persists for moderate tilts, and eventually undergoes a direct transition to the stripe phase. It is shown that tilting of the field probes the geometrical degree of freedom of fractional quantum Hall fluids, and can be partly related to the effect of band-mass anisotropy.
    Physical review. B, Condensed matter 06/2013; 87(24). · 3.77 Impact Factor
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    ABSTRACT: We have studied the $\nu=5/2$ fractional quantum Hall state in the regime of extremely low densities, for which the Landau level mixing parameter $\kappa$ spans the so far unexplored $2.52<\kappa<2.82$ range. In the vicinity of $\kappa = 2.6$ an unexpectedly large change in the density dependence of the energy gap is observed which is suggestive of a transition in the $\nu=5/2$ state. Origins of such a transition are discussed, including the possibility of a topological phase transition.


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