Particle-Hole Symmetry and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mn>5</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math>Quantum Hall State

Lee, Sung-Sik; Ryu, Shinsei; Nayak, Chetan; Fisher, Matthew P. A.

doi:10.1103/physrevlett.99.236807

Cited by 428 publications

(577 citation statements)

References 27 publications

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“…These modes, which carry energy without net charge [2][3][4][5][6][7][8][9][10] , are at the focus of recent experimental and theoretical studies, and are encouraged by the advent of the search for Majorana quasiparticles 11,12 . Certain fractional states, dubbed as holeconjugate states 13,14 , with the most prominent one v ¼ 2/3, support reconstructed chiral edge modes, which due to interaction and disorder, give birth to counter propagating neutral modes [2][3][4] .…”

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confidence: 99%

Extracting net current from an upstream neutral mode in the fractional quantum Hall regime

et al. 2012

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Upstream neutral modes, counter propagating to charge modes and carrying energy without net charge, had been predicted to exist in some of the fractional quantum Hall states and were recently observed via noise measurements. Understanding such modes will assist in identifying the wavefunction of these states, as well as shedding light on the role of Coulomb interactions within edge modes. Here, operating mainly in the n ¼ 2/3 state, we place a quantum dot a few micrometres upstream of an ohmic contact, which serves as a 'neutral modes source'. We show that the neutral modes heat the input of the dot, causing a net thermo-electric current to flow through it. Heating of the electrons leads to a decay of the neutral mode, manifested in the vanishing of the thermo-electric current at T4110 mK. This set-up provides a straightforward method to investigate upstream neutral modes without turning to the more cumbersome noise measurements.

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confidence: 99%

Extracting net current from an upstream neutral mode in the fractional quantum Hall regime

et al. 2012

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“…[15][16][17][18][19][20] Recent tunneling shot-noise experiments have confirmed the e / 4 fundamental quasihole charge of the =5/ 2 state expected for the MR state. 21 Further recent evidence from the scaling behavior in dc transport experiments 22 at =5/ 2 best agrees with the particle-hole conjugate of MR. 23,24 Although the remaining observed filling fractions in the second Landau level have odd denominators, numerics indicate that the electron correlations for 7 / 3 Յ Յ 8 / 3 have a non-Laughlin character similar to that of =5/ 2, 25 and so only =14/ 5 is expected to be an Abelian state. Aside from the Abelian hierarchy states, the non-Abelian Read-Rezayi ͑RR͒ k-body clustered states 26 ͑which include MR͒ and their particle-hole conjugates are essentially the only single layer spin-polarized descriptions that have been proposed for these FQH plateaus.…”

Section: Introductionmentioning

confidence: 99%

Fractional quantum Hall hierarchy and the second Landau level

2008

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We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the =5/ 2 Moore-Read state, we construct explicit trial wave functions to describe the fractional quantum Hall effect in the second Landau level. The resulting hierarchy of states, which reproduces the filling fractions of all observed Hall conductance plateaus in the second Landau level, is characterized by electron pairing in the ground state and an excitation spectrum that includes nonAbelian anyons of the Ising type. We propose this as a unifying picture in which p-wave pairing characterizes the fractional quantum Hall effect in the second Landau level.

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“…Therefore, a Pfaffian/anti-Pfaffian phase transition happens in the B2 phase. This Pfaffian/anti-Pfaffian phase transition has been seen in the context of the ν = 5/2 fractional quantum Hall effect [22,23]. The model we present here is exactly the same as a toy model on square lattice to study the Pfaffian and anti-Pfaffian physics [22].…”

Section: Introductionmentioning

confidence: 78%

“…This Pfaffian/anti-Pfaffian phase transition has been seen in the context of the ν = 5/2 fractional quantum Hall effect [22,23]. The model we present here is exactly the same as a toy model on square lattice to study the Pfaffian and anti-Pfaffian physics [22]. The B1 and B2 phases when the next nearest neighbor hopping is absent are corresponding to the particle-hole symmetry is conserved or spontaneously broken.…”

Section: Introductionmentioning

confidence: 84%

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Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds

2008

Nuclear Physics B

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We construct an exactly soluble spin-1 2 model on a honeycomb lattice, which is a generalization of Kitaev model. The topological phases of the system are analyzed by study of the ground state sector of this model, the vortex-free states. Basically, there are two phases, A phase and B phase. The behaviors of both A and B phases may be studied by mapping the ground state sector into a general p-wave paired states of spinless fermions with tunable pairing parameters on a square lattice. In this p-wave paired state theory, the A phase is shown to be the strong paired phase, an insulating phase. The B phase may be either gapped or gapless determined by the generalized inversion symmetry is broken or not. The gapped B is the weak pairing phase described by either the Moore-Read Pfaffian state of the spinless fermions or anti-Pfaffian state of holes depending on the sign of the next nearest neighbor hopping amplitude. A phase transition between Pfaffian and anti-Pfaffian states are found in the gapped B phase. Furthermore, we show that there is a hidden SU(2) gauge symmetry in our model. In the gapped B phase, the ground state has a non-trivial topological number, the spectral first Chern number or the chiral central charge, which reflects the chiral anomaly of the edge state. We proved that the topological number is identified to the reduced eta-invariant and this anomaly may be cancelled by a bulk Wess-Zumino term of SO(3) group through an index theorem in 2+1 dimensions.

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Particle-Hole Symmetry and theν=52Quantum Hall State

Cited by 428 publications

References 27 publications

Extracting net current from an upstream neutral mode in the fractional quantum Hall regime

Extracting net current from an upstream neutral mode in the fractional quantum Hall regime

Fractional quantum Hall hierarchy and the second Landau level

Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds

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