Nonlinear Quasiparticle Tunneling between Fractional Quantum Hall Edges

Roddaro, Stefano; Pellegrini, Vittorio; Beltram, Fabio; Biasiol, G.; Sorba, L.; Raimondi, Roberto; Vignale, Giovanni

doi:10.1103/physrevlett.90.046805

Cited by 63 publications

(84 citation statements)

References 22 publications

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“…The anti-Pfaffian order corresponds [27] to g = 1/2. Experimental results for g exceed [19,27,37,38] the theoretical values at all fractional filling factors [39]. This is explained by a combination of three mechanisms that suppress low-temperature tunneling: Coulomb repulsion across the constriction [27,38], edge reconstruction [40,41] and dissipation [42].…”

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confidence: 93%

Stabilization of the Particle-Hole Pfaffian Order by Landau-Level Mixing and Impurities That Break Particle-Hole Symmetry

2016

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Numerical results suggest that the quantum Hall effect at ν = 5/2 is described by the Pfaffian or anti-Pfaffian state in the absence of disorder and Landau level mixing. Those states are incompatible with the observed transport properties of GaAs heterostructures, where disorder and Landau level mixing are strong. We show that the recent proposal of a PH-Pfaffian topological order by Son is consistent with all experiments. The absence of the particle-hole symmetry at ν = 5/2 is not an obstacle to the existence of the PH-Pfaffian order since the order is robust to symmetry breaking.One of the most interesting features of topological insulators and superconductors is their surface behavior. A great variety of gapless and topologically-ordered gapped surface states have been proposed [1]. Such states are anomalous, that is, they can only exist on the surface of a 3D bulk system and not in a stand-alone film. Finding experimental realizations of exotic surface states proved difficult and most of them have remained theoretical proposals. Thus, it came as a surprise when Son [2] argued that one such exotic state [3], made of Dirac composite fermions with the particle-hole symmetry (PHS), has long been observed experimentally in a two-dimensional system: the electron gas in the quantum Hall effect (QHE) with the filling factor ν = 1/2.At first sight, Son's idea violates the fermion doubling theorem [4]. However, the theorem does not apply to interacting systems such as the one Son considered. Besides, in contrast to the conditions of the doubling theorem, the action of PHS is nonlocal in QHE since it involves filling a Landau level. Interestingly, the picture of composite Dirac fermions sheds light on the geometrical resonance experiments [5] which the classic theory [6] of the 1/2 state could not explain. In this paper we show that a closely related idea [2] provides a natural explanation of the observed phenomenology on the enigmatic QHE plateau at ν = 5/2 in GaAs.Cooper pairing of Dirac composite fermions in the s channel results in a fractional QHE state dubbed PHPfaffian [2,7], where "PH" stands for "particle-hole". We argue that the PH-Pfaffian topological order is present on the QHE plateau at ν = 5/2. This might seem unlikely because the particle-hole symmetry is violated by the Landau level mixing (LLM) in the observed states of the second Landau level in GaAs. Besides, numerics [11][12][13][14][15][16] supports the Pfaffian [8] and anti-Pfaffian [9,10] states at ν = 5/2 even in the presence of PHS. At the same time, the existing numerical work, which always neglects strong disorder and typically neglects strong LLM, is not yet in the position to explain the physics of the 5/2 state, as is evidenced by a large discrepancy between numerical and experimental energy gaps [17]. Note that a recent attempt to incorporate LLM [16] into simulations led to the manifestly wrong conclusion that the 5/2 state does not exist at realistic LLM. Indeed, as discussed in Ref. [16], the existing perturbative methods are justifi...

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Stabilization of the Particle-Hole Pfaffian Order by Landau-Level Mixing and Impurities That Break Particle-Hole Symmetry

2016

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“…VII we present a perturbative study of the nonlinear resistance R xx (I,T) of a quantum point contact situated within a constriction in a quantum Hall bar. 36 The perturbation theory is valid for R xx Ӷh/e 2 . This study generalizes Wen's original treatment of this phenomenon 37 and the later study by Moon and Girvin 38 by including the effect of an inhomogeneous short-ranged interedge interaction, i.e., an interaction that is strong in the region of the quantum point contact, but becomes weak as one moves away from it.…”

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confidence: 99%

“…1. 36 The resistance R xx of the quantum point contact is measured between terminals 3 and 4 in Fig. 1…”

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confidence: 99%

“…We note that similar crossover effects in the temperature and voltage behavior have been discussed also in the context of transport in quantum wires. [25][26][27] Finally we would like to comment about recent measurements of tunneling characteristics through a constriction 36 in the weak interedge tunneling regime at high magnetic field. At relatively high temperatures (TϾ400mK) the experiment FIG.…”

Section: ͑112͒mentioning

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Transport properties of a two-dimensional electron liquid at high magnetic fields

D’Agosta

Raimondi²,

Vignale³

2003

Phys. Rev. B

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The chiral Luttinger liquid model for the edge dynamics of a two-dimensional electron gas in a strong magnetic field is derived from coarse-graining and a lowest Landau level projection procedure at arbitrary filling factors Ͻ1 -without reference to the quantum Hall effect. Based on this model, we develop a formalism to calculate the Landauer-Büttiker conductances in generic experimental setups including multiple leads and voltage probes. In the absence of tunneling between the edges the ''ideal'' Hall conductances (G i j ϭe 2 /h if lead j is immediately upstream of lead i, and G i j ϭ0 otherwise͒ are recovered. Tunneling of quasiparticles of fractional charge e* between different edges is then included as an additional term in the Hamiltonian. In the limit of weak tunneling we obtain explicit expressions for the corrections to the ideal conductances. As an illustration of the formalism we compute the current-and temperature-dependent resistance R xx (I,T) of a quantum point contact localized at the center of a gate-induced constriction in a quantum Hall bar. The exponent ␣ in the low-current relation R xx (I,0)ϳI ␣Ϫ2 shows a nontrivial dependence on the strength of the inter-edge interaction, and its value changes as e*V H , where V H ϭhI/ e 2 is the Hall voltage, falls below a characteristic crossover energy បc/d, where c is the edge wave velocity and d is the length of the constriction. The consequences of this crossover are discussed vis-a-vis recent experiments in the weak tunneling regime.

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“…A LJ is formed by using a gate voltage to create a narrow barrier which divides a fractional QH state such that there are two chiral edges flowing in opposite directions (counter propagating) on the two sides of the barrier [13,14,15,16,17]. For a QH system corresponding to a filling fraction which is the inverse of an odd integer such as 1, 3, 5, · · · , the edge consists of a single mode which can be described by a chiral bosonic theory [18].…”

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confidence: 99%

AC conductivity of a quantum Hall line junction

Agarwal¹,

Sen²

2009

J. Phys.: Condens. Matter

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We present a microscopic model for calculating the AC conductivity of a finite length line junction made up of two counter or co-propagating single mode quantum Hall edges with possibly different filling fractions. The effect of density-density interactions and a local tunneling conductance (σ) between the two edges is considered. Assuming that σ is independent of the frequency ω, we derive expressions for the AC conductivity as a function of ω, the length of the line junction and other parameters of the system. We reproduce the results of Phys. Rev. B 78, 085430 (2008) in the DC limit (ω → 0), and generalize those results for an interacting system. As a function of ω, the AC conductivity shows significant oscillations if σ is small; the oscillations become less prominent as σ increases. A renormalization group analysis shows that the system may be in a metallic or an insulating phase depending on the strength of the interactions. We discuss the experimental implications of this for the behavior of the AC conductivity at low temperatures.

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Nonlinear Quasiparticle Tunneling between Fractional Quantum Hall Edges

Cited by 63 publications

References 22 publications

Stabilization of the Particle-Hole Pfaffian Order by Landau-Level Mixing and Impurities That Break Particle-Hole Symmetry

Stabilization of the Particle-Hole Pfaffian Order by Landau-Level Mixing and Impurities That Break Particle-Hole Symmetry

Transport properties of a two-dimensional electron liquid at high magnetic fields

AC conductivity of a quantum Hall line junction

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