Correlated transport of FQHE quasiparticles in a double-antidot system

Averin, D. V.; Nesteroff, James A.

doi:10.1016/j.physe.2007.05.008

Cited by 4 publications

(9 citation statements)

References 38 publications

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“…Coherent quasiparticle dynamics requires that the relaxation rate Γ d created by direct Coulomb antidot-edge coupling is weak. This condition should be satisfied if the edge-state confinement is sufficiently strong [20]. The requirement on the confinement is less stringent in the case of the antidot line (Fig.…”

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confidence: 99%

“…Here Γ(z) is the gamma-function and ω c is the cut-off energy of the edge excitations. The rates Γ j (E) can be used in the standard kinetic equation to calculate the conductance of the antidot system [20]. Anyonic statistics of quasiparticles affects the position and amplitude of the conductance peaks through the shift of the energy levels by quasiparticle tunneling (described, e.g., by Eq.…”

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Coulomb Blockade of Anyons in Quantum Antidots

Averin

Nesteroff

2007

Phys. Rev. Lett.

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Coulomb interaction turns anyonic quasiparticles of a primary quantum Hall liquid with filling factor ν = 1/(2m + 1) into hard-core anyons. We have developed a model of coherent transport of such quasiparticles in systems of multiple antidots by extending the Wigner-Jordan description of 1D abelian anyons to tunneling problems. We show that the anyonic exchange statistics manifests itself in tunneling conductance even in the absence of quasiparticle exchanges. In particular, it can be seen as a non-vanishing resonant peak associated with quasiparticle tunneling through a line of three antidots. [5,6]. The situation with fractional statistics is so far less certain even in the case of the abelian statistics, which is the subject of this work. Although the recent experiments [7] demonstrating unusual flux periodicity of conductance of a quasiparticle interferometer can be interpreted as a manifestation of the fractional statistics [8,9], this interpretation is not universally accepted [10,11]. There is a number of theoretical proposals (see, e.g., [12,13]) suggesting tunnel structures where the statistics manifests itself through noise properties. Partly due to complexity of noise measurements, such experiments have not been performed successfully up to now. In this work, we show that coherent quasiparticle dynamics in multiantidot structures should provide clear signatures of the exchange statistics in dc transport. Most notably, in tunneling through a line of three antidots, fractional statistics leads to a non-vanishing peak of the tunnel conductance which would vanish for integer statistics.These effects rely on the ability of quantum antidots to localize individual quasiparticles of the QH liq- uids [4,14,15]. The resulting transport phenomena in antidots are very similar to those associated with the Coulomb blockade [16] in tunneling of individual electrons in dots. For instance, similarly to a quantum dot [19], the linear conductance of one antidot shows periodic oscillations with each period corresponding to the addition of one quasiparticle [4,14,15,17,18]. Recently, we have developed a theory of such Coulomb-blockade-type tunneling for a double-antidot system [20], where quasiparticle exchange statistics does not affect the transport. The goal of this work is to extend this theory to antidot structures where the statistics does affect the conductance. The two simplest structures with this property consist of three antidots and have quasi-1D geometries with either periodic or open boundary conditions (Fig. 1). A technical issue that needed to be resolved to calculate the tunnel conductance is that the anyonic field operators defined through the Wigner-Jordan transformation [21,22,23,24], are not fully sufficient in the situations of tunneling. As we show below, to obtain correct matrix elements for anyon tunneling, one needs to keep track of the appropriate boundary conditions of the wavefunctions which are not accounted for in the field operators.Specifically, we consider the antidots coupled by tunneli...

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Coulomb Blockade of Anyons in Quantum Antidots

Averin

Nesteroff

2007

Phys. Rev. Lett.

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“…We see that the number of quasiparticles n is a good quantum number n |n 0 = n |n 0 . These two sectors are coupled to each other because L = 2πR and R = √ 2N B in terms of magnetic length B = /eB, but we can assume that the antidots are large enough so that the radius of |n 0 and |n + 1 0 are effectively the same [29] and assume that charge and neutral sectors decouple. This corresponds to the constant interaction model in quantum dots [48].…”

Section: Appendix B: Antidotsmentioning

confidence: 99%

“…However, there is still a considerable gap between theoretical and experimental studies of abelian anyons in the FQH edge states which motivates a more thorough study of their properties. Here, we study the problem of elastic co-tunnelling of Laughlin quasiparticles through two antidots and show that in certain limits, it maps to a Kondo impurity [12,13] embedded between two chiral Luttinger liquids [14,15,[17][18][19]44] and exhibits interesting transport signatures.Transport through antidots in the FQH regime has been studied in the past, experimentally [20][21][22][23][24][25] and theoretically [26][27][28][29] in a regime where the transport was dominated by correlated but incoherent transfers of individual quasiparticles. In contrast, in this paper we are interested in a regime where this sequential tunnelling is blocked due to a large inter-antidot capacitive coupling.…”

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“…Transport through antidots in the FQH regime has been studied in the past, experimentally [20][21][22][23][24][25] and theoretically [26][27][28][29] in a regime where the transport was dominated by correlated but incoherent transfers of individual quasiparticles. In contrast, in this paper we are interested in a regime where this sequential tunnelling is blocked due to a large inter-antidot capacitive coupling.…”

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Orbital Kondo effect in fractional quantum Hall systems

Komijani¹,

Simon²,

Affleck³

2015

Phys. Rev. B

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We study transport properties of a charge qubit coupling two chiral Luttinger liquids, realized by two antidots placed between the edges of an integer ν = 1 or fractional ν = 1/3 quantum Hall bar. We show that in the limit of a large capacitive coupling between the antidots, their quasiparticle occupancy behaves as a pseudo-spin corresponding to an orbital Kondo impurity coupled to a chiral Luttinger liquid, while the inter antidot tunnelling acts as an impurity magnetic field. The latter tends to destabilize the Kondo fixed point for the ν = 1/3 fractional Hall state, producing an effective inter-edge tunnelling. We relate the inter-edge conductance to the susceptibility of the Kondo impurity and calculate it analytically in various limits for both ν = 1 and ν = 1/3.Introduction -Fractional quantum Hall (FQH) systems [1] are strongly correlated topological states, realized in clean two-dimensional electron gases under a large perpendicular magnetic field, where the bulk contains an incompressible fluid and the low energy dynamics is controlled by chiral Luttinger liquids at the edges [2]. There has recently been a renewed interest in these systems due to a promise of the celebrated topological quantum computation using non-abelian anyons [3][4][5][6] and also in connection to impurities in helical liquids of the quantum spin Hall systems [7][8][9][10][11]. However, there is still a considerable gap between theoretical and experimental studies of abelian anyons in the FQH edge states which motivates a more thorough study of their properties. Here, we study the problem of elastic co-tunnelling of Laughlin quasiparticles through two antidots and show that in certain limits, it maps to a Kondo impurity [12,13] embedded between two chiral Luttinger liquids [14,15,[17][18][19]44] and exhibits interesting transport signatures.Transport through antidots in the FQH regime has been studied in the past, experimentally [20][21][22][23][24][25] and theoretically [26][27][28][29] in a regime where the transport was dominated by correlated but incoherent transfers of individual quasiparticles. In contrast, in this paper we are interested in a regime where this sequential tunnelling is blocked due to a large inter-antidot capacitive coupling.Combining the pseudo-spin of a double dot with the intrinsic spin, Borda et al. [30] predicted an SU(4) Kondo effect which has been recently observed [31]. The use of double dots to realize pseudo-spin SU(2) Kondo model and its generalizations at ν = 1 integer quantum Hall regime was proposed in [32]. Here, we extend those ideas by studying the realization and transport properties of a Kondo impurity coupled to chiral Luttinger liquid edge states in the FQH regime. A similar model arises in the study of a double dot inserted in a spinless non-chiral Luttinger liquid, once the occupancy of the dots is limited so that they act as an effective spin. In contrast to most previous studies that focus on zero temperature, we provide analytical expressions for the conductance in all asymptotic temp...

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