Experimental realization of Laughlin quasiparticle interferometers

Zhou, Wei; Goldman, V. J.

doi:10.1016/j.physe.2007.09.177

Cited by 6 publications

(9 citation statements)

References 22 publications

(52 reference statements)

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“…Similar interference fringes have been also reported considering several fractional filling factors [96,99,100,105,120]. Importantly, it has been recognized that, together with the interfering edge, the number of fully transmitted channels f t , belonging to the lowest Landau levels, comes into play in determining the periodicity of the FPI oscillations [88,92,99].…”

Section: Implementation and Resultssupporting

confidence: 76%

Anyons in Quantum Hall Interferometry

Carrega,

Chirolli,

Heun

et al. 2021

Preprint

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The quantum Hall (QH) effect represents a unique playground where quantum coherence of electrons can be exploited for various applications, from metrology to quantum computation. In the fractional regime it also hosts anyons, emergent quasiparticles that are neither bosons nor fermions and possess fractional statistics. Their detection and manipulation represent key milestones in view of topologically protected quantum computation schemes. Exploiting the high degree of phase coherence, edge states in the QH regime have been investigated by designing and constructing electronic interferometers, able to reveal the coherence and statistical properties of the interfering constituents. Here, we review the two main geometries developed in the QH regime, the Mach-Zehnder and the Fabry-Perot interferometers. We present their basic working principles, fabrication methods, and the main results obtained both in the integer and fractional QH regime. We will also show how recent technological advances led to the direct experimental demonstration of fractional statistics for Laughlin quasiparticles in a Fabry-Perot interferometric setup.

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Section: Implementation and Resultssupporting

confidence: 76%

Anyons in Quantum Hall Interferometry

Carrega,

Chirolli,

Heun

et al. 2021

Preprint

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“…The physical area of the structure that we considered is 5.9 µm× 5.9 µm, and the 2DES is 280 nm below the surface in z direction, similar to the experimental case [7][8][9]. The 2DES is generated at the interface of the GaAs-AlGaAs heterostructure.…”

Section: Resultsmentioning

confidence: 70%

“…Next, the electrostatic potential is determined by the electron density profile in a self-consistent loop, at zero magnetic field and temperature. To start the self-consistent calculation we focus on the lithographically defined sample, resembling the experimental structures [7][8][9]. By considering the crystal growth parameters together with the surface image of the quantum dot pattern, we calculate the charge distribution at the 2DES.…”

Section: The Modelmentioning

confidence: 99%

“…In the case of a two dimensional electron gas subject to strong perpendicular magnetic field, these anyonic particles are called Laughlin quasi-particles (LQPs) which obey fractional statistics and have an effective fractional electric charge e * = e/(2i + 1). Laughlin describes the Landau level filling for FQH states as f = 1/(2i + 1) where i is an integer [6] and LQPs are described by elementary charged excitations of FQH condensate [7].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the overall interference pattern also strongly depends on the spatial distribution of these states. To understand the properties of Laughlin quasi-particles, a number of experiments has been performed by Camino et al [7][8][9]. A key element of these experiments are the quantum point contacts (QPCs) and the electrostatic potential profile near these QPCs together with the quantum dot.…”

Section: Introductionmentioning

confidence: 99%

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Screening theory based modeling of the quantum Hall based quasi-particle interferometers defined at quantum dots

Salman¹,

Koymen²,

Yücel³

et al. 2012

Physica E: Low-dimensional Systems and Nanostructures

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In this work, we investigate the spatial distributions and the widths of the incompressible strips, i.e. the edgestates. The incompressible strips that correspond to ν = 1, 2 and 1/3 filling factors are examined in the presence of a strong perpendicular magnetic field. We present a microscopic picture of the fractional quantum Hall effect based interferometers, within a phenomenological model. We adopt Laughlin quasi-particle properties in our calculation scheme. In the fractional regime, the partially occupied lowest Landau level is assumed to form an energy gap due to strong correlations. Essentially by including this energy gap to our energy spectrum, we obtain the properties of the incompressible strips at ν = 1/3. The interference conditions are investigated as a function of the gate voltage and steepness of the confinement potential, together with the strength of the applied magnetic field.

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Anyons and Lowest Landau Level Anyons

Ouvry

2009

The Spin

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Intermediate statistics interpolating from Bose statistics to Fermi statistics are allowed in two dimensions. This is due to the particular topology of the two dimensional configuration space of identical particles, leading to non trivial braiding of particles around each other. One arrives at quantum many-body states with a multivalued phase factor, which encodes the anyonic nature of particle windings. Bosons and fermions appear as two limiting cases. Gauging away the phase leads to the so-called anyon model, where the charge of each particle interacts "à la AharonovBohm" with the fluxes carried by the other particles. The multivaluedness of the wave function has been traded off for topological interactions between ordinary particles. An alternative Lagrangian formulation uses a topological Chern-Simons term in 2+1 dimensions. Taking into account the short distance repulsion between particles leads to an Hamiltonian well defined in perturbation theory, where all perturbative divergences have disappeared. Together with numerical and semi-classical studies, perturbation theory is a basic analytical tool at disposal to study the model, since finding the exact N -body spectrum seems out of reach (except in the 2-body case which is solvable, or for particular classes of N -body eigenstates which generalize some 2-body eigenstates). However, a simplification arises when the anyons are coupled to an external homogeneous magnetic field. In the case of a strong field, by projecting the system on its lowest Landau level (LLL, thus the LLL-anyon model), the anyon model becomes solvable, i.e. the classes of exact eigenstates alluded to above provide for a complete interpolation from the LLL-Bose spectrum to the LLL-Fermi spectrum. Being a solvable model allows for an explicit knowledge of the equation of state and of the mean occupation number in the LLL, which do interpolate from the Bose to the Fermi cases. It also provides for a combinatorial interpretation of LLL-anyon braiding statistics in terms of occupation of single particle states. The LLL-anyon model might also be relevant experimentally: a gas of electrons in a strong magnetic field is known to exhibit a quantized Hall conductance, leading to the integer and fractional quantum Hall effects. Haldane/exclusion statistics, introduced to describe FQHE edge excitations, is a priori different from 1 arXiv:0712.2174v1 [cond-mat.stat-mech] 13 Dec 2007 anyon statistics, since it is not defined by braiding considerations, but rather by counting arguments in the space of available states. However, it has been shown to lead to the same kind of thermodynamics as the LLL-anyon thermodynamics (or, in other words, the LLL-anyon model is a microscopic quantum mechanical realization of Haldane's statistics). The one dimensional Calogero model is also shown to have the same kind of thermodynamics as the LLL-anyons thermodynamics. This is not a coincidence: the LLL-anyon model and the Calogero model are intimately related, the latter being a particular limit of the former...

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Experimental realization of Laughlin quasiparticle interferometers

Cited by 6 publications

References 22 publications

Anyons in Quantum Hall Interferometry

Anyons in Quantum Hall Interferometry

Screening theory based modeling of the quantum Hall based quasi-particle interferometers defined at quantum dots

Anyons and Lowest Landau Level Anyons

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