Superperiods in interference of $e/3$ Laughlin quasiparticles encircling filling 2/5 fractional quantum Hall island

Superperiods in interference of $e / 3$ Laughlin quasiparticles encircling filling 2/5 fractional quantum Hall island

Ping V. Lin, F. E. Camino, and V. J. Goldman

Phys. Rev. B 80, 235301 – Published 1 December 2009

Abstract

We report experiments in a large, $2.5 μ m$ diameter Fabry-Perot quantum Hall interferometer with two tunneling constrictions. Interference fringes are observed as conductance oscillations as a function of applied magnetic field (the Aharonov-Bohm flux through the electron island) or a global backgate voltage (electronic charge in the island). Depletion is such that in the fractional quantum Hall regime, filling 1/3 current-carrying chiral edge channels pass through constrictions when the island filling is 2/5. The interferometer device is calibrated with fermionic electrons in the integer quantum Hall regime. In the fractional regime, we observe magnetic flux and charge periods $5 h / e$ and $2 e$ , respectively, corresponding to creation of ten $e / 5$ Laughlin quasiparticles in the island. These results agree with our prior report of the superperiods in a much smaller interferometer device. The observed experimental periods are interpreted as imposed by anyonic statistical interaction of fractionally charged quasiparticles.

Received 10 September 2009

DOI:https://doi.org/10.1103/PhysRevB.80.235301

Authors & Affiliations

Ping V. Lin¹, F. E. Camino², and V. J. Goldman¹

¹Department of Physics, Stony Brook University, Stony Brook, New York 11794-3800, USA
²Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA

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Vol. 80, Iss. 23 — 15 December 2009

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Images

Figure 1
(Color online) The longitudinal $R_{X X}$ (lower trace) and Hall $R_{X Y}$ magnetoresistance of the interferometer. The quantized plateaus (bulk $f_{B}$ , constriction $f_{C}$ ) allow to determine the filling factor in the constrictions. The fine structure is due to quantum interference effects, sharp peaks are due to impurity-assisted tunneling. Inset: electron micrograph of the interferometer device. The front gates (light) are deposited in shallow etch trenches (dark). Depletion potential of the trenches defines the electron island. The edge channels circling the island are coupled by tunneling in the two constrictions, thus forming a Fabry-Perot interferometer. The backgate (not shown) extends over the entire $4 \times 4 {mm}^{2}$ sample.Reuse & Permissions
Figure 2
(Color online) Representative interference conductance oscillations for electrons, $f = 1$ , and for $e / 3$ quasiparticles in $f = 1 / 3$ edge channel circling around an island of 2/5 FQH fluid. Both are plotted on the same magnetic field scale, the magnetic field period ratio is $5.4 \pm 0.3$ . The flux scales are slightly different because the 2/5 island area is $\sim 7 %$ less than the $f = 1$ edge ring area.Reuse & Permissions
Figure 3
(Color online) Representative oscillatory $δ R$ traces in the regime of $e / 3$ quasiparticles encircling the 2/5 FQH island. Moderate front-gate $V_{FG}$ is applied, the $δ R$ traces are labeled ( $V_{FG 1, 2, 3}$ , $V_{FG 4}$ ); the three voltages $V_{FG 1, 2, 3}$ are equal. Successive traces are shifted by $1 k Ω$ . A positive front-gate voltage increases the island electron density and shifts the region of oscillations to higher $B$ .Reuse & Permissions
Figure 4
(Color online) A matched set of interference conductance oscillations in the regime of $e / 3$ quasiparticles circling an island of the 2/5 FQH fluid. (a) Magnetic flux through the island period $Δ_{Φ} = 5 h / e$ corresponds to creation of ten $e / 5$ quasiparticles in the 2/5 fluid, two per $h / e$ . (b) The backgate voltage island charging period $Δ_{Q} = 2 e = 10 (e / 5)$ agrees with incremental addition of ten $e / 5$ quasiparticles. The ratio of the two periods confirms that the interference originates in the $f = 2 / 5$ FQH island. The interferometer device is calibrated using conductance oscillations for electrons, $f = 1$ .Reuse & Permissions
Figure 5
(Color online) (a) Atomic force micrograph of the interferometer device with an illustration of the FQH filling profile. The transport current is carried in the 1/3 chiral edge channels. The path of the edge $- e / 3$ quasielectrons is closed by tunneling in the two constrictions, and thus encircles the 2/5 island. (b) Illustration of the 2/5 island surrounded by 1/3 FQH fluid in the Haldane-Halperin hierarchy. The total 2D electron system is broken into three components: the incompressible exact filling 1/3 FQH condensate, the incompressible maximum density droplet of hierarchy $- e / 3$ quasielectrons (QE), and the excited $e / 5$ quasiholes (QH), appropriate for the $ν < f = 2 / 5$ situation. A circling $- e / 3$ QE is shown to the left of the island.Reuse & Permissions

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