Invariance of charge of Laughlin quasiparticles

Abstract

A Quantum Antidot electrometer has been used in the first direct observation of the fractionally quantized electric charge. In this paper we report experiments performed on the integer i = 1, 2 and fractional f = 1/3 quantum Hall plateaus extending over a filling factor range of at least 27%. We find the charge of the Laughlin quasiparticles to be invariantly e/3, with standard deviation of 1.2% and absolute accuracy of 4%, independent of filling, tunneling current, and temperature.PACS numbers: 73.40. Hm, 73.40.Gk, 71.10.Pm The most fundamental aspect of the quantum Hall effect (QHE) is the constancy of the Hall conductance over a finite range of the filling factor ν. [1-3] Indeed, this property defines the phenomenon of QHE, and the quantized value of the Hall conductance σ xy of a particular QH state in units of e 2 /h is a principal quantum number of that QH state i or f , called "exact filling". Specifically, the electric charge of the quasiparticles is expected to be determined by the relevant quantum numbers, including i or f , and thus not expected to vary on a QH plateau as ν is varied from the exact filling. [3][4][5] On a QH plateau the charge of quasiparticles localized in the interior of a two dimensional electron system (2DES) is well defined. [6] In the case of the integer QH plateau at ν ≈ i the quasielectrons are simply electrons in the Landau level i + 1, and the quasiholes are the holes in the i th level. It is easy to understand the properties of FQHE quasiparticles using composite fermions. [7,8] In the case of the FQH plateau at f = i 2pi+1 quasielectrons are composite fermions (an electron binding 2p vortices) in the "Landau level" i + 1 of composite fermions, and the quasiholes are the holes in the i th level. It has been predicted theoretically that the electric charge of these quasiparticles is q = e 2pi+1 , positive for the quasiholes and negative for quasielectrons. [9,3] This fascinating fractional quantization of electric charge is a fundamental property of the strongly correlated FQH fluid.Although six years have passed since the first direct observation of 1 3 e particles in quantum antidot (QAD) electrometer experiments [10] one crucial aspect of theory remained untested: the invariance of charge at ν far from exact filling. In this paper we report experiments performed on the integer i = 1, 2 and fractional f = 1 3 quantum Hall plateaus which extend over a filling factor ν range of 27% to 45%. The charge of the QAD-bound quasiparticles has been measured to be constant, independent of ν over the entire plateau extent, with relative accuracy of ±1.2% and absolute accuracy of 4%. In addition, we observe no variation of the quasiparticle charge upon variation of temperature or applied current, in the experimentally accessible range.The QAD electrometer is illustrated in Fig. 1. [10,11] The antidot is defined lithographically in a constriction between two front gates in a 2DES. The antidot and the front gates create depletion potential hills in the 2DES plane and, in quantizing ma...

Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics

“…A quantum antidot electrometer has been used in the direct observation of the charge 3 / e and 5 / e quasiparticles, 6,13,14 subsequently confirmed in shot noise measurements. 15,16 A quantum antidot is a potential hill lithographically defined in a 2D electron layer in the quantum Hall regime.…”

e/3Laughlin Quasiparticle Primary-Fillingν=1/3Interferometer

“…The coefficient α in Eq. (1) is known a priori in quantum antidots to a good accuracy because the antidot is completely surrounded by the quantum Hall fluid [6,11]. But, in an interferometer, the island is separated from the 2D electron plane by the front-gate etch trenches, so that its electron density is not expected to increase by precisely the same amount as B n , which necessitates the calibration.…”

“…Deviation of the filling factor from the exact value is achieved by excitation of either quasielectrons or quasiholes out of the condensate; at such fillings the ground state of an FQH fluid consists of the quasiparticle-containing condensate. The FQH quasiparticles have fractional electric charge [2-6] and obey fractional statistics [7][8][9][10].Fractionally charged quasiparticles were first observed in quantum antidot experiments, where quasiperiodic resonant conductance peaks are observed when the occupation of the antidot is incremented by one quasiparticle [6,11,12]. A quantum antidot is a small potential hill, defined lithographically in the 2D electron system.…”

“…Fractionally charged quasiparticles were first observed in quantum antidot experiments, where quasiperiodic resonant conductance peaks are observed when the occupation of the antidot is incremented by one quasiparticle [6,11,12]. A quantum antidot is a small potential hill, defined lithographically in the 2D electron system.…”

“…The integer regime oscillations have an e h / fundamental flux period, we conclude that the flux period of the 1/3 FQH oscillations is also e h / = ∆ Φ . We use the backgate technique [6,11] to directly measure the charge period in the fractional regime. We calibrate the backgate action…”