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

Abstract

We report experimental realization of a quasiparticle interferometer where the entire system is in 1/3 primary fractional quantum Hall state. The interferometer consists of chiral edge channels coupled by quantum-coherent tunneling in two constrictions, thus enclosing an Aharonov-Bohm area. We observe magnetic flux and charge periods h/e and e/3, equivalent to creation of one quasielectron in the island. Quantum theory predicts a 3h/e flux period for charge e/3, integer statistics particles. Accordingly, the observed periods demonstrate the anyonic statistics of Laughlin quasiparticles.A clean system of 2D electrons subjected to high magnetic field at low temperatures condenses into the fractional quantum Hall (FQH) fluids [1][2][3][4]. An exact filling f FQH condensate is incompressible and gapped, the celebrated examples of FQH condensates are the Laughlin many-electron wave functions for the primary fillings ), with j an integer. The elementary charged excitations of an FQH condensate are the Laughlin quasiparticles. 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. Complementary geometry where a 2D electron island is defined by two nearly open constrictions comprises an electron interferometer [13][14][15][16]. had never been reported before in any system. The superperiod is interpreted as imposed by the topological order of the underlying FQH condensates [18], manifested by the anyonic statistical interaction of the quasiparticles [19,20].Our present experiment utilizes a comparable quasiparticle interferometer, but with much less depleted constrictions, Fig. 1. This results in the entire island being at the primary filling 3 / 1 = f under coherent tunneling conditions, so that 3 / e quasiparticles execute a closed path around an island of the 3 / 1 FQH fluid containing other 3 / e quasiparticles. This simpler regime should help theoretical consideration of the quasiparticle interferometer physics. For the first time in such devices we report interferometric oscillations. The flux and charge periods of e h / = ∆ Φ and 3 / e Q = ∆ , respectively, correspond to addition of one quasiparticle to the area enclosed by the interference path. These periods are the same as in quantum antidots, but the quasiparticle path encloses no electron vacuum in the interferometer. The results are consistent

Measurements of quasiparticle tunneling in theυ=52fractional quantum Hall state

“…The peak positions deviate from I DC = 0 by ~0.2 nA because of hysteresis in the sweep direction; all measurements shown in this paper are taken with increasing DC bias, and the small offset is subtracted when fitting. The magnetic field and gate voltage are 6 chosen, following the measurement technique described in Radu et al, 24 to maximize the temperature range exhibiting a zero-DC-bias peak and to minimize variations in the background resistance. 35 The magnetic field is set to 4.31 T, which is the center of the R XY plateau for υ = 5/2.…”

“…Studies of such tunneling have led to measurements of the quasi-particle charge 3,4 and creation of quasi-particle interferometers. 5,6 The states comprising the FQHE are determined by the filling factor ) / /( 0 Φ = B n υ , where n is the electron sheet density and e h / 0 = Φ is the quantum of magnetic flux. The υ = 5/2 state 7 is of particular interest because it is one of only a few physically realizable systems thought to possibly exhibit non-Abelian particle statistics.…”

Fractional quantum Hall hierarchy and the second Landau level

“…2,3 The observed filling fractions, the measured fractional charge of quasiparticles, 4-6 and recent results from interferometric experiments 7,8 all support this picture, and are backed up by a wealth of theoretical and numerical evidence. The physics of the second Landau level, however, remains far more perplexing, with the prominence of an evendenominator =5/ 2 FQH state 9,10 that cannot be explained by the standard hierarchy.…”

Suppression of Interference in Quantum Hall Mach-Zehnder Geometry by Upstream Neutral Modes

“…Experimental evidence for fractional charge dates back almost two decades ago [2][3][4]. Notwithstanding intriguing results [5][6][7], fractional statistics has remained elusive to date. A natural probe of statistics is through its effect on the AharonovBohm (AB) interferometry of anyons moving along the gapless edges of a FQH system.…”