In two dimensions, the laws of physics permit existence of anyons, particles with fractional statistics which is neither Fermi nor Bose. That is, upon exchange of two such particles, the quantum state of a system acquires a phase which is neither 0 nor π , but can be any value ) into the island. The corresponding e 2 charge period is confirmed directly in calibrated gate experiments. These results constitute direct observation of fractional statistics of Laughlin quasiparticles.

In experiments on resonant tunneling through a "quantum antidot" (a potential hill) in the quantum Hall (QH) regime, periodic conductance peaks were observed as a function of both magnetic field and back gate voltage. A combination of the two periods constitutes a measurement of the charge of the tunneling particles and implies that charge deficiency on the antidot is quantized in units of the charge of quasi-particles of the surrounding QH condensate. The experimentally determined value of the electron charge e is 1.57 x 10(-19) coulomb = (0.98 +/- 0.03) e for the states v = 1 and v = 2 of the integer QH effect, and the quasi-particle charge is 5.20 x 10(-20) coulomb = (0.325 +/- 0.01)e for the state v = (1/3) of the fractional QH effect.

We report observations of an electric-field threshold conduction and of related ac voltage (broad-band noise) generation in low-disorder two-dimensional electron systems in the extreme magnetic quantum limit. We interpret these phenomena as definitive evidence for formation of a pinned quantum Wigner crystal and determine its melting phase diagram from the disappearance of threshold and noise behavior at higher temperatures.

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We report an Aharonov-Bohm superperiod of five magnetic flux quanta (5h/e) observed in a Laughlin quasiparticle interferometer, where an edge channel of the 1/3 fractional quantum Hall fluid encircles an island of the 2/5 fluid. This result does not violate the gauge invariance argument of the Byers-Yang theorem because the magnetic flux, in addition to affecting the Aharonov-Bohm phase of the encircling 1/3 quasiparticles, creates the 2/5 quasiparticles in the island. The superperiod is accordingly understood as imposed by the anyonic statistical interaction of Laughlin quasiparticles.

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

We report experiments on Fabry-Perot electron interferometers in the integer quantum Hall regime. The GaAs/AlGaAs heterostructure devices consist of two constrictions defined by etch trenches in 2D electron layer, enclosing an approximately circular island. The interferometer is formed by counterpropagating chiral edge channels coupled by tunneling in the two constrictions. Interference fringes are observed as conductance oscillations, similar to the Aharonov-Bohm effect. Front gates deposited in etch trenches allow to fine-tune the device and to change the constriction filling f relative to the bulk filling. Quantum-coherent conductance oscillations are observed on the f = 1 - 4 plateaus. On plateau f we observe f conductance oscillations per fundamental flux period h/e. This is attributed to the dominance of the electron-electron Coulomb interaction, effectively mixing Landau level occupation. On the other hand, the back-gate charge period is the same (one electron) on all plateaus, independent of filling. This is attributed to the self-consistent electrostatics in the large electron island. We also report dependence of the oscillation period on front-gate voltage for f = 1, 2 and 4 for three devices. We find a linear dependence, with the slope inversely proportional to f for f = 1 and 2