The quantum Hall effect takes place in a two-dimensional electron gas under a strong magnetic field and involves current flow along the edges of the sample. For some particle-hole conjugate states of the fractional regime (for example, with fillings between 1/2 and 1 of the lowest Landau level), early predictions suggested the presence of counter-propagating edge currents in addition to the expected ones. When this did not agree with the measured conductance, it was suggested that disorder and interactions will lead to counter-propagating modes that carry only energy--the so called neutral modes. In addition, a neutral upstream mode (the Majorana mode) was expected for selected wavefunctions proposed for the even-denominator filling 5/2. Here we report the direct observation of counter-propagating neutral modes for fillings of 2/3, 3/5 and 5/2. The basis of our approach is that, if such modes impinge on a narrow constriction, the neutral quasiparticles will be partly reflected and fragmented into charge carriers, which can be detected through shot noise measurements. We find that the resultant shot noise is proportional to the injected current. Moreover, when we simultaneously inject a charge mode, the presence of the neutral mode was found to significantly affect the Fano factor and the temperature of the backscattered charge mode. In particular, such observations for filling 5/2 may single out the non-Abelian wavefunctions for the state.

Interference of edge channels is expected to be a prominent tool for studying statistics of charged quasiparticles in the quantum Hall effect (QHE). We present here a detailed study of an electronic Fabry-Perot interferometer (FPI) operating in the QHE regime [C. Chamon, et al. (1997) Phys Rev B 55:2331-2334, with the phase of the interfering quasiparticles controlled by the Aharonov-Bohm effect. Our main finding is that Coulomb interactions among the electrons dominate the interference, even in a relatively large area FPI, leading to a strong dependence of the area enclosed by the interference loop on the magnetic field. In particular, for a composite edge structure, with a few independent edge channels propagating along the edge, interference of the outmost edge channel (belonging to the lowest Landau level) was insensitive to magnetic field-suggesting a constant enclosed flux. However, when any of the inner edge channels interfered, the enclosed flux decreased when the magnetic field increased. By intentionally varying the enclosed area with a biased metallic gate and observing the periodicity of the interference pattern, charges e (for integer filling factors) and e∕3 (for a fractional filling factor) were found to be expelled from the FPI. Moreover, these observations provided also a novel way of detecting the charge of the interfering quasiparticles.Aharonov-Bohm | edge channels | fractional charge | interference A considerable amount of work has been focused in recent years on interference of quantum particles, aiming at understanding "single-particle" as well as "correlated-particles" physics. Experiments were designed to measure the quantum coherence time (1), to determine phase of the scattering amplitudes (2), to test entanglement between a pair of quantum particles (3), and, more recently, to probe their charge and coherence properties in the integer and fractional quantum Hall effect (QHE) regimes (IQHE and FQHE, respectively) (4-8). However, even though the statistics of identical quantum particles upon exchange is at the core of many physical phenomena, experiments to directly observe this intrinsic property are scarce (4, 5). Recent interest in topological quantum computation (9-11) led to a series of theoretical proposals aimed at demonstrating the statistics of quasiparticles in the FQHE (12). The ideas are primarily based on performing interference in an electronic version of a FabryPerot interferometer (FPI) (13,14) or in a similar Mach-Zehnder interferometer (MZI) (15, 16), with distinct "fingerprints" of the interfering quasiparticles. The MZI, although more difficult to fabricate, is a "true two-path" interferometer. On the other hand, in the FPI, which is a simpler device, many trajectories contribute to the interference. Understanding the physics governing these interferometers is crucial if they are to be used to probe the statistics of quasiparticles.We performed a detailed study of an electronic FPI operating in the IQHE and the FQHE regimes. Different from previous works, our devices...

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We have measured the resistances (and resistivities) of Ag and Cu nanowires of diameters ranging from 15 nm to 200 nm in the temperature range 4.2 K-300 K with the specific aim to assess the applicability of the Bloch-Grüneisen formula for electron phonon resistivity in these nanowires. The wires were grown within polymeric templates by electrodeposition. We find that in all the samples the resistance reaches a residual value at T=4.2 K and the temperature dependence of resistance can be fitted to the Bloch-Grüneisen formula in the entire temperature range with a well defined transport Debye temperature (ΘR). The value of Debye temperature obtained from the fits lie within 8% of the bulk value for Ag wires of diameter 15 nm while for Cu nanowires of the same diameter the Debye temperature is significantly lesser than the bulk value. The electron-phonon coupling constants (measured by α el−ph or αR) in the nanowires were found to have the same value as that of the bulk. The resistivities of the wires were seen to increase as the wire diameter was decreased. This increase in the resistivity of the wires may be attributed to surface scattering of conduction electrons. The specularity p was estimated to be about 0.5. The observed results allow us to obtain the resistivities exactly from the resistance and gives us a method of obtaining the exact numbers of wires within the measured array (grown within the template).

The exact structure of edge modes in "hole conjugate" fractional quantum Hall states remains an unsolved issue despite significant experimental and theoretical efforts devoted to their understanding. Recently, there has been a surge of interest in such studies led by the search for neutral modes, which in some cases may lead to exotic statistical properties of the excitations. In this Letter, we report on detailed measurements of shot noise, produced by partitioning of the more familiar 2/3 state. We find a fractional charge of (2/3)e at the lowest temperature, decreasing to e/3 at an elevated temperature. Surprisingly, strong shot noise had been measured on a clear 1/3 plateau upon partitioning the 2/3 state. This behavior suggests an uncommon picture of the composite edge channels quite different from the accepted one.