Ever since Milliken's 1 famous experiment it is well known that the electrical charge is quantized in units of the electronic chargee. For that reason, Laughlin's 2 theoretical prediction of the existence of fractionally charged quasi particles, put forward in order to explain the Fractional Quantum Hall (FQH) effect, is very counter intuitive. The FQH effect is a phenomenon that occurs in a Two Dimensional Electron Gas (2DEG) subjected to a strong perpendicular magnetic field. This effect results from the strong interaction among the electrons and consequently current is carried by the above mentioned quasi particles. We directly observed this elusive fractional charge by utilizing a measurement of quantum shot noise. Quantum shot noise results from the discreteness of the current carrying charges and thus is proportional to their charge, Q, and to the average current I, namely, S i =2QI . Our quantum shot noise measurements unambiguously show that current in a 2DEG in the FQH regime, at a fractional filling factor ν ν=1/3, is carried by fractional charge portions e/3; in agreement with Laughlin's prediction.The energy spectrum of a Two Dimensional Electron Gas (2DEG) subjected to a strong perpendicular magnetic field, B, consists of highly degenerate Landau levels with a degeneracy per unit area p=B/φ 0 , with φ 0 =h/e the flux quantum (h being Plank's constant). Whenever the magnetic field is such that an integer number ν (the filling factor) of Landau levels are occupied, that is ν=n s /p equals an integer (n s being the 2DEG areal density), the longitudinal conductivity of the 2DEG vanishes while the Hall conductivity equals νe 2 /h with very high accuracy. This phenomenon is known as the Integer Quantum Hall (IQH) effect 3 . A similar phenomenon occurs at fractional filling factors, namely, when the filling factor equals a rational fraction with an odd denominator q and is known as the Fractional Quantum Hall effect 4 . In contrast to the IQH effect, which is well understood in terms of non interacting electrons, the FQH effect can not be explained in such terms and is believed to result from interactions among the electrons, brought about by the strong magnetic field.Laughlin 2 had argued that the FQH effect could be explained in terms quasi particles of a fractional charge -Q=e/q. Although his theory is consistent with a considerable amount of the experimental data, no experiment directly showing the existence of the fractional charge exists. The early Aharonov-Bohm measurements 5 were proved to be in principle inadequate to reveal the fractional charge 6 . A more recent experiment based on resonant tunneling by Goldman and Su 7 was reproduced and interpreted differently by Franklin et al 8 . The difficulty in such experiments is that the results provide only the average charge per state and not the charge of individual particles. Quantum shot noise, on the other hand, probes the temporal behavior of the current and thus offers a direct way to measure the charge. Indeed, as early as in 1987, Tsui 9 sugges...
Wideband shot noise, associated with dc current flow through a quantum point contact (QPC), is measured in the microwave frequency range of 8-18 GHz. As the number of conducting channels in the QPC changes the noise power oscillates. Consistent with existing theories, the noise peaks depend linearly on the dc current. Surprisingly, however, in the pinch off region, where QPC is expected to behave as a classical injector, we find strong noise suppression, possibly mediated by the Coulomb interaction.
A novel method, invented to measure the minute thermodynamic magnetization of dilute two dimensional fermions, is applied to electrons in a silicon inversion layer. The interplay between the ferromagnetic interaction and disorder enhances the low temperature susceptibility up to 7.5 folds compared with the Pauli susceptibility of non-interacting electrons. The magnetization peaks in the vicinity of the density, where transition to strong localization takes place. At the same density, the susceptibility approaches the free spins value (Curie susceptibility), indicating an almost perfect compensation of the kinetic energy toll associated with spin polarization by the energy gained from the Coulomb correlation. Yet, the balance favors a paramagnetic phase over spontaneous magnetization in the whole density range.
The fractional quantum Hall effect 1 occurs in the conduction properties of a two-dimensional electron gas subjected to a strong perpendicular magnetic field. In this regime, the Hall conductance shows plateaux, or fractional states, at rational fractional multiples of e 2 /h, where e is the charge of an electron and h is Planck's constant. The explanation 1-3 of this behaviour invokes strong Coulomb interactions among the electrons that give rise to fractionally charged quasiparticles which can be regarded as noninteracting current carriers 1-5 . Previous studies 4,5 have demonstrated the existence of quasiparticles with one-third of an electron's charge, the same fraction as that of the respective fractional state. An outstanding ambiguity is therefore whether these studies measured the charge or the conductance. Here we report the observation of quasiparticles with a charge of e/5 in the 2/5 fractional state, from measurements of shot noise in a twodimensional electron gas 4 . Our results imply that charge can be measured independently of conductance in the fractional quantum Hall regime, generalizing previous observations of fractionally charged quasiparticles.In the fractional quantum Hall (FQH) regime, the first Landau level is partly populated, or 'fractionally filled'. Laughlin's explanation of the FQH effect 1-3 involved the emergence of new, fractionally charged, quasiparticles. Shot-noise measurements 4,5 have confirmed the existence of these quasiparticles in the FQH regime. Shot noise, resulting from the granular nature of the particles, is proportional to the charge of the current carriers, in this case quasiparticles 4,5 . In these experiments a quantum point contact (QPC) embedded in a two-dimensional electron gas (2DEG), serving as a potential constriction, was used as an electronic 'beam splitter'. Its purpose is to partly reflect back the incoming current and lead to partitioning of carriers and hence to shot noise. An applied magnetic field corresponding to fractional filling factors (in the bulk far from the QPC) of n B ¼ 1=3 in ref. 4 or 2/3 in ref. 5, was employed. Charge was deduced via the generalized equation for shot noise of non-interacting particles (the classical and simplified version is the Schottky formula: S ¼ 2qI B , with S the low-frequency spectral density of current fluctuations, I B the reflected current, and q the charge of the current-carrying particle). For small reflection by the QPC (small I B ) the quasiparticle's charge was found to be e/3 (ref. 4 and 5), as predicted theoretically 6-8 . The theories are based on the chiral Luttinger-liquid model and are applicable only for Laughlin fractional states, for example, 1/3, 1/5, and so on. For other, more general filling factors (such as n ¼ 2=5), however, such calculations become exceedingly complicated. Still, one can gain insight into the characteristics of the expected shot noise in such cases by considering the more intuitive composite fermion (CF) model 9,10 .Laughlin suggested that in the FQH regime the current is c...
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