co nd - m at / 9 70 72 89 29 J ul 1 99 7 Direct Observation of a Fractional Charge

Ever since Milliken’s famous experiment it is well known that the electrical charge is quantized in units of the electronic charge e. For that reason, Laughlin’s 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, Si=2QI. Our quantum shot noise measurements unambiguously show that current in a 2DEG in the FQH regime, at a fractional filling factor 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/φ0 , with φ0=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=ns/p equals an integer (ns being the 2DEG areal density), the longitudinal conductivity of the 2DEG vanishes while the Hall conductivity equals νe/h with very high accuracy. This phenomenon is known as the Integer Quantum Hall (IQH) effect. 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. 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 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 were proved to be in principle inadequate to reveal the fractional charge. A more recent experiment based on resonant tunneling by Goldman and Su was reproduced and interpreted differently by Franklin et al. 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 suggested that the quasi particle’s charge could in principle be determined by measuring quantum shot noise in the FQH regime. However, no theory was available until Wen recognized that transport in the FQH regime could be treated within a framework of One Dimensional (1D) interacting electrons, propagating along the edge of the two dimensional plane, making use of the so called Luttinger liquid model. Based on this model subsequent theoretical works predicted that quantum shot noise, generated due to weak backscattering of the current, at fractional filling factors ν=1/q and at zero temperature, should be proportional to the quasi particle’s charge Q=e/q and to the backscattered current IB : S I i B = 2Q . (1)