The charge of quasiparticles in a fractional quantum Hall (FQH) liquid, tunneling through a partly reflecting constriction with transmission t, was determined via shot noise measurements. In the ν = 1/3 FQH state, a charge smoothly evolving from e * = e/3 for t 1/3 ∼ = 1 to e * = e for t 1/3 ≪ 1 was determined, agreeing with chiral Luttinger liquid theory. In the ν = 2/5 FQH state the quasiparticle charge evolves smoothly from e * = e/5 at t 2/5 ∼ = 1 to a maximum charge less than e * = e/3 at t 2/5 ≪ 1. Thus it appears that quasiparticles with an approximate charge e/5 pass a barrier they see as almost opaque.PACS numbers: 73.20. Hm, 71.10.Pm, 73.50.Td The fractional quantum Hall (FQH) effect is a manifestation of the prominent and unique effects resulting from the Coulomb interactions between electrons in a two-dimensional electron gas (2DEG) under the influence of a strong magnetic field [1]. In this regime the lowest Landau level is partially populated. Laughlin's seminal explanation of the FQH effect [2] involved the emergence of intriguing fractionally charged quasiparticles. Recently, shot noise measurements confirmed the existence of such quasiparticles with charge e/3 and e/5 at filling factors ν = 1/3 [3] and ν = 2/5 [4], respectively. These experiments relied on the fact that shot noise, resulting from the granular nature of the quasiparticles, is proportional to their charge. Since current flowing in an ideal Hall state is noiseless [4] a quantum point contact (QPC) constriction was used to weakly reflect the incoming current, leading to partitioning of the incoming carriers and hence to shot noise. A charge e * was then deduced from the shot noise expression derived for non-interacting particles [5]. In this paper, we extend the range of QPC reflection to the strong back-scattering limit, where the apparent noise-producing quasiparticle charge is expected to be different. Specifically, an opaque barrier is expected to allow only the tunneling of electrons, as both sides of the barrier should be quantized in units of the electronic charge. How this charge evolves is an important question in the understanding of the behavior of quasiparticles, and here we explore the evolution of the charge of the e/3 and e/5 quasiparticles. We first briefly describe the expected dependence of shot noise on charge and transmission.At zero temperature (T = 0), the shot noise contribution of the p'th channel is [5,6]:where S is the low frequency (f << eV /h) spectral density of current fluctuations (S∆f = i 2 ), V the applied source-drain voltage, g p the conductance of the fully transmitted p'th channel in the QPC, and t p is its transmission coefficient. This reduces to the well known classical Poissonian expression for shot noise when t p ≪ 1 (the 'Schottky equation'), S T =0 = 2eI, with I = V g p t p the DC current in the QPC.The justification for the use of Eq. (1) comes from current theoretical studies of shot noise in the FQH regime, based on the chiral Luttinger liquid model. They are applicable only for Laug...
Shot noise measurements were recently exploited to measure the charge of the quasiparticles in the Fractional Quantum Hall (FQH) regime. For fractional filling factors ν = 1/3 and 2/5 of the first Landau level, fractional charges q = e/3 and e/5, respectively, were measured [1][2][3]. We investigate here the interaction of e/3 quasiparticles with a strong backscatterer and find unexpected results.When a weak backscatterer is introduced in the path of an otherwise noiseless current of quasiparticles, stochastic partitioning of the quasiparticles takes place and shot noise proportional to their charge appears. Specifically, at ν = 1/3, noise corresponding to q = e/3 appears. However, the measured charge increases monotonically as backscattering becomes stronger, approaching asymptotically q = e [4,5]. In other words, only electrons, or alternatively, three bunched quasiparticles, tunnel through high potential barriers when impinged by a noiseless current of quasiparticles. Here we show that such bunching of quasiparticles by a strong backscatterer depends on the average occupation (dilution) of the impinging quasiparticle current. For a very dilute impinging current, bunching ceases altogether and the transferred charge approaches q = e/3.
We employ shot noise measurements to characterize the effective charge of quasiparticles, at filling factor nu=1/3 of the fractional quantum Hall regime, as they scatter from an array of identical weak backscatterers. Upon scattering, quasiparticles are known to bunch, e.g., only three e/3 charges, or "electrons" are found to traverse a rather opaque potential barrier. We find here that the effective charge scattered by an array of scatterers is determined by the scattering strength of an individual scatterer and not by the combined scattering strength of the array, which can be very small. Moreover, we also rule out intraedge equilibration of e/3 quasiparticles over a length scale of hundreds of microns.
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