Evolution of Quasiparticle Charge in the Fractional Quantum Hall Regime

Abstract

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...

Bunching of fractionally charged quasiparticles tunnelling through high-potential barriers

“…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.…”

“…1a, utilizes a noiseless current I inc that impinges on a relatively open QPC1 and partially scatters toward QPC2 (although in this case the small reflection coefficient of QPC1 is responsible for the dilution of the current, for uniformity we stick to the notation of transmission coefficient t 1 → 0). Most of the current continues toward D 1 while the scattered part is a very dilute beam of quasiparticles with charge q 1 = e/3 [1,2,5] and dilution determined by t 1 . Much of that dilute current is reflected back by QPC2 toward drain D 2 and a small part t 2 is transmitted.…”

“…A fraction t 1 t 2 of the incident current reaches the amplifier. This method cannot be applied, however, to achieve a moderately sparse beam of quasiparticles since a partly pinched QPC1 would lead to bunching of quasiparticles and to an effective charge q 1 > e/3 [5]. Hence, we employ also a geometry shown in Fig.…”

“…2b to t 1 ≈ 0.2. Calculating the expected noise [5] we take into account the finite temperature of the electrons (T ≈ 65 mK) and the energy (or current) dependence of the total transmission t tot = t 1 t 2 (current dependent transmissions are shown in the insets of Fig. 2).…”

Shot noise in coupled dots and the “fractional charges”

“…Yet, despite intensive efforts, the nature of these quasi-particles is not completely understood. An important progress, however, has been made in this direction with experiments on quantum shot-noise [2][3][4] leading to direct measurement of the quasi-particle fractional charge. In fact, for noninteracting particles of charge q the zero frequency spectral density at zero temperature is given by [5] S(0) = 2qI(1 − t) ,…”