Quasi-particle tunneling at a constriction in a fractional quantum Hall state

Abstract

Split-gate constrictions can be used to produce controllable scattering in a fractional quantum Hall state and constitute a very versatile model system for the investigation of non-Fermi physics in edge states. Controllable inter-edge tunneling can be achieved by tuning the constriction parameters and its out-of-equilibrium behavior can be explored as well. Here we review our results of tunneling non-linearities at a split-gate constriction in a wide range of temperatures and inter-edge coupling. The results are compared to available theoretical predictions of tunneling characteristics between Luttinger liquids. We show how partial agreement with these theoretical models is obtained in selected ranges of temperatures and inter-edge coupling, while striking deviations are obtained especially in the low-coupling, low-temperature regimes. A two-dimensional electron system (2DES) in the fractional quantum Hall (FQH) regime can give rise to many "exotic" phenomena driven by electron-electron interactions [1]. Under the application of a strong magnetic field and for peculiar ratios of the charge (n) and flux quanta (n φ = eB/h) densities the 2DES undergoes transitions to insulating Hall phases. For "magic" values of the fractional filling factor ν = n φ /n the ground state excitations are expected to be fractionally charged and to obey fractional statistics [2]. In both the integer and FQH effect, bulk states are characterized by an excitation gap while the only low-energy charged excitations propagate at the edge of the quantum Hall liquid thus creating a conducting, chiral one-dimensional (1D) channel. Wen predicted [3] that the edge of a FQH phase at ν = 1/q, where q is an odd integer, should be completely equivalent to a Luttinger liquid (LL) with interaction parameter g = ν. This peculiar model is known as chiral LL (χLL) and represents one of the simplest and most remarkable conceptual examples of a non-Fermi metal.The FQH edge state is not the only electronic system that is expected to support a non-fermionic behavior. In recent years, the experimental realization of a LL has become a target of several research efforts that also explored different fabrication strategies of condensed matter systems. In particular cleaved-edge overgrowth (CEO) was used to produce clean and long quantum wires: temperature power laws as well as resonant transport were measured and compared with LL predictions [4]. Finally carbon nanotubes are emerging as a promising model system for the verification of LL physics [5,6].Edge FQH states are expected to lead to a particularly robust realization of a LL: edge channels at ν = 1/q with q odd integer, in fact, can only propagate in one direction and do not suffer from backscattering by random impurities. No localization occurs and the residual * Electronic address: roddaro@sns.it disorder only affects the electrons giving a mere phase shift. These issues stimulated much experimental effort that provided striking indications of non-Fermi physics at work for edge-states in the fractional QH...

Experimental probe of topological orders and edge excitations in the second Landau level

“…As the QPC is pinched off further, a situation can arise in which QPC and bulk have different filling factors. This intermediate tunneling regime has been studied theoretically 54 and experimentally 55,56 in detail. Fig.…”

Quasiparticle tunneling in the lowest Landau level

“…However, to date it has not been verified that the expected scaling parameters are obtained for states of which the wave function and the effective charge is known with a high degree of confidence, such as the Laughlin state at ν = 1 /3 [10][11][12][13]. Experimental studies of QP tunneling between edge modes of Laughlin states have yielded unexpected results [14][15][16][17][18][19], and a quantitative analysis based on a fit to Wen's model has not been reported to date. Interpretations of the scaling parameters measured in the second Landau level, be it in terms of dependence on constriction geometry or competition between possible ground states, thus lack a solid experimental basis.…”

Conductance plateaus and shot noise in fractional quantum Hall point contacts

“…The dissipated powers, P A = P B due to the voltage drops are given by Eqs. (40). The temperatures at the noise spots C and D are then obtained as…”

“…In particular, when ν Q < 0, the noise is constant as a function of the edge length up to exponentially small corrections in L/l eq . Another powerful tool for probing the FQH edge structure is the quantum point contact (QPC) geometry [38][39][40][41][42][43]. By using appropriately etched gates that locally deplete the 2D electron gas, local constrictions in the FQH sample are formed.…”

“…Another powerful tool for probing the FQH edge structure is the quantum point contact (QPC) geometry [38][39][40][41][42][43]. By using appropriately etched gates that locally deplete the 2D electron gas, local constrictions in the FQH sample are formed.…”