Experimental evidence for composite fermions

Abstract

The study of correlated two-dimensional (2D) electron systems in the extreme quantum limit has been advanced by development of a field-theoretic model and associated experimental findings. The fundamental theoretical construction transforms the interacting 2D electrons into quasiparticles referred to as composite fermions. The properties of such an interacting particle system have recently been described, with the principal hypothesis that Fermi surfaces should form from the quasiparticle seas at specific ratios of the electron density to applied magnetic field. This model serves to provide an explanation for an extensive body of experimental data, including a description of the fractional quantum Hall effect as the integer quantum Hall effect for the quasiparticles. This review will present the experimental findings which both motivated and subsequently have verified aspects of this model. Following a brief introduction to 2D systems, early experimental findings pre-dating and influencing the composite fermion theory are examined. The theoretical construction and in particular the hypothesis of Fermi surface formation at high magnetic fields are briefly reviewed with respect to their experimental predictions. Experiments subsequent to the main theoretical developments are then presented. Emphasized are surface acoustic wave experiments which were responsible for measuring the composite fermion Fermi wave-vector and mean free path. Further demonstrations of semiclassical motion of the quasiparticles at the Fermi surface are also reviewed, including antidot experiments, magnetic focusing measurements, and transport studies through nar/ostructures. Experimental determination of the composite fermion effective mass is examined, considering results from measurements in dc transport, surface acoustic waves and thermopower. Extension of the theory and experi-ments to multiple filling factors in the magnetic field spectrum is also reviewed. Experimental findings are summarized and potential future studies are finally discussed. ContentsPAGE 1. Introduction 448 2. Background 450 2.1. Two-dimensional electron systems and the integer quantum Hall effect 450 2.2. Electron correlations and the fractional quantum Hall effect; Laughlin's wavefunction 451 2.3. Hierarchy of fractional quantum Hall states and the nonquantized Hall effect 454 2.4. Early surface acoustic wave results at a filling factor of 1/2 457 2.4.1. Surface acoustic wave technique as a probe of Crxx (co, q) 458 2.4.2. Surface acoustic wave technique at u= 1/2; enhanced conductivity at small length scales 464

Theory of magnetoacoustic transport in modulated quantum Hall systems nearν=1/2

“…This corresponds to the minimum in the SAW velocity shift at ν = 1/2. This minimum was observed repeatedly in non-modulated FQHE systems [6].…”

“…Again we emphasize that our analysis is carried out in both local and non-local regimes. Since the SAW experiments [6,12] are done in non-local regime it is essential to use the theory for this regime in any interpretation.…”

“…For typical experimental conditions [6,12] ωτ << 1 therefore ωτ is neglected in (13). Making the change of variables:…”

“…It is known from SAW experiments in unmodulated 2DEG in the quantum Hall regime [6] and from theory [7] [See also Eq. (44)] that ρ CF yy (∆n = 0) and, correspondingly, σ xx has a maximum at ν = 1/2 and decreases when ∆ν grows.…”

“…Hence, the SAW experiments provide an efficient tool for experimental studies of the conductivity of two dimensional electron systems in Quantum Hall states at even denominator filling factors ν [1,2,3,4,5,6]. It was observed repeatedly that the dependence of the SAW velocity shift on the magnetic field B exhibits a pronounced minimum at B corresponding to ν = 1/2, implying a maximum in the conductivity.…”