How real are composite fermions?

Abstract

According to recent theories, a system of electrons at the half-filled Landau level can be transformed to an equivalent system of composite fermions at zero effective magnetic field. In order to test for these new particles, we have studied transport in antidot superlattices in a two-dimensional electron gas. At low magnetic fields electron transport exhibits well-known resonances at fields where the classical cyclotron orbit becomes commensurate with the antidot lattice. At v=y we observe the same dimensional resonances. This establishes the semiclassical behavior of composite fermions.PACS numbers: 73.40.HmDuring the past decade two-dimensional electron systems at low temperature and high magnetic field have repeatedly surprised us with exotic electron correlation phenomena. The quantum liquids of the fractional quantum Hall effect (FQHE) [1-3], the still enigmatic electron crystal [4] at very low filling factors, and the vanishing and reappearance of certain quantum Hall states in double layer electron systems [5][6][7] all reflect the dominance of electron-electron interaction at very high magnetic fields. Recently the nature of the electronic interaction at the half-filled Landau level has received much attention. There is now mounting evidence for a novel particle called a "composite fermion" [8] that plays a crucial role in the physics of two-dimensional (2D) electron systems in the lowest Landau level. In this paper we present results of an experiment that demonstrates the semiclassical motion of such a particle.The significance of the physics at the half-filled Landau level was foreshadowed in exceptional electrical transport and surface acoustic wave anomalies exactly at v = y. At this filling fraction Jiang et al.[9] observed a deep minimum in the magnetoresistivity p xx that persisted to unusually high temperatures, exhibiting a temperature dependence distinctly different from the neighboring FQHE states. Surface acoustic wave (SAW) experiments by Willett et al [10] at v= y revealed attenuation and velocity changes that were opposite to those observed in the regime of the FQHE liquids.Independently, the hierarchical model of the FQHE that orders the various odd-denominator states at v=p/q (p=integer, g=odd integer) had come under increasing criticism. Starting from the Laughlin liquids [11] condensed from electrons at v = l/m and v = l-1/m, the higher order FQHE states are derived from lower order states as Laughlin states of fractionally charged quasiparticles [12,13]. In particular, the two prominent series of liquids at v=p/(2p ± 1) represent a succession of parental and daughter states starting from v=y and v=y and converging towards v = y. However, questions were raised [14] regarding the density of quasiparticles and their apparent noninteracting nature.Jain proposed an innovative model for these series of FQHE liquids based on hypothetical particles which he termed composite fermions [14]. The liquids of the FQHE are then derived as the integral quantum Hall effect of such composite fermions. T...

Edge state propagation direction in the fractional quantum Hall regime: multi-terminal magnetocapacitance experiment

“…the same as for electrons. In the ballistic regime, the individual CF moves at the Fermi velocity and the average drift force e(v) x B~has negligible effect on the semiclassical motion of CFS near B~fi,consistent with experiments [10].…”

“…[9,10] Recently, the CF approach has been extended to edge states in the FQHE regime [11,12], which are all expected to propagate in the same direction as for the IQHE. To date few experiments have addressed the propagation direction of edge states.…”

Composite fermions, edge currents, and the fractional quantum Hall effect

“…A simple-minded way to think of this is as follows: References 29 and 30 take m* to be a constant, independent of B eff . But if m* diverges strongly enough where B eff = 0, both the effective potential energy term V eff given by equation (20) and the kinetic energy on the LHS of (19) should vanish where B eff = 0. Thus the upturn of ε near B eff = 0 that is predicted by the argument that is presented immediately below equation (20) (and occurs in the Hartree approximation) should not happen.…”

“…These remarkable predictions have been confirmed experimentally. 19,20,21 Working in the Corbino geometry, Jain demonstrated that composite fermion theory yields the experimentally observed fractionally quantized Hall conductances. His proof 11 was a generalization of the arguments that Laughlin 3 had used earlier to explain the integer quantum Hall effect.…”

Spin and Charge Ordering in the Quantum Hall Regime

“…The validity of the CF concept is further supported by the determination of the CF Fermi wavevector [84,85] and the demonstration of the quasiclassical motion of composite fermions in their effective magnetic field * [86][87][88]. Cyclotron resonances of composite fermions have been measured directly by microwave absorption [89].…”