Composite-fermion effective masses

Abstract

Fractional quantum-Hall-effect features around filling factor v= 2 have been analyzed using the compositefermion approach. Effective masses deduced from the temperature dependence of the Shubnikovde Haas (SdH) oscillations, in agreement with other measurements, show a divergence as the fiiling factor approaches v= z and scale as (density) U . The magnetic-field dependence of the amplitude is explained quantitatively in terms of normal impurity scattering and a strong dephasing term associated with density inhomogeneities of order 0.5%. It is pointed out that assumptions made in the derivation of the standard theory used to analyze SdH oscillations are less likely to be satisfied for composite fermions and that some caution should therefore be used in interpreting effective-mass results obtained in this way. Recently several grou s have used the compositefermion (CF) approach ' to analyze fractional quantum-Hall-effect (FQHE) data. In contrast to the hierarchical model this provides a natural explanation for the strength as well as the position of the FQHE features in terms of Landau-level quantization around even denominator filling factors, in particular around v=-, '. The FQHE energy gaps are then given by the Landau-level spacing fi~, =efiB*/m " where B*=B B / is th-e deviation of the field from the v= -, ' value and m is the composite-fermion effective mass. For electrons the measured values of m are significantly larger than the conventional value (0.067mo)for GaAs and, as predicted, ' scale approximately as B According to gauge arguments the effective mass should diverge logarithmically

Semiclassical theory of transport in a random magnetic field

“…The resistivity data in zero external magnetic field (as contrasted to zero effective magnetic field acting on CFs) indeed indicate that the model of statistically independent impurity positions overestimates the amount of disorder [23,22]. It is also worth noting here, in view of the controversy about the effective mass of the CFs [2,[24][25][26], that in the RMF model σ xx at zero B [Eqs. (2), (16)] does not depend on m (neglecting the corrections [27] related to the interaction between the CFs).…”

“…8, in comparison with experimental data on the magnetoresistivity in the vicinity of ν = 1/2 from Refs. [26,32]. We recall, that although a simple model of uncorrelated impurities with the concentration n i = n gives α = 1/ √ 2, the actual value of α may be somewhat smaller because of impurity correlations.…”

“…Composite fermion conductivity σxx as a function of the effective magnetic field extracted from the data of Ref. [26]. The magnetooscillations start to develop when the conductivity (in units of e 2 /h) drops down to a value ∼ 1.…”

“…[26] are represented in terms of the CF conductivity. Finally, the damping of oscillations with decreasing B is extremely fast, so that the Dingle plot is strongly non-linear [25,26]. Composite fermion conductivity σxx as a function of the effective magnetic field extracted from the data of Ref.…”

“…Let us emphasize that the crossover to the adiabatic regime occurs in the CF system at a small deviation from half-filling ν = 1/2: B ∼ B 0 corresponds to the shift |ν − 1/2| ∼ 1/k F d ≪ 1. [31], [32], and [26], respectively (in this case ωc refers to the effective magnetic field B = B − 2hcn/e). The sample parameters (carrier density n, undoped spacer width d and zero-field mobility µ) are:…”