Effective Mass of the Four Flux Composite Fermion at $\nu =1/4$

Abstract

We have measured the effective mass ($m^{\ast }$) of the four flux composite fermion at Landau level filling factor $\nu =1/4$ (${}^4$CF), using the activation energy gaps at the fractional quantum Hall effect (FQHE) states $\nu$ = 2/7, 3/11, and 4/15 and the temperature dependence of the Shubnikov-de Haas (SdH) oscillations around $\nu =1/4$. We find that the energy gaps show a linear dependence on the effective magnetic field $B_{eff}$ ($\equiv B-B_{\nu =1/4}$), and from this linear dependence we obtain $m^{\ast }=1.0m_e$ and a disorder broadening $\Gamma \sim$ 1 K for a sample of density $n=0.87\times 10^{11}$ /cm${}^2$. The $m^{\ast }$ deduced from the temperature dependence of the SdH effect shows large differences for $\nu >1/4$ and $\nu <1/4$. For $\nu >1/4$, $m^{\ast }\sim 1.0m_e$. It scales as $\sqrt{B_{\nu }}$ with the mass derived from the data around $\nu =1/2$ and shows an increase in $m^{\ast }$ as $\nu \to 1/4$, resembling the findings around $\nu =1/2$. For $\nu <1/4$, $m^{\ast }$ increases rapidly with increasing $B_{eff}$ and can be described by $m^{\ast }/m_e=-3.3+5.7\times B_{eff}$. This anomalous dependence on $B_{eff}$ is precursory to the formation of the insulating phase at still lower filling.

5 pages, 3 figures

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