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

Abstract

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