Temperature-Dependent Magnetotransport around $\nu =1/2$ in ZnO Heterostructures

The sequence of prominent fractional quantum Hall states up to $\nu =5/11$ around $\nu =1/2$ in a high-mobility two-dimensional electron system confined at oxide heterointerface (ZnO) is analyzed in terms of the composite fermion model. The temperature dependence of $R_{xx}$ oscillations around $\nu =1/2$ yields an estimation of the composite fermion effective mass, which increases linearly with the magnetic field. This mass is of similar value to an enhanced electron effective mass, which in itself arises from strong electron interaction. The energy gaps of fractional states and the temperature dependence of $R_{xx}$ at $\nu =1/2$ point to large residual interactions between composite fermions.

Figure 1

$R_{xx}$ and $R_{xy}$ for sample $A$. In the lowest Landau level, a series of fractional quantum Hall states is observed. Temperature dependence of $R_{xx}$ at high magnetic field and in low field (inset) are shown. Triangles indicate the extrema of Shubnikov–de Haas oscillations used to evaluate the electron effective mass.

Figure 2

The effective mass of electrons in low magnetic fields against $B$, and the effective mass of composite fermions against $B_{\mathrm{eff}}$. The mass in low magnetic fields is increased by about 60% with respect to the electron band mass (horizontal line) in ZnO. The inset shows a linear dependence of the composite fermion effective mass $m_{\mathrm{CF}}$ on the applied magnetic field $B$. The linear fit goes through the origin.

Figure 3

Comparison of the composite fermion cyclotron energy $\hslash {\omega }_{\mathrm{CF}}$ evaluated from Fig. 2, and the energy gap of quasiparticles $\Delta$ against $B_{\mathrm{eff}}$. The dashed lines serve as guides to the eye. The open symbols in the negative-energy region represent the difference $\Gamma$ of energy gap $\Delta$ and cyclotron energy $\hslash {\omega }_{\mathrm{CF}}$.

Figure 4

Temperature dependence of $R_{xx}$ at $B=0\mathrm{T}$ and $\nu =1/2$, i.e., $B_{\mathrm{eff}}=0\mathrm{T}$, for sample $A$. Squares represent the measured data points, while lines are the best fits with Eq. (1). The Bloch-Grüneisen temperature is the same for electrons and for composite fermions.