Dispersion of the Composite-Fermion Cyclotron-Resonance Mode

The dispersion of the composite-fermion cyclotron-resonance mode is measured with an optical detection scheme under the combined excitation of microwave radiation and a surface acoustic wave from an interdigital transducer. The slowly traveling surface wave defines the transferred wave vector. Momenta up to ${10}^8{\mathrm{m}}^{-1}$ are accessible. The cyclotron-resonance mode exhibits strong negative dispersion, which suggests predominant short range residual interaction among composite fermions. From an extrapolation, the cyclotron mass at $k=0$ is obtained and investigated as a function of electron density.

Figure 1

(a) The microwave absorption strength near filling $\nu =1/2$ as a function of the microwave frequency $f_{\mathrm{cr}}$ for different power levels $P_{\mathrm{cr}}$ at a constant field of 8.4 T. The SAW and sample parameters are as follows: $f_{\mathrm{SAW}}=18\mathrm{GHz}$, $P_{\mathrm{SAW}}=-5\mathrm{dBm}$, the density $n_s=1.09\times {10}^{11}{\mathrm{cm}}^{-2}$, and temperature $T=0.4\mathrm{K}$. The right inset plots the amplitude of the absorption peak as a function of $P_{\mathrm{cr}}$. The left insets show the microwave circuit board and the sample geometry described in the text. (b) $B$-field dependence of the microwave absorption strength near $\nu =1/2$ for different SAW power levels $P_{\mathrm{SAW}}$ and for sample parameters as in (a). The microwave power $P_{\mathrm{cr}}$ equals $-10\mathrm{dBm}$ and the frequency $f_{\mathrm{cr}}=45\mathrm{GHz}$. The SAW-frequency is $f_{\mathrm{SAW}}=18\mathrm{GHz}$. The inset illustrates the amplitude of the absorption peak as a function of $P_{\mathrm{SAW}}$.

Figure 2

Absortpion spectra measured for different $B$ fields in the vicinity of filling $\nu =1/2$. The SAW frequency and power are fixed at 18 GHz and $-5\mathrm{dBm}$. The electron density is $1.09\times {10}^{11}{\mathrm{cm}}^{-2}$ and the temperature $T=0.4\mathrm{K}$.

Figure 3

$B$-field dependence of the composite-fermion cyclotron-resonance mode for two values of the wave vector, $k_{\mathrm{SAW}}=10.5\times {10}^7{\mathrm{m}}^{-1}$ (open symbols) and $3.9\times {10}^7{\mathrm{m}}^{-1}$ (solid symbols), and two electron densities: $n_s=1.09\times {10}^{11}{\mathrm{cm}}^{-2}$ (a) and $0.59\times {10}^{11}{\mathrm{cm}}^{-2}$ (b).

Figure 4

Left: $k$ dependence of the cyclotron-resonance mode energy of composite fermions (expressed in terms of inverse cyclotron mass) for $n_s=1.09\times {10}^{11}{\mathrm{cm}}^{-2}$ and $0.59\times {10}^{11}{\mathrm{cm}}^{-2}$. Right: The composite-fermion cyclotron mass in the limit $k\to 0$ as a function of density. The inset plots the $B$-field location of the cyclotron-resonance mode versus the SAW frequency. The dashed line marks the commensurability condition where the SAW wavelength equals the composite-fermion cyclotron diameter.