Collective excitations in two-dimensional electron stripes: Transport and optical detection of resonant microwave absorption

Transport and optical detection schemes are used for the investigation of resonant microwave absorption of two-dimensional electrons in stripes with different sizes. Fundamental and several excited transverse collective magneto-plasma modes have been detected. The transport and optical methods are found to be in good agreement with each other. The influence of retardation on the collective excitations is investigated in wide stripes with large electron densities.

Figure 1

Comparison of the magnetoresistance $R_{xx}$ for $T=1.8\mathrm{K}$ (dotted line) and $T=4.2\mathrm{K}$ (solid line) at an electron density $n_{\mathrm{s}}$ of $2.13\bullet {10}^{11}{\mathrm{cm}}^{-2}$. The temperature sensitivity of $R_{xx}$ can be exploited to detect heating of the electonic system due to resonant absorption.

Figure 2

The influence of 40 and $51\mathrm{GHz}$ microwave radiation on the magnetoresistance $R_{xx}$. Solid curves are taken at $1.8\mathrm{K}$, the dotted curve at $4.2\mathrm{K}$. For the sake of comparison, the $R_{xx}$ trace in the absence of microwave radiation is also shown (bottom). Curves are offset for clarity. The microwave power at the entrance of the waveguide is $1\mathrm{mW}$ and the electron density equals $2.13\bullet {10}^{11}{\mathrm{cm}}^{-2}$.

Figure 3

Evolution of the microwave absorption resonances in the magnetoresistance with excitation frequency. The frequency range from $30\text{to}75\mathrm{GHz}$ is covered. The microwave power inserted into the waveguide is approximately equal to $1\mathrm{mW}$, the electron density is $2.13\bullet {10}^{11}{\mathrm{cm}}^{-2}$.

Figure 4

The position of the microwave absorption resonance versus excitation frequency $f$. Open circles are data points collected from transport curves, whereas closed symbols represent data points acquired from differential luminescence spectra. The microwave power inserted into the waveguide is approximately equal to $1\mathrm{mW}$. The electron density is $2.13\bullet {10}^{11}{\mathrm{cm}}^{-2}$ in these experiments and the sample width is $0.4\mathrm{mm}$. The dotted line marks the magnetic field dependence of the cyclotron frequency $f_{\mathrm{c}}$ assuming an electron effective mass of 0.071 $m_0$. The inset shows microwave absorption spectra measured simultaneously in a transport measurement and with the luminescence detection scheme. These curves were taken at $47\mathrm{GHz}$ and $4.2\mathrm{K}$.

Figure 5

The dependence of the resonance frequency $f$ at zero magnetic field of the lowest plasma mode on the retardation parameter $A=\sqrt{\frac{n_s{e}^{2}W}{2\pi {ϵ}_0{m}^{*}{c}^2}}$. Frequencies have been normalized to the value predicted by theory when ignoring retardation effects $f_0$. The inset plots $f∕f_0$ as a function of electron density $n_s$ for a stripe with $W=0.4\mathrm{mm}$.