Spectrum of one-dimensional plasmons in a single stripe of two-dimensional electrons

Microwave absorption spectra of a single, narrow stripe of two-dimensional electrons have been recorded with an optical detection scheme in order to investigate the dispersion of one-dimensional (1D) plasmons. For narrow stripes the dispersion of 1D plasmons is linear up to momentum values $K=1∕W$, where $W$ is the width of the stripe. The dependencies of the 1D plasmon velocity on electron density, length, and width of the stripe were measured. We also address the behavior of the 1D transverse and longitudinal plasma modes in a perpendicular magnetic field.

Figure 1

Microwave absorption spectra measured at $B=0$ and $1.5\mathrm{K}$ on stripes with the following geometries and electron concentrations: $2\times 0.1{\mathrm{mm}}^2$ and $1.2\times {10}^{11}{\mathrm{cm}}^{-2}$; $2\times 0.2{\mathrm{mm}}^2$ and $1.9\times {10}^{11}{\mathrm{cm}}^{-2}$; $1\times 0.1{\mathrm{mm}}^2$ and $1.2\times {10}^{11}{\mathrm{cm}}^{-2}$. The inset plots the frequency of the fundamental mode for disk-shaped mesas as a function of the disk diameter $d$ as well as for stripes with a width of $0.1\mathrm{mm}$ as a function of their length $L$ at a density of $1.2\times {10}^{11}{\mathrm{cm}}^{-2}$.

Figure 2

The plasmon dispersion measured on a stripe with a length of $2\mathrm{mm}$, a width of $0.1\mathrm{mm}$, and an electron density of $1.2\times {10}^{11}{\mathrm{cm}}^{-2}$. The dispersion of 2D plasmons and of 1D plasmons (in the limit of small wave vectors $KW⪡1$) predicted by theory are also shown for the sake of comparison. The observed linear dispersion points to 1D plasmon behavior with a velocity of $1.82\times {10}^7\mathrm{m}∕\mathrm{s}$. The inset depicts the dependence of the 1D plasmon velocity $v_{1\mathrm{D}}$ in units of ${10}^7\mathrm{m}∕\mathrm{s}$ on parameter ${\left(n_{S}W\right)}^{1∕2}$.

Figure 3

Magnetic field dependence of the fundamental transverse and longitudinal plasma modes of a stripe of 2D electrons with a length of $2\mathrm{mm}$, a width of $0.2\mathrm{mm}$, and an electron density of $1.2\times {10}^{11}{\mathrm{cm}}^{-2}$. The functional dependencies predicted with Eqs. (2, 3) are plotted as solid lines. The dashed line represents the cyclotron frequency. The inset shows absorption spectra recorded at different magnetic fields (0, 0.3, and $0.6\mathrm{T}$) for a stripe with the same dimensions but a larger electron density of $1.9\times {10}^{11}{\mathrm{cm}}^{-2}$.

Figure 4

Magnetic field dependence of the fundamental and higher order longitudinal 1D plasma modes of a stripe with a length of $2\mathrm{mm}$, a width of $0.2\mathrm{mm}$, and a density of $1.2\times {10}^{11}{\mathrm{cm}}^{-2}$. The inset plots the magnetic field dependence of the linewidth of the fundamental mode.