Magnetoplasmons in nondegenerate quantum wires on suspended helium films

Magnetoplasmon spectra for the nondegenerate surface electrons confined in a quasi-one-dimensional channel over a liquid helium film are determined within a microscopic approach in the limit of strong magnetic fields when the electrons occupy the lowest spin-split Landau level. It is shown that the dispersion relation and the spatial structure, transverse to the channel, of the magnetoplasmons have a length scale ${\ell }_T=\sqrt{2T∕m{\Omega }^2}⪢{\ell }_0$, where $\Omega$ is the confining frequency and ${\ell }_0$ is the magnetic length. We find acoustic modes, whose velocities as a function of the gate distance exhibit a highly nonlinear behavior under certain conditions, in particular, the appearance of anticrossings.

Figure 1

Schematic drawing of the structure from Ref. 16.

Figure 2

Fundamental mode spectrum ${\omega }_0\left(q\right)$ in units of ${\omega }_{\ast }=2\sqrt{\pi }\mid e\mid {\mathit{cn}}_s^0∕ϵ{\ell }_{T}B$ for the NQ1DES in the absence of gate $(d\to \infty )$ indicated by the solid line and for gate distances $d={10}^{-2}\mathrm{cm}$ (dashed line) and $d={10}^{-3}\mathrm{cm}$ (dotted line). In the inset, the mode velocity is shown, in units of $u_{\ast }=2\pi \mid e\mid {\mathit{cn}}_s^0∕ϵB$. The spectrum was calculated from the $10\times 10$ equation system in Eq. (18). The parameters are chosen to be the same as in the experiment of Ref. 16.

Figure 3

Spatial structure of the fundamental mode $\rho (q,y,\omega )$, in units of ${\rho }_{\ast }={\rho }^{\left(0\right)}(q,\omega )∕\sqrt{\pi }{\ell }_T$, calculated from the $10\times 10$ system, for $(q{\ell }_T{)}^{-1}=100$. The solid, the dashed and the dotted curves parameters coincide with those of pertinent curves in Fig. 2. In the inset the solid (dashed) curve plots $\rho ∕{\rho }_{\ast }$ for ${\omega }_{0+}({\omega }_{0-})$ mode in the absence of gate.

Figure 4

Dispersion relations for the first (upper curve) and second (lower curve) excited Q1D magnetoplasmons. The solid and the dotted curves correspond to the same parameters as the pertinent curves in Fig. 2. In the inset the mode velocities are shown with the dashed curve corresponding to $d={10}^{-2}\mathrm{cm}$.

Figure 5

Dispersion relation for the fundamental (top curve) and two excited magnetoplasmons (curves below) for the structure without the gate for $T=1\mathrm{K}$ (solid line) and $T=0.4\mathrm{K}$ (dashed line). Other parameters are the same as in Fig. 2. In the inset we show the mode velocities.

Figure 6

Spatial structure of charge density for the first excited modes in the channel without the metallic gate calculated for $q{\ell }_T=0.01$. The solid (dashed) line represent the first (second) excited magnetoplasmon.

Figure 7

Mode velocity versus gate distance for the first five modes represented by the solid, dashed, dotted, dot-dashed and dot-dot-dashed curves. In the inset these modes are indicated by five solid (dashed) curves when the $C\left(Q\right)$ term of Eq. (18) is neglected. Here $n_s=2\times {10}^7{\mathrm{cm}}^{-2}$, $\Omega =5\times {10}^8{\mathrm{cm}}^{-1}$ and the other parameters are the same as in Fig. 2.

Figure 8

Same as Fig. 7 in a wide region of $d∕{\ell }_T$. We clearly see additional anticrossings for larger $d∕{\ell }_T$.