Many-Electron System on Helium and Color Center Spectroscopy

Electrons on the helium surface display sharp resonant absorption lines related to the transitions between the subbands of quantized motion transverse to the surface. A magnetic field parallel to the surface strongly affects the absorption spectrum. We show that the effect results from admixing the intersubband transitions to the in-plane quantum dynamics of the strongly correlated electron liquid or a Wigner crystal. This is similar to the admixing of electron transitions in color centers to phonons. The spectrum permits a direct characterization of the many-electron dynamics and also enables testing the theory of color centers in a system with controllable coupling.

Figure 1

Left: The many-electron system on helium in a magnetic field with components parallel ($B_{\parallel }\equiv B_x$) and perpendicular ($B_{\perp }\equiv B_z$) to the helium surface. Right: The energy spectrum of an electron in the two lowest bands of motion normal to the surface. The energy difference between the bands ${ϵ}_{21}$ is the distance between the levels of the quantized motion along the $z$ axis. The single-electron kinetic energy of motion along the surface is quadratic in the in-plane momentum $\mathbf{p}$ for $B_{\perp }=0$. The field $B_{\perp }$ transforms the spectrum into the Landau levels, which are broadened by the electron-electron interaction. The field $B_{\parallel }$ shifts the bands of the in-plane motion by $\mathrm{\Delta }{p}_B$, see Eq. (1).

Figure 2

The spectra of the relative microwave-induced change of the low-frequency admittance $Y$ for different $B_{\parallel }\equiv B_x$. The data refer to the microwave frequency $f=150\mathrm{GHz}$, $T=0.2\mathrm{K}$, $B_{\perp }\equiv B_z=0.5\mathrm{T}$, and $n_s=21.5\times {10}^6{\mathrm{cm}}^{-2}$. The ac bias is 30 mV. The dashed lines show Gaussian fit to the data with the variance $\delta E_z^2$ given by Eq. (4).

Figure 3

The dependence of the typical width of the spectral peaks $\delta E_z$ on $B_{\parallel }\equiv B_x$ for different temperatures. The other parameters are the same as in Fig. 2. The dashed lines are the linear fit. In the strong-coupling range they are described by Eq. (4). The inset shows the slope of $\delta E_z/B_{\parallel }$ as a function of $T^{1/2}$. The dashed black line is given by Eq. (4) with no adjustable parameters.

Figure 4

The dependence of the squared linewidth scaled by the ratio of the magnetic fields $B_{\parallel }\equiv B_x$ and $B_{\perp }\equiv B_z$ on the electron density $n_s$. The excitation frequency is 174 GHz except for the data at $B_{\perp }\equiv B_z=0.3\mathrm{T}$, which refers to $f=144\mathrm{GHz}$. The black line shows the prediction of Eq. (4) for the effective electron temperature $T_e=0.6\mathrm{K}$. Inset: the linewidth as a function of the microwave power for $B_z=0.5\mathrm{T}$, $B_x=0.75\mathrm{T}$, $f=150\mathrm{GHz}$, and $n_s=21.5\times {10}^6{\mathrm{cm}}^{-2}$.