Thermoelectric Transport in a Correlated Electron System on the Surface of Liquid Helium

We report on the direct observation of the thermoelectric transport in a nondegenerate electron system trapped on the surface of liquid helium. The microwave-induced excitation of the vertical transitions of electrons between the surface-bound states results in their lateral flow, which we were able to detect by employing a segmented electrode configuration. We show that this flow of electrons arises due to the Seebeck effect. Our experimental results are in good agreement with the theoretical calculations based on kinetic equations. This demonstrates the importance of the fast electron-electron collisions, which, in particular, leads to the violation of the Wiedemann-Franz law in this system.

Figure 1

(a) Schematic view of the segmented electrode geometry used in the experiment and the equilibrium electron density profile calculated as described in the text. The horizontal arrows indicate direction of electron flow induced by resonant MW excitation. (b) The image-current response obtained at $T=200\mathrm{mK}$ using pulse-modulated ($f_m=400\mathrm{kHz}$) excitation of SEs by 130-GHz radiation. The measured image currents $I_{\mathrm{tc}}$ and $I_{\mathrm{bc}}$ at the central segments of the capacitor’s top and bottom plates, respectively, are plotted by solid (black) and dashed (black) lines, respectively.

Figure 2

Color map of the measured lateral displacement current $I_{\text{later}}$ versus $E_{\perp }^{(c)}$ and $E_{\perp }^{(m)}$ for SEs under pulse-modulated ($f_m=200\mathrm{kHz}$) excitation by 130-GHz radiation at $T=600\mathrm{mK}$. The dashed line marks $E_{\perp }^{(c)}=E_{\perp }^{(m)}$.

Figure 3

(a) Measured transient traces of $I_{\text{later}}(t)$ for SEs under pulsed-modulated ($f_{\mathrm{m}}=200\mathrm{kHz}$) 130-GHz radiation for different values of the MW-source power (indicated in decibels with respect to the maximum power). The dashed black line is the current response calculated using Eqs. (3) for $E_{\mathrm{MW}}=0.42\mathrm{V}/\mathrm{m}$. (b) The first harmonic of $I_{\text{later}}(t)$ measured by the lock-in amplifier (open red circles) and extracted from transient traces shown in (a) (closed blue circles) versus input MW power $P_{\mathrm{MW}}$. Dashed line represents $I_{\text{later}}$ versus $E_{\mathrm{MW}}^2$ extracted from the calculated transient traces (see Supplemental Material [29]).