Sliding of an electron crystal of finite size on the surface of superfluid $^{4}\mathrm{He}$ confined in a microchannel

Sliding of an electron crystal of finite size on the surface of superfluid ${}^{4}{He}$ confined in a microchannel

J.-Y. Lin, A. V. Smorodin, A. O. Badrutdinov, and D. Konstantinov

Phys. Rev. B 98, 085412 – Published 7 August 2018

Abstract

We present a new study of the nonlinear transport of a two-dimensional electron crystal on the surface of liquid helium confined in a $10 − μ m$ -wide channel in which the effective length of the crystal can be varied from 10 to $215 μ m$ . At low driving voltages, the moving electron crystal is strongly coupled to deformation of the liquid surface arising from resonant excitation of surface capillary waves, ripplons, while at higher driving voltages the crystal decouples from the deformation. We find strong dependence of the decoupling threshold of the driving electric field acting on the electrons, on the size of the crystal. In particular, the threshold electric field significantly decreases when the length of the crystal becomes shorter than $25 μ m$ . We explain this effect as arising from weakening of surface deformations due to radiative loss of resonantly excited ripplons from an electron crystal of finite size, and we account for the observed effect using an instructive analytical model.

Received 25 May 2018

DOI:https://doi.org/10.1103/PhysRevB.98.085412

Physics Subject Headings (PhySH)

Electrical conductivity Friction Surface & interfacial phenomena

Wigner crystal

Lithography Resistivity measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

J.-Y. Lin, A. V. Smorodin^*, A. O. Badrutdinov^†, and D. Konstantinov^‡

Quantum Dynamics Unit, Okinawa Institute of Science and Technology (OIST) Graduate University, Onna, 904-0495 Okinawa, Japan

^*Current address: Electronic and Quantum Magnetism Unit, Okinawa Institute of Science and Technology (OIST) Graduate University, Onna, 904-0495 Okinawa, Japan.
^†Current address: Mechanical Engineering and Microfabrication Support Section, Okinawa Institute of Science and Technology (OIST) Graduate University, Onna, 904-0495 Okinawa, Japan.
^‡denis@oist.jp

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Vol. 98, Iss. 8 — 15 August 2018

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Figure 1
(a) False-color scanning electron microscopic image of Sample 1 consisting of two reservoirs connected by a 215- $μ m$ channel and filled with superfluid ${}^{4}{He}$ . The bottom electrode of the channel is segmented into pieces of different length as indicated in the Figure. (b) In-phase and quadrature components of the measured current $I_{out}$ due to electrons in the channel for different values of channel voltage $V_{ch}$ (solid circles connected by lines). Arrows indicate variation of $I_{out}$ as $V_{ch}$ increases from zero to 2 V. Other symbols plot measured components of $I_{out}$ when the voltage applied to a group of segments $V_{tr}$ is varied from 0.3 to 2 V, while the rest of segments is kept at 0.3 V. Dashed line (red) is the fitting to the date using the lumped-circuit model shown in Fig. 1. (c) Electrical lumped-circuit model of the device used for the analysis. $R$ represents the resistance of the electron system which mostly comes from the resistance of the electrons in the channel.
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Figure 2
$I V$ curves measured at $T = 0.88$ K in Sample 1 for different lengths of WS in the microchannel (the corresponding length of WS is given in the legend in $μ m)$ . $I V$ curve for the channel entirely filled with electron liquid is given by solid circles (EL, red). The dashed (black) line is the calculated current for WS obtained from the fitting of experimental data using the value of $I_{BC}$ as an adjustable parameter.
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Figure 3
$I V$ curves measured at $T = 0.88$ K in Sample 2 for different lengths of WS in the microchannel. $I V$ curve for the channel entirely filled with electron liquid is given by solid circles (EL, red). The dashed (black) line is the calculated current for WS obtained from the fitting of experimental data using the value of $I_{BC}$ as an adjustable parameter.
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Figure 4
Electric field $E_{s}$ across solid phase of the microchannel for different lengths of WS plotted as a function of driving voltage. The values of $E_{s}$ are calculated from the data in Fig. 3 using Eq. (3) as described in the text.
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Figure 5
Threshold electric field $E_{th}$ at the onset of sliding of WS plotted as a function of WS length. The values of $E_{th}$ are extracted from data taken using Sample 1 (opened symbols) and Sample 2 (closed symbols) for electron densities of $n_{s} = 4.37 \times 10^{13}$ (opened squares, blue), $4.49 \times 10^{13}$ (opened circles, green), $5.24 \times 10^{13} m^{- 2}$ (closed squares, orange), and $5.27 \times 10^{13}$ (closed circles, red). The data plotted by closed (orange) squares were taken using the driving frequency $f = 30$ kHz, while all other data were taken at $f = 99$ kHz. In addition, the data plotted by closed (red) circles were taken at $T = 0.91$ K, while all other data were taken at $T = 0.88$ K. The dashed line (black) shows the dependence $E_{th} = E_{0} [1 - exp (- L / L_{c})]$ with $E_{0} = 265$ V/m and $L_{c} = 10 μ m$ ; see explanation in the text.
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Physical Review B

covering condensed matter and materials physics

Sliding of an electron crystal of finite size on the surface of superfluid ${}^{4}{He}$ confined in a microchannel

J.-Y. Lin, A. V. Smorodin, A. O. Badrutdinov, and D. Konstantinov

Phys. Rev. B 98, 085412 – Published 7 August 2018

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Physical Review B

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Sliding of an electron crystal of finite size on the surface of superfluid He4 confined in a microchannel

J.-Y. Lin, A. V. Smorodin, A. O. Badrutdinov, and D. Konstantinov

Phys. Rev. B 98, 085412 – Published 7 August 2018

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Sliding of an electron crystal of finite size on the surface of superfluid ${}^{4}{He}$ confined in a microchannel