Stick-Slip Motion of the Wigner Solid on Liquid Helium
David G. Rees1,2*, Niyaz R. Beysengulov2,3, Juhn-Jong Lin1,2,4, Kimitoshi Kono1,2,3
1Institute of Physics, National Chiao Tung University, Hsinchu, Taiwan
2CEMS, RIKEN, Wako-shi, Japan
3Institute of Physics, Kazan Federal University, Kazan, Russian Federation
4Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan
* presenting author:David Rees, email:drees@nctu.edu.tw
Surface-state electrons (SSEs) on liquid helium substrates form a model 2D Coulomb system, the ground state of which remains the clearest example of the classical Wigner solid (WS)[1]. At rest, the WS is ‘dressed’ by a cloud of quantised capillary waves (ripplons), the Bragg scattering of which from the electron lattice gives rise to a commensurate deformation of the He surface known as the dimple lattice (DL)[2]. Under a sufficiently high driving force, the electron lattice decouples from the DL and ‘slides’ along the helium surface with high velocity[3]. Such dynamics are analogous to the detrapping of polaron states in which electrons are dressed by a cloud of virtual phonons[4]. The study of the WS-DL decoupling therefore provides insights into polaron dynamics as well as a unique oppourtunity to investigate collective electron motion on a perfectly clean substrate.
Here we present the first time-resolved measurements of the WS-DL decoupling. We measure the flow of SSEs along a helium substrate confined in a microchannel 100 μm long and 7.5 μm wide. The electron density, and so the number of electron rows in the quasi-1D WS, is controlled electrostatically using gate electrodes. We ramp the driving potential over several tens of microseconds, and record the current flowing in the microchannel. The electron system first exhibits a dynamical pinning at a particular electron velocity due to resonant Bragg-Cherenkov ripplon scattering[5]. Then, as the driving force builds, the WS slides from the DL and the current increases sharply, before relaxing as the driving force decreases. We find that this stick-slip process can occur repeatedly as the driving potential is ramped, giving rise to spontaneous narrow-band current noise. Such behavior can be compared with similar observations for degenerate electron systems in the WS regime[6]. We demonstrate a quantitative understanding of the nonlinear electron motion and that our microchannel device allows sensitive control of the current oscillation frequency. SSEs are therefore a promising system for the study of polaron-type decoupling dynamics and stick-slip friction at the nanoscale[7].

[1] C. C. Grimes and G. Adams, Phys. Rev. Lett. 42, 795 
(1979).
[2] Y. P. Monarkha and V. B. Shikin, Sov. Phys. JETP 41, 
710 (1975). 

[3] K. Shirahama and K. Kono, Phys. Rev. Lett. 74, 781 (1995).
[4] P. Gaal, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, Nature 450, 1210 (2007).
[5] M. I. Dykman and Y. G. Rubo, Phys. Rev. Lett. 78, 4813 (1997).
[6] G. A. Csathy, D. C. Tsui, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. 98, 066805 (2007).
[7] A. Bylinskii, D. Gangloff, and V. Vuletic, Science 348, 
1115 (2015). 



Keywords: Electrons on helium, Wigner solid, Stick-slip friction, Microchannel, Bragg-Cherenkov scattering