The movement of a one-dimensional Wigner solid explained by a modified Frenkel-Kontorova model
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
The movement of a one-dimensional Wigner solid explained by a modified Frenkel-Kontorova model Wolfgang Quapp 1,a , Jui-Yin Lin 2 , and Josep Maria Bofill 3 1 2
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Mathematisches Institut, Universit¨ at Leipzig, PF 100920, 04009 Leipzig, Germany Quantum Dynamics Unit, Okinawa Institute of Science and Technology (OIST) Graduate University, Tancha 1919-1, Okinawa 904-0495, Japan Departament de Qu´ımica Inorg` anica i Org` anica, Secci´ o de Qu´ımica Org` anica, and Institut de Qu´ımica Te` orica i Computacional, (IQTCUB), Universitat de Barcelona, Mart´ı i Franqu`es 1, 08028 Barcelona, Spain Received 17 August 2020 / Received in final form 5 October 2020 / Accepted 9 October 2020 Published online 7 December 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. We propose a Frenkel-Kontorova model for a 1D chain of electrons forming a Wigner solid over 4 He. It is a highly idealized picture, but with the model at hand we can study the movement of the chain. We find out that the energetically most preferable movement is the successive sliding of a kink or an antikink through the chain. Then the force for a movement does not depend on the length of the chain. The force uniformly applied to all electrons must be larger than a force exciting only a kink or an antikink. We calculate two cases, one with stiff ‘springs’ between the electrons and one with weak ‘springs’. The side potential of the ‘dimples’ is additionally damped at the periphery. We study the cases with 33, 66, and 101 particles.
1 Introduction A Wigner solid (WS) is an experimental fact [1] that has first been observed in a system of two-dimensional surfacestate electrons (SSE) floating above a liquid helium-4 surface [2,3]. Given that liquid helium is weakly polarized, the unscreened Coulomb interaction of electrons benefits a WS formation from SSE crystallization at densities of order 1013 m−2 and at temperatures around 1 K. The strong inter-electron interaction makes this SSE system an ideal system for studying many-particle problems [4–7] especially for the driven dynamics of strongly correlated systems. Typical experimental devices for studying the driven dynamics of SSE on helium are similar to a semiconductor field-effect transistor [8,9]. Here SSE are capacitively coupled to the source, channel and drain electrodes beneath liquid helium. A pair of split gates on the liquid helium level is used to reduce the effective width of the channel, so that a quasi one dimensional (1D) configuration of SSE can be realized. Confining the SSE in capillary-condensed micro-channel structures is practical for investigating nonlinear electron transport and phase transitions. The strongly-correlated WS phase gives rise to many interesting phenomena, such as the re-entrant melting of quasi-1D electron crystals [10–12], stick-slip motion of a WS [13,14], a
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the bistable transport properties of a quasi-1D WS [15], th
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