Regular Article

The movement of a one-dimensional Wigner solid explained by a modified Frenkel-Kontorova model

¹ Mathematisches Institut, Universität Leipzig, PF 100920, 04009 Leipzig, Germany
² Quantum Dynamics Unit, Okinawa Institute of Science and Technology (OIST) Graduate University, Tancha 1919-1, Okinawa 904-0495, Japan
³ Departament de Química Inorgànica i Orgànica, Secció de Química Orgànica, and Institut de Química Teòrica i Computacional, (IQTCUB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain

^a e-mail: quapp@math.uni-leipzig.de

Received: 17 August 2020
Received in final form: 5 October 2020
Accepted: 9 October 2020
Published online: 7 December 2020

Abstract

We propose a Frenkel-Kontorova model for a 1D chain of electrons forming a Wigner solid over ⁴He. 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.