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

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.

An Analysis of Some Properties and the Use of the Twist Map for the Finite Frenkel–Kontorova Model

“…If one pulls the ends, all of the bellows relax. Newton trajectories with force f can be used to calculate many kinds of solitones of the FK chain and, thus, intermediate minima of the potential energy surface and saddle points with an increasing index [3,6,19,[46][47][48].…”

“…The latter acts on the extracted subsystem by a potential. Of special interest may be electronic applications [2][3][4][5][6][7] for Wigner electrons or Josephson junctions. Further models are chargedensity wave conductors [8][9][10], charge transport in solids and on crystal surfaces [11], magnetic or ferro-and antiferromagnetic domain walls [12], magnetic superlattices [13], superconductivity [14,15], and vortex matter [16][17][18], to name a few.…”