# Self-Diffusion in a Spatially Modulated System of Electrons on Helium

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## Abstract

We present results of molecular dynamics simulations of the electron system on the surface of liquid helium. The simulations are done for 1600 electrons with periodic boundary conditions. Electron scattering by capillary waves and phonons in helium is explicitly taken into account. We find that the self-diffusion coefficient superlinearly decreases with decreasing temperature. In the free-electron system, it turns to zero essentially discontinuously, which we associate with the liquid-to-solid transition. In contrast, when the system is placed in the fully commensurate one-dimensional potential, the freezing of the diffusion occurs smoothly. We relate this change to the fact that, as we show, a Wigner crystal in such a potential is stable, in contrast to systems with a short-range inter-particle coupling. We find that the freezing temperature nonmonotonically depends on the commensurability parameter. We also find incommensurability solitons in the solid phase. The results reveal peculiar features of the dynamics of a strongly correlated system with long-range coupling placed into a periodic potential.

## Keywords

Electrons on helium Commensurate–incommensurate transitions Wigner crystallization Self-diffusion## Notes

### Acknowledgements

We are grateful for the discussion of the results of this paper to the participants of the International Workshop on Electrons and Ions in Quantum Fluids and Solids (Japan 2018) and the organizer of this workshop K. Kono. This research was supported in part by the NSF-DMR Grant 1708331.

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