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Title: Solitons in a one-dimensional Wigner crystal

Abstract

In one-dimensional quantum systems with strong long-range repulsion particles arrange in a quasi-periodic chain, the Wigner crystal. Here, we demonstrate that besides the familiar phonons, such one-dimensional Wigner crystal supports an additional mode of elementary excitations, which can be identified with solitons in the classical limit. Furthermore, we compute the corresponding excitation spectrum and argue that the solitons have a parametrically small decay rate at low energies. Finally, we discuss implications of our results for the behavior of the dynamic structure factor.

Authors:
 [1];  [2]
  1. Georgia Inst. of Technology, Atlanta, GA (United States). School of Physics
  2. Argonne National Lab. (ANL), Argonne, IL (United States). Materials Science Division
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1357011
Alternate Identifier(s):
OSTI ID: 1180712
Grant/Contract Number:
AC02-06CH11357
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review. B, Condensed Matter and Materials Physics
Additional Journal Information:
Journal Volume: 91; Journal Issue: 16; Journal ID: ISSN 1098-0121
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE

Citation Formats

Pustilnik, M., and Matveev, K. A. Solitons in a one-dimensional Wigner crystal. United States: N. p., 2015. Web. doi:10.1103/PhysRevB.91.165416.
Pustilnik, M., & Matveev, K. A. Solitons in a one-dimensional Wigner crystal. United States. doi:10.1103/PhysRevB.91.165416.
Pustilnik, M., and Matveev, K. A. Thu . "Solitons in a one-dimensional Wigner crystal". United States. doi:10.1103/PhysRevB.91.165416. https://www.osti.gov/servlets/purl/1357011.
@article{osti_1357011,
title = {Solitons in a one-dimensional Wigner crystal},
author = {Pustilnik, M. and Matveev, K. A.},
abstractNote = {In one-dimensional quantum systems with strong long-range repulsion particles arrange in a quasi-periodic chain, the Wigner crystal. Here, we demonstrate that besides the familiar phonons, such one-dimensional Wigner crystal supports an additional mode of elementary excitations, which can be identified with solitons in the classical limit. Furthermore, we compute the corresponding excitation spectrum and argue that the solitons have a parametrically small decay rate at low energies. Finally, we discuss implications of our results for the behavior of the dynamic structure factor.},
doi = {10.1103/PhysRevB.91.165416},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 16,
volume = 91,
place = {United States},
year = {Thu Apr 16 00:00:00 EDT 2015},
month = {Thu Apr 16 00:00:00 EDT 2015}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 5works
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  • Cited by 5
  • ({ital V}{sub {ital p}} is the amplitude of the pinning potential, {ital T}{sub 0}={h_bar}{ital v}{sub {ital F}}/{ital L}, {ital v}{sub {ital F}}{similar_to}{h_bar}/{ital ma} is the drift velocity of a Wigner crystal ring with lattice spacing {ital a}). For very weak pinning, {ital V}{sub {ital p}}{much_lt}{ital T}{sub 0}, the influence of the barrier on the persistent current of a Wigner crystal ring is negligibly small. We have also shown that unscreened, long-range Coulomb interactions increase the stiffness of the Wigner lattice. This leads to additional suppression of the amplitude of Aharonov-Bohm oscillations, but makes the predicted anomalous temperature dependence of themore » persistent current in the strong pinning limit even more pronounced. The corresponding temperature of the peak will also be shifted by a factor which depends on the number of particles in the ring. The impact of dissipation on the persistent current of a Wigner crystal ring is also studied.« less
  • Equilibration of a one-dimensional system of interacting electrons requires processes that change the numbers of left- and right-moving particles. At low temperatures such processes are strongly suppressed, resulting in slow relaxation towards equilibrium. We study this phenomenon in the case of spinless electrons with strong long-range repulsion, when the electrons form a one-dimensional Wigner crystal. We find the relaxation rate by accounting for the umklapp scattering of phonons in the crystal. For the integrable model of particles with inverse-square repulsion, the relaxation rate vanishes.
  • We study scattering of charge and spin excitations in a system of interacting electrons in one dimension. At low densities, electrons form a one-dimensional Wigner crystal. To a first approximation, the charge excitations are the phonons in the Wigner crystal, and the spin excitations are described by the Heisenberg model with nearest-neighbor exchange coupling. This model is integrable and thus incapable of describing some important phenomena, such as scattering of excitations off each other and the resulting equilibration of the system. We obtain the leading corrections to this model, including charge-spin coupling and the next-nearest-neighbor exchange in the spin subsystem.more » We apply the results to the problem of equilibration of the one-dimensional Wigner crystal and find that the leading contribution to the equilibration rate arises from scattering of spin excitations off each other. We discuss the implications of our results for the conductance of quantum wires at low electron densities« less