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Degeneracy and inversion of band structure for Wigner crystals on a closed helix

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Zampetaki,  Alexandra V.
International Max Planck Research School for Ultrafast Imaging & Structural Dynamics (IMPRS-UFAST), Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany;

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PhysRevA.91.023409.pdf
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Citation

Zampetaki, A. V., Stockhofe, J., & Schmelcher, P. (2015). Degeneracy and inversion of band structure for Wigner crystals on a closed helix. Physical Review A, 91(2): 023409. doi:10.1103/PhysRevA.91.023409.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002A-6011-D
Abstract
Constraining long-range interacting particles to move on a curved manifold can drastically alter their effective interactions. As a prototype we explore the structure and vibrational dynamics of crystalline configurations formed on a closed helix. We show that the ground state undergoes a pitchfork bifurcation from a symmetric polygonic to a zigzag-like configuration with increasing radius of the helix. Remarkably, we find that, for a specific value of the helix radius, below the bifurcation point, the vibrational frequency spectrum collapses to a single frequency. This allows for an essentially independent small-amplitude motion of the individual particles and, consequently, localized excitations can propagate in time without significant spreading. Upon increasing the radius beyond the degeneracy point, the band structure is inverted, with the out-of-phase oscillation mode becoming lower in frequency than the mode corresponding to the center-of-mass motion.