Degeneracy and Inversion of Band Structure for Wigner Crystals on a Toroidal Helix

Abstract

We explore the formation of Wigner crystals for charged particles on a toroidal helix. Focusing on certain commensurate cases we show that the ground state undergoes a pitchfork bifurcation from the totally symmetric polygonic to a zig-zag-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. 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.

4 pages, 3 figures

References in corpus (5)

• Structural phase transitions in low-dimensional ion crystals
• Quantum zigzag transition in ion chains
• Nanofiber-Based Double-Helix Dipole Trap for Cold Neutral Atoms
• Quantum Phase Transition between (Luttinger) Liquid and Gas of Cold Molecules
• Stability and dynamics of ion rings in linear multipole traps

Cited by in corpus (6)

• Pinned-to-sliding transition and structural crossovers for helically confined charges
• Local equilibria and state transfer of charged classical particles on a helix in an electric field
• External field-induced dynamics of a charged particle on a closed helix
• Driven toroidal helix as a generalization of Kapitzas pendulum
• Formation and crossover of multiple helical dipole chains
• Long-Range Interacting Particles on a Helix: A Statistical and Correlation Analysis of Equilibrium Configurations