Dynamics of the Wigner Crystal of Composite Particles

Abstract

Conventional wisdom had long held that a composite particle behaves just like an ordinary Newtonian particle. In this paper, we derive the effective dynamics of a type-I Wigner crystal of composite particles directly from its microscopic wave function. It indicates that the composite particles are subjected to a Berry curvature in the momentum space as well as an emergent dissipationless viscosity. Therefore, contrary to the general belief, composite particles follow the more general Sundaram-Niu dynamics instead of the ordinary Newtonian one. We show that the presence of the Berry curvature is an inevitable feature for a dynamics consistent with the dipole picture of composite particles and Kohn's theorem. Based on the dynamics, we determine the dispersions of magneto-phonon excitations numerically. We find an emergent magneto-roton mode which signifies the composite-particle nature of the Wigner crystal. It occurs at frequencies much lower than the magnetic cyclotron frequency and has a vanishing oscillator strength in the long wavelength limit.

13 pages, 4 figures

References in corpus (8)

• Melting of a 2D Quantum Electron Solid in High Magnetic Field
• Microwave Resonance of 2D Wigner Crystal around integer Landau fillings
• Evidence for Two Different Solid Phases of Two Dimensional Electrons in High Magnetic Fields
• Fractional Quantum Hall Effect and Wigner Crystal of Two-Flux Composite Fermions
• Possible Reentrance of the Fractional Quantum Hall Effect in the Lowest Landau Level
• Topological Phonon Modes in A Two-Dimensional Wigner Crystal
• The Dirac composite fermion of the fractional quantum Hall effect
• Chern-Simons Theory and Dynamics of Composite Fermions

Cited by in corpus (7)

• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Lowest Landau level theory of the bosonic Jain states
• Berry phase of the composite Fermi-liquid
• Quantum mechanics of composite fermions
• Asymmetry of the Geometrical Resonances of Composite Fermions
• Emergence of Dirac Composite Fermions: Dipole Picture