Dynamics of the Wigner Crystal of Composite Particles

TL;DR

This paper derives the effective dynamics of a Wigner crystal of composite particles, revealing Berry curvature effects and emergent viscosity, which lead to novel magneto-phonon and magneto-roton excitations distinct from classical particles.

Contribution

It demonstrates that composite particles follow Sundaram-Niu dynamics with Berry curvature, challenging the conventional Newtonian assumption and providing new insights into their collective excitations.

Findings

Composite particles exhibit Berry curvature in momentum space.

Emergent dissipationless viscosity affects particle dynamics.

Discovery of a low-frequency magneto-roton mode with vanishing oscillator strength.

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.