Defects in Wigner crystals: fracton-elasticity duality and vacancy proliferation

TL;DR

This work develops a low-energy theory for three-dimensional Wigner crystals of charged particles by extending fracton-elasticity duality to incorporate the magnetic 1-form symmetry of electromagnetism. By introducing the displacement field $u_i$, the phase field $\phi$, and dual gauge fields, the authors formulate a unified dual description of vacancies/interstitials, dislocations, and disclinations, and derive their mutual interactions and conservation laws. A key result is the vacancy-induced anti-Higgs mechanism: condensation of charged defects can generate or suppress gapless longitudinal modes depending on the plasma background, reshaping the long-wavelength dynamics and possibly enabling defect-mediated melting. The framework provides predictive formulas for defect interactions, screening, and dispersions, offering a platform for studying defect dynamics and transport in charged crystals and guiding explorations in 2D/3D analogues and related systems.

Abstract

We develop a low-energy field theory for electrically charged crystals. Using the tools of fracton-elasticity duality, generalized to accommodate the magnetic 1-form symmetry of electromagnetism, we show how the elastic and electromagnetic degrees of freedom couple to the different crystal defects and to one another. The resulting field theory is then used to calculate vacancy-vacancy interaction energy, and to study the consequences of vacancy proliferation. We find that the longitudinal mode, which in a perfect crystal has a finite gap due to plasma oscillations, becomes gapless in the presence of vacancies. Our framework lays a foundation for a study of defect interactions, their collective dynamics, and consequences of defect-mediated melting in charged crystals.

Figures (4)

• Figure 1: A cross-section view of a Wigner crystal. The electrons $e^-$ form a lattice inside a background medium with a uniform charge density $+n_0$. The displacement of the electrons (full blue spheres) from their equilibrium positions (dashed blue circles) is given by $d_i=x_i-X_i$, with $d_x$ along one vertical line visualized in the plot. The dashed red circle with the $X$ mark represents a vacancy.
• Figure 2: A translation of the charged background relative to the electrons by $\boldsymbol\delta$ creates surface charge $\pm n_0\delta$ on the opposite sides, which in turn induces the electric field $\mathbf{E} = -n_0\boldsymbol\delta$.
• Figure 3: Visualization of a line defect (red line) and a point defect (orange sphere). An integral of the line defect density over the auxiliary surface (yellow) yields a topological invariant.
• Figure S1: Points and curves used in the calculation of the Maurer-Cartan form.