Tunable Skyrmions in a Topological Wigner Crystal

In low density systems with strong interactions electrons are expected to crystallize into a Wigner solid. Recently, advances in two-dimensional systems where electrons carry Berry curvature have added a topological dimension to Wigner crystallization. Using a model for pseudospin interactions in a topological Wigner crystal, here we show that the competition between ferromagnetic Heisenberg exchange $J$ and the chiral interaction $\gamma$ on the triangular lattice stabilizes a zero-field skyrmion crystal whose density is continuously tunable through the ratio $\gamma/J$. The chiral interaction originates from finite Berry curvature in an underlying time-reversal broken Wigner crystal. In the continuum limit, the chiral interaction acts as a chemical potential for skyrmions, while higher-order gradient terms beyond the nonlinear sigma model select the skyrmion density. At large chiral coupling, we uncover a 24-site tetra-skyrmion crystal carrying four units of topological charge per magnetic unit cell, which becomes degenerate with four-sublattice tetrahedral order as $J \to 0$. We characterize the magnon structure for these phases and discuss the transition between the tunable skyrmion crystal to these states at large $\gamma/J$. Our results establish the phase diagram of ferromagnetic topological Wigner crystals.