Fig. 1: Schematic of the skyrmion molecule lattice.

The left panel (outlined by the dashed box) illustrates the key steps for its realization. Two orthogonal in-pane \(p\)-orbitals, \(\left|{p}_{x}\right\rangle\) and \(\left|{p}_{y}\right\rangle\), serve as the basis to construct a graphene lattice. Each unit cell contains two sublattice sites. Enabled by graphene’s lattice symmetry, \(\left|{p}_{x}\right\rangle\) and \(\left|{p}_{y}\right\rangle\) acquire a \({90}^{\circ}\) phase difference at the Dirac points, superposing into vortices. Due to the inversion symmetry, vortices at different sublattice sites carry opposite topological charges, locked together into a neutral, stable configuration termed a vortex molecule. When coupled to an evanescent field with in-plane spin angular momentum, vortex molecules evolve into skyrmion molecules composed of symmetry-locked skyrmion pairs with opposite skyrmion numbers (see the following section for mechanistic details). As eigenstates of the system, these molecules enable stable transport and flexible control over their creation, deformation, annihilation, and even polarizability inversion by fine-tuning the material boundaries, as depicted in the right panel.