Abstract
Emergent quasiparticles in solids often exhibit unique topological properties as a result of the complex interplay between charge, orbital, spin, and lattice degrees of freedom. Among these quasiparticles, the polaron occupies a special place as the first known manifestation of the interaction between a fermion and a boson field. While polarons have been investigated for almost a century, whether these quasiparticles exhibit topological properties and why remain open questions. Here, we establish the universal symmetry principles governing the topology of polar textures in large polarons. Using a group-theoretic analysis, we identify four distinct classes of polar textures in time-reversal-invariant systems, and we show that they carry integer topological charges. We validate this classification by performing state-of-the-art first-principles calculations of materials representative of each class. For these materials, we compute the fingerprints of polaron topology in Huang diffuse scattering and propose ultrafast electron and X-ray scattering experiments to detect these quasiparticles.