Soliton-Lattice Origin of Incommensurability in High-Pressure Antimony

The microscopic origin of incommensurability in host-guest crystals remains unresolved. Here we show that the high-pressure antimony host-guest phase Sb-II is a soliton lattice, where localized guest-host misregistries decorate a commensurate 4/3 reference structure. First-principles calculations reveal a corrugated and hysteretic registry landscape, motivating a Frenkel-Kontorova description that accounts for soliton-lattice approximants of the form $(4n+1)/(3n+1)$. Machine-learning-potential calculations of these approximants show an energetically preferred soliton spacing, and their localized misregistry cores are also verified by first-principles relaxations. At finite temperature, the thermally broadened soliton lattice appears as an atomic density wave along the guest chains, consistent with experimental diffraction. This soliton-registry picture provides a microscopic mechanism for host-guest incommensurability in Sb-II.