Incommensurate guest-host phase in compressed Sb is a soliton lattice

An antimony phase known as SbII forms an interesting incommensurate lattice structure: 3/4 of the Sb atoms form a 3D cage with comparatively large channels parallel to the crystallographic $z$ ("host"), while the remaining 1/4 form 1D chains ("guest") filling these channels (similar structures are formed by Bi and a few other elements). The two systems are incommensurate, with the incommensurability ratio close to 1.301. The channels are too narrow for the naive interpretation of two decoupled periodic systems. Indeed our calculation show formation of guest/host covalent bonds. No indication of a Peirls-like instability can be found. We find, through DFT calculations and LAMMPS molecular dynamics that the real picture is more complex, and equivalent to soliton lattice formation: there are two different periodicities of a free host and and a free-standing guest chain, but these are different from the correspondibg periodicities in the combined solids. Basically, one subsystem adjusts to the other (mostly guests to the host), at an internal elastic energy cost, which is accumulated, and after approximately 9 laticce periods the guest subsystems forms a soliton, jumping into another local minimum, similar to the old Frenkel-Kontorova model. We will present first principles, second principles, and analytical calculations illustrating this mechanism.