Commensurate-incommensurate transitions in rare-gas monolayers adsorbed on graphite and in layered charge-density-wave systems

Existing theories for commensurate-incommensurate transitions in one-dimensionally-modulated systems show that these transitions are continuous and are associated with domainwall formation. We consider the effect of domain-wall crossing in two-dimensionally modulated systems with hexagonal symmetry such as rare-gas layers adsorbed on graphite and the layered compound $2H$-TaSe₂. We show that if the commensurate-incommensurate transition is continuous, the hexagonal symmetry is broken in the incommensurate phase, while if the transition is first order the hexagonal symmetry can be maintained in the incommensurate phase. The experimental consequences of this prediction are discussed.