Commensurate and incommensurate phase transitions of the (001) InAs surface under changes of bulk lattice constant, As chemical potential, and temperature

We report the observation of both commensurate-commensurate and commensurate-incommensurate transitions of the surface of a covalent material (InAs). Its 2D phase diagram is determined for independent changes of temperature, chemical potential of As surface atoms, and bulk lattice parameter. In agreement with models describing the surface as a frustrated system, all transitions are shown to be controlled by the relationship between the bulk lattice parameter and the mean surface one and are obtained for the first time upon changes of either parameter.