Step-density-wave phase of crystalline interfaces

The combined effect of striction and crystallinity can produce a state for vicinal crystalline interfaces, which we call the step-density-wave (StDW) phase due to its resemblance to the charge-density-wave phase of one-dimensional conductors. This phase arises due to a spontaneous periodic distortion of the surface commensurate with the steps, which creates a potential that localizes them. In many cases of interest the energy gain of step localization is greater than the energy cost of the elastic distortion, thus favoring the StDW phase. There is true long-range translational order of the step positions relative to the surface distortion, which makes the StDW phase similar to traditional smooth interfaces. The surface distortion and associated step waves are not fixed rigidly in space, however, but only relative to each other. Therefore, in the absence of pinning by impurities, the combined system of steps with associated surface elastic distortion can move freely in response to an external force (for example, under crystal growth conditions) so that in this respect it resembles a rough interface. In this paper we demonstrate the existence of the StDW phase and study the phase transitions between the rough phase of wandering steps and the StDW phase.