Structural phase transitions in planar bilayer crystals with long range interaction

We have studied theoretically a bilayer electronic crystal, which may be realized in a stratifying mixture of helium isotopes or in a superfluid helium film. In the limiting cases of weak and intermediate coupling between the layers we have studied the dynamics of such a crystal and described a structural transition at which the transverse sound velocity decreases and goes to zero. It is shown that in the strong coupling limit between the layers the system becomes equivalent to a two-dimensional binary mixture on a triangular Ising lattice with a long range potential of mixing V∼r−3. We have studied the phase transitions which arise in such a binary mixture as the temperature and concentration are varied. It is shown that as the temperature is lowered from the disordered phase a superstructure (√3×√3) always appears first. A (2×2) superstructure is unstable with respect to formation of antiphase domains.

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