Piezoelectric mechanism of orientation of a bilayer Wigner crystal in a GaAs matrix

A mechanism for orientation of bilayer classical Wigner crystals in a piezoelectric medium is considered. For the GaAs system the piezoelectric correction to the electrostatic interaction between electrons is calculated. It is shown that taking into account the correction due to the piezoelectric effect leads to a dependence of the total energy of the electron crystal on its orientation with respect to the crystallographic axes of the surrounding matrix. A generalization of Ewald's method is obtained for calculating the anisotropic interaction between electrons in a Wigner crystal. The method is used to calculate the energy of bilayer Wigner crystals in electron layers parallel to the crystallographic planes (001), (0-11), and (111) as a function of their orientation and the distance between layers, and the energetically most favorable orientation for all types of electron lattices in a bilayer system is found. It is shown that phase transitions between structures with different lattice symmetry in a Wigner crystal can be accompanied by a change of its orientation.