Landau-Ginsburg-Devonshire theory of thin ferroelectric polar-active nanofilms in Incommensurate Phases and semiconductor heterostructures

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Landau-Ginsburg-Devonshire theory of thin ferroelectric polar-active nanofilms in incommensurate phases and semiconductor heterostructures is presented. The self-consistent solutions of the Euler-Lagrange equation for the polarization vector and the Maxwell equations for light which propagates along Oz axis in thin ferroelectric polar-active nanofilms have been found. Quantized solutions of one-dimensional Maxwell equations for thin ferroelectric films in Incommensurate phase with space dispersion have been specified. The analytical solutions of the Maxwell wave equations as well as natural optical gyrotropy effects are found in Rb_{2}ZnBr_{4} as well as K_{2}SeO_{4} Incommensurate phases crystals connected with giant light velocity as well as via interaction with coherent phonon oscillations. In the framework of the superspace symmetry group theories the Maxwell wave equations are solved which are shown to be connected with the symmetry group of D_{2h}^{16} or isomorphic groups. In the paper the non-zero gyration g_{33} and gyrotropic birefringence epsilon_{12} tensors of K_{2}SeO_{4} and Rb_{2}ZnBr_{4} materials based on D_{2h}^{16} space symmetry group were found. The values of natural optical gyrotropy as well as Rashba spin splitting are shown to be specified like (k^{(0)}\pm\tilde{k}^{(2)})^{2} as displacements of two symmetrically allocated parabolas from Brillouin zone center. In the article the natural optical gyrotropy effects are shown to be found with light velocity like epsilon=\hbar\,ck/eV=14.0798 eV but the corresponding wave vector was estimated to be k=7.161*10^{5} cm^{-1}. The found strong natural optical gyrotropy has been based on available experimental data [Phys. Rev. B 38, 8075, (1988)]. The three-dimensional Poisson's equation which includes local exchange-correlation potential for semiconductor of the space region z>0 for motion of carriers in space confined quantum well along Oz axis in consideration of dipoles on interface of ferroelectric thin film in incommensurate phase/semiconductor nanoheterostructures as well as free charges for specifying of charge quantization has been solved.