Reconfigurable Quantum Anomalous Spin Hall Effect from Phonon dispersion in Weil 2D half materials: Group-VI Dichalcogenides and PtCl_{3}, PdBr_{3}, RuCl_{3}, PtI_{3}

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In the article we have found that the Weyl Hall semiconductor (WHS) states allow the topological phase transition happened between two quantum anomalous Hall (QAH) insulator phase with opposite Chern numbers and we have based on phonon dispersion of Weil 2D half semiconductor monolayers group like PtCl_{3}. The ground state of monolayer PtCl_{3} allows the creation of the 2D WHS states with the pairs of fully polarized fermions at Weyl points which robust under spin-orbit coupling (SOC). The two QAH phases with C=\pm 1 have edge channels propagating in opposite directions. Because the chirality of the edge channel is determined by the sign of Chern number. We have predicted the switching of the Quantum Anomalous Spin Hall states by rotating the magnetization vector on the basis of PtCl_{3} monolayer and we have based on phonon dispersion of Weil 2D half semiconductor monolayers group like PtCl_{3}. 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)].

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