Fractional Quantum Spin Hall Effects specified by Excitonic and Topological Insulator Transitions in Graphene and ZnO/Zn(Mg)O Quantum Wells without Landau levels

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In the article the Quantum Spin Hall effects are shown to be related with intraband transitions of bulk GaN. We have presented  the microscopic many-body theory which based on the semiconductor Bloch equations that are Heisenberg equations for optical polarizations and carriers populations related with the variation methods for founding the grounds states of graphene in the optical responses of these materials on laser excitations. In the framework of the effective mass theories the Schrödinger equation is solved which are shown to be connected with the symmetry group of D_{3h}^{1}. The exact solutions of the Schrödinger equations for MoS_{2} materials as well as Quantum Spin Hall effect of intersubband transitions of bulk GaN are found. For the honeycomb lattice of Graphene and MoS_{2} the Effective Hamiltonian of group-VI Dichalcogenides based on D_{3h} point symmetry group was found. Derivation of expressions of momentum matrix elements of intersubband phototransitions for bulk GaN are considered. In the article for Quantum Spin Hall effect of intersubband phototransitions of bulk GaN the expressions of Berry curvature as well as Hall conductivities have been found. I think in the article ~\cite{Stroucken:2011jd} the derived of Optical Response and Ground States of Graphene by T. Stroucken, J.H. Grönqvist and S.W. Koch were not allowed and consequently were not found by means of the uncertain inference of just these similar symmetrical expressions into \eqref{deq121imag&}, \eqref{deq122imag&}.

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