We consider the energy spectrum of the planar quantum well which consisted oftwo ribbons of narrow-gap semiconductors and a graphene ribbon between ones. Itis shown that the gapless mode appears only in case of inverted narrow-gapsemiconductors. Spin splitting of the energy spectrum for a nonsymmetricquantum well is calculated taking into account a specificity of graphene. Weinvestigate interface states and optical transitions. It is shown that theoptical transitions are possible only with a conservation of a parity.
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