Spinor-electron wave guided modes in coupled quantum wells structures by solving the Dirac equation

A quantum analysis based on the Dirac equation of the propagation of spinor-electron waves in coupled quantum wells, or equivalently coupled electron waveguides, is presented. The complete optical wave equations for Spin-Up (SU) and Spin-Down (SD) spinor-electron waves in these electron guides couplers are derived from the Dirac equation. The relativistic amplitudes and dispersion equations of the spinor-electron wave-guided modes in a planar quantum coupler formed by two coupled quantum wells, or equivalently by two coupled slab electron waveguides, are exactly derived. The main outcomes related to the spinor modal structure, such as the breaking of the non-relativistic degenerate spin states, the appearance of phase shifts associated with the spin polarization and so on, are shown.