Fractional-dimensional approach for excitons in GaAs films on Al _x Ga _{1− x} As substrates

Abstract

Binding energies of excitons in GaAs films on Al x Ga 1−x As substrates are studied theoretically with the fractionaldimensional approach. In this approach, the real anisotropic "exciton + film" semiconductor system is mapped into an effective fractional-dimensional isotropic space. For different aluminum concentrations and substrate thicknesses, the exciton binding energies are obtained as a function of the film thickness. The numerical results show that, for different aluminum concentrations and substrate thicknesses, the exciton binding energies in GaAs films on Al x Ga 1−x As substrates all exhibit their maxima with increasing film thickness. It is also shown that the binding energies of heavy-hole and light-hole excitons both have their maxima with increasing film thickness.

Effect of disorders on topological phases in one-dimensional optical superlattices

“…Topological properties have long been used to characterize the two-dimensional (2D) electron systems. [1][2][3][4][5][6][7][8][9][10][11] For example, the integer quantum Hall (IQH) effect and the quantum spin Hall (QSH) effect in the 2D system with periodic potentials can both be related to the topological properties of occupied energy bands. [2][3][4][5][6][7] A topological invariant called the Chern number can be used to characterize the integer quantum Hall effect and the Chern number is directly related to the quantum Hall conductance.…”