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%'e consider the image potential and its effect in calculating the binding energy of the ground bound state of an exciton in a finite quantum we11 subjected to an external electric field by means of the variational technique. The influence of the image potential is obtained as a function of the well width, the electric-field strength, and the ratio of the dielectric constants of different media. It is found that the image-potential effect will give significant corrections to the exciton binding energy and its Stark shift. The self-image potential and mutual-image potential have opposite effects on the Stark shift.

The transport properties and shot noise in Thue-Morse (TM) sequence graphene superlattice are investigated using transfer matrix methods. The results indicate perfect transport with T = 1 is always obtained at normal incidence when incident electrons tunnel through different barrier widths and heights. The zero-k¯-gap and other Bragg gap exhibit different behavior as the barrier width or incident angle increases. Furthermore, the changing of the structure parameters and generation of the TM sequence has a great effect on transmission coefficient, conductance, and Fano factor. It is shown that the Fano factor has a maximum close to 1/3 in the vicinity of Dirac point, which result in robust electronic transport properties.