Trapping of an electron in coupled quantum dots in graphene

Due to Klein's tunneling the electronic states of a quantum dot in graphene have finite widths and an electron in quantum dot has a finite trapping time. This property introduces a special type of interdot coupling in a system of many quantum dots in graphene. The interdot coupling is realized not as a direct tunneling between quantum dots but as coupling through the continuum states of graphene. As a result the interdot coupling modifies both the positions and the widths of the energy levels of the quantum dot system. We study the system of quantum dots in graphene theoretically by analyzing the complex energy spectra of the quantum dot system. We show that in a double-dot system some energy levels become strongly localized with an infinite trapping time. Such strongly localized states are achieved only at one value of the interdot separation. We also study a periodic array of quantum dots in graphene within a tight-binding mode for a quantum dot system. The values of the hopping integrals in the tight-binding model are found from the expression for the energy spectra of the double quantum dot system. In the array of quantum dots the states with infinitely large trapping time are realized at all values of interdot separation smaller than some critical value. Such states have nonzero wave vectors.