Spectrum of localized states in graphene quantum dots and wires

We developed semiclassical method and show that any smooth potential in graphene describing elongated a quantum dot or wire may behave as a barrier or as a trapping well or as a double barrier potential, Fabry–Perot structure, for 1D Schrödinger equation. The energy spectrum of quantum wires has been found and compared with numerical simulations. We found that there are two types of localized states, stable and metastable, having finite life time. These life times are calculated, as is the form of the localized wave functions which are exponentially decaying away from the wire in the perpendicular direction.

► Energy spectrum of quantum wires and elongated quantum dots described for arbitrary potential.
► A new quasi-classical method for graphene and relativistic quantum mechanics has been developed.
► Any potential in graphene behaves as a barrier, as potential well and as Fabry–Perot interferometer