QUASI-BOUND STATES OF DIRAC ELECTRONS IN ELECTRIC AND MAGNETIC QUANTUM DOTS

The problem of quasi-bound states for ultra-relativistic Dirac electrons and holes in electric and magnetic quantum dots in graphene is discussed. It is shown that these states with a rather long lifetime appear in an electric quantum dot in the case of a large orbital momentum, and in a magnetic quantum dot if its dimensions exceed the Larmor radius of the electron. The quasibound state properties are analysed by using the local density of states technique the application of which is demonstrated by a simple one-dimensional model of the decaying state. In addition, the analogy between two-dimensional graphene and onedimensional polymers is discussed, which helps in understanding and interpreting the sophisticated features of the electron spectrum.