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 quasi-bound 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 one-dimensional polymers is discussed, which helps in understanding and interpreting the sophisticated features of the electron spectrum.