\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
We theoretically study the quasi bound state of Dirac electrons in cylindrically
symmetric quantum dots with sharp boundary. According to the existing picture, due to Klein
tunneling ârelativistic electronsâ can not be localized by any confinement potential. We show
however that despite of Klein tunneling, interference effects can cause the trapping of electron
in quantum dots. Considering the quasi bound state as the state with complex energy, to
find the energy of this state we solve the wave-equation with outgoing boundary condition at
infinity. The imaginary part of complex energy determines the trapping time of electron within
the quantum dot. We show that for any finite confining potential corresponding to any set
of quantum numbers (n, m) where n is the principal quantum number and m the magnetic
quantum number, there exists a continuous band of states with finite life time. Upper and
lower edges of each band corresponds to infinitely long lived states trapped inside and outside
the wall of the same radius. We term this phenomenon the intrinsic broadening as it is not
caused by scattering from any external potential, nor by many-body effects. This broadening
appears to arise from a combination of relativistic and interference effects. The imaginary part
of energy which is different for energies along the energy band is controlled by the orbital angular
momentum of electron and the depth of the confining potential.
\end{document}