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Paper   IPM / Physic / 13872
School of Physics
  Title:   Intrinsic broadening of the energy levels of Dirac electrons in quantum dots
  Author(s): 
1.  E. Ahmadi
2.  S.A. Jafari
  Status:   Published
  Journal: J. Phys.: Conf. Series
  Vol.:  603
  Year:  2015
  Pages:   012016
  Supported by:  IPM
  Abstract:
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 “relativistic electrons” 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.


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