Article
Tunneling of Dirac electrons through onedimensional potentials in graphene: a Tmatrix approach
Theoretical Department, Institute of Physics, VAST, PO Box 429 Bo Ho, Hanoi 10000, Vietnam.
Journal of Physics Condensed Matter (Impact Factor: 2.35). 01/2009; 21(4):045305. DOI: 10.1088/09538984/21/4/045305 Source: PubMed
ABSTRACT
The standard Tmatrix method can be effectively used for studying the dynamics of Dirac electrons under onedimensional potentials in graphene. The transmission probability expressed in terms of Tmatrices and the corresponding ballistic current are derived for any smooth onedimensional potential, taking into account the chirality of Dirac massless carriers. Numerical calculations are illustrated for the potential approximately describing graphene np junctions.

 "In the following, the integral constants C = (C (1) , C (2) ) t will be referred to as wave amplitudes. In 1D problems and in the standard representation, the two wave amplitudes are just the coefficients of the forward and backward waves [3] [4]. A similar interpretation can be seen when we represent W in terms of Hankel functions [21]. "
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ABSTRACT: We adapt the transfer matrix (Tmatrix) method originally designed for onedimensional quantum mechanical problems to solve the circularly symmetric twodimensional problem of graphene quantum dots. In similarity to onedimensional problems, we show that the generalized Tmatrix recapitulates important physical properties of these quantum dots. In particular, it is shown that the spectral equations for bound states as well as quasibound states of a circular graphene quantum dot and related quantities such as the local density of states and the scattering coefficients are all expressed exactly in terms of the Tmatrix for the radial confinement potential. As an example, we use the developed formalism to analyze physical aspects of a graphene quantum dot induced by a trapezoidal radial potential. Among the obtained results, it is in particular suggested that the thermal fluctuations and electrostatic disorders may appear as an obstacle to controlling the valley polarization of Dirac electrons.  [Show abstract] [Hide abstract]
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