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
n?p?junctions.
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
n?p?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]
ABSTRACT: The transport properties of a graphene multiquantum well system are investigated numerically using transfermatrix method. There are transmission gaps for electrons and holes in the transmission spectra at tilted incidence. In the transmission gaps, a few resonant tunneling peaks appear, defined as transmission windows, which are related with the bound states in the quantum wells. Unlike conventional semiconductor nanostructures, the location and the width of the transmission windows are sensitive not only to the quantum well width but also the incident angle. The number of the quantum wells determines the fine structure of the transmission windows. The anisotropic property is affected in the following way: the increase in well width makes the nonzerotransmission incident angle range decrease, and the interference effect is enhanced as the well number increases. Tiny oscillation of the conductance and fine structures in the middle energy range are due to the resonant tunneling induced by the multiquantum well structure. These oscillating features may be helpful in explaining the oscillatory characteristics in experiment.  [Show abstract] [Hide abstract]
ABSTRACT: We have investigated the electron tunneling through a trapezoidal barrier in graphene. The dependence of the transmission on the applied bias is obtained. The trapezoidal barrier removes the negative differential resistance in the currentvoltage characteristics. Furthermore the slope of the trapezoidal barrier can also be used as a parameter to control the angular distribution of the transmitted electrons. The result can be used to design graphenebased tunneling devices such as an energy filter.
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