Tunneling of Dirac electrons through one-dimensional potentials in graphene: a T-matrix 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: 10.1088/0953-8984/21/4/045305
Source: PubMed


The standard T-matrix method can be effectively used for studying the dynamics of Dirac electrons under one-dimensional potentials in graphene. The transmission probability expressed in terms of T-matrices and the corresponding ballistic current are derived for any smooth one-dimensional potential, taking into account the chirality of Dirac massless carriers. Numerical calculations are illustrated for the potential approximately describing graphene n-p junctions.

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    • "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 (T-matrix) method originally designed for one-dimensional quantum mechanical problems to solve the circularly symmetric two-dimensional problem of graphene quantum dots. In similarity to one-dimensional problems, we show that the generalized T-matrix recapitulates important physical properties of these quantum dots. In particular, it is shown that the spectral equations for bound states as well as quasi-bound 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 T-matrix 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.
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    ABSTRACT: The transport properties of a graphene multiquantum well system are investigated numerically using transfer-matrix 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 nonzero-transmission 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.
    Journal of Applied Physics 07/2010; 107(12-107):123718 - 123718-6. DOI:10.1063/1.3445782 · 2.18 Impact Factor
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    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 current-voltage 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 graphene-based tunneling devices such as an energy filter.
    Japanese Journal of Applied Physics 08/2010; 49(8). DOI:10.1143/JJAP.49.085201 · 1.13 Impact Factor
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