Charge confinement and Klein tunneling from doping graphene

Popovici, Carina; Oliveira, Orlando; Paula, W. de; Frederico, T.

doi:10.1103/physrevb.85.235424

Cited by 19 publications

(22 citation statements)

References 45 publications

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“…Again, in that theory one has in general also potentials with Lorentz structure other than vector, and, in this case, the third component of a four-vector potential (γ 0 γ 3 = α z ) (note that the Lorentz character of V O O is given by its form in the covariant form of the Dirac equation, i.e., γ 0 V O O). This opens the possibility of looking into what would be the effect of these symmetries on the continuum [14] and discrete spectrum of the Dirac electrons, as well as its breaking due the other potentials or to the fact that the condition V 2v ± V z = C ± is not fulfilled. In this way, the Dirac electrons in graphene could be a tool to study the consequences of the generalized spin and pseudospin symmetries in a controllable form.…”

Section: Discussionmentioning

confidence: 99%

Generalizing spin and pseudospin symmetries for relativistic spin 1/2 fermions

Alberto

Malheiro

Frederico

et al. 2016

J. Phys.: Conf. Ser.

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We propose a generalization of pseudospin and spin symmetries, the SU(2) symmetries of Dirac equation with scalar and vector mean-field potentials originally found independently in the 70's by Smith and Tassie, and Bell and Ruegg. As relativistic symmetries, they have been extensively researched and applied to several physical systems for the last 18 years. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schrödinger-like equations, i.e, without a matrix structure. In this paper we use the original formalism of Bell and Ruegg to derive general requirements for the Lorentz structures of potentials in order to have these SU(2) symmetries in the Dirac equation, again allowing for the suppression of the matrix structure of the second-order equation of either the upper or lower components of the Dirac spinor. Furthermore, we derive equivalent conditions for spin and pseudospin symmetries with 2-and 1-dimensional potentials and list some possible candidates for 3, 2, and 1 dimensions. We suggest applications for physical systems in three and two dimensions, namely electrons in graphene.

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Section: Discussionmentioning

confidence: 99%

Generalizing spin and pseudospin symmetries for relativistic spin 1/2 fermions

Alberto

Malheiro

Frederico

et al. 2016

J. Phys.: Conf. Ser.

Self Cite

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show abstract

“…[14,15]). One example is the continuum spectrum of the Dirac electron interacting with two dimensional potentials embedded in a 3+1 space [16]. Again, in that theory one has in general also potentials with Lorentz structure other than vector, and, in this case, the third component of a four-vector potential (γ 0 γ 3 = α z ) (note that the Lorentz character of V O O is given by its form in the covariant form of the Dirac equation, i.e., γ 0 V O O), but it may be interesting to assess the effect of this symmetry on the continuum and discrete spectrum of the Dirac electrons as well as its breaking due the other potentials.…”

Section: Discussionmentioning

confidence: 99%

General spin and pseudospin symmetries of the Dirac equation

et al. 2015

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In the 70's Smith and Tassie, and Bell and Ruegg independently found SU(2) symmetries of the Dirac equation with scalar and vector potentials. These symmetries, known as pseudospin and spin symmetries, have been extensively researched and applied to several physical systems. Twenty years after, in 1997, the pseudospin symmetry has been revealed by Ginocchio as a relativistic symmetry of the atomic nuclei when it is described by relativistic mean field hadronic models. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schrödinger-like equations, i.e, without a matrix structure. In this paper we propose a generalization of these SU(2) symmetries for potentials in the Dirac equation with several Lorentz structures, which also allow for the suppression of the matrix structure of second-order equation equation of either the upper or lower components of the Dirac spinor. We derive the general properties of those potentials and list some possible candidates, which include the usual spin-pseudospin potentials, and also 2-and 1-dimensional potentials. An application for a particular physical system in two dimensions, electrons in graphene, is suggested.

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“…As the final step, the overlap of Eqs. (18) and (20) at the interface region m = 0, 1 gives the continuity condition |Φ i (m) +|Φ r (m) = |Φ t (m) for m = 0, 1 [see the dashed square in Fig. 2(b)].…”

Section: A Tight-binding Model For Uniform Graphenementioning

confidence: 99%

Perfect transmission at oblique incidence by trigonal warping in graphene P-N junctions

Zhang

Yang

2018

Phys. Rev. B

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We develop an analytical mode-matching technique for the tight-binding model to describe electron transport across graphene P-N junctions. This method shares the simplicity of the conventional mode-matching technique for the low-energy continuum model and the accuracy of the tight-binding model over a wide range of energies. It further reveals an interesting phenomenon on a sharp P-N junction: the disappearance of the well-known Klein tunneling (i.e., perfect transmission) at normal incidence and the appearance of perfect transmission at oblique incidence due to trigonal warping at energies beyond the linear Dirac regime. We show that this phenomenon arises from the conservation of a generalized pseudospin in the tight-binding model. We expect this effect to be experimentally observable in graphene and other Dirac fermions systems, such as the surface of threedimensional topological insulators.

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Charge confinement and Klein tunneling from doping graphene

Cited by 19 publications

References 45 publications

Generalizing spin and pseudospin symmetries for relativistic spin 1/2 fermions

Generalizing spin and pseudospin symmetries for relativistic spin 1/2 fermions

General spin and pseudospin symmetries of the Dirac equation

Perfect transmission at oblique incidence by trigonal warping in graphene P-N junctions

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