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arXiv:1408.5333

Statistical magnitudes and the Klein tunneling in bi-layer graphene: influence of evanescent waves

Jaime Sañudo A, Ricardo López‐Ruiz

Published Aug 22, 2014• 1 citation
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Abstract

The problem of the Klein tunneling across a potential barrier in bi-layer graphene is addressed. The electron wave functions are treated as massive chiral particles. This treatment allows us to compute the statistical complexity and Fisher-Shannon information for each angle of incidence. The comparison of these magnitudes with the transmission coefficient through the barrier is performed. The role played by the evanescent waves on these magnitudes is disclosed. Due to the influence of these waves, it is found that the statistical measures take their minimum values not only in the situations of total transparency through the barrier, a phenomenon highly anisotropic for the Klein tunneling in bi-layer graphene.

DOI
10.48550/arxiv.1408.5333

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The problem of the Klein tunneling across a potential barrier in bi-layer graphene is addressed. The electron wave functions are treated as massive chiral particles. This treatment allows us to compute the statistical complexity and Fisher-Shannon information for each angle of incidence. The comparison of these magnitudes with the transmission coefficient through the barrier is performed. The role played by the evanescent waves on these magnitudes is disclosed. Due to the influence of these waves, it is found that the statistical measures take their minimum values not only in the situations of total transparency through the barrier, a phenomenon highly anisotropic for the Klein tunneling in bi-layer graphene.
We obtain the solutions for the tunneling zone of a one-dimensional electrostatic potential in the relativistic (Dirac to Klein–Gordon) wave equation regime when the incoming wave packet exhibits the possibility of being almost totally transmitted through the potential barrier. The conditions for the occurrence of accelerated and, eventually, superluminal tunneling transmission probabilities are all quantified and the problematic superluminal interpretation originated from the study based on non-relativistic dynamics of tunneling is reevaluated. The treatment of the problem suggests revealing insights into condensed-matter experiments using electrostatic barriers in single- and bi-layer graphenes, for which the accelerated tunneling effect deserves a more careful investigation.
In this paper, we have solved a quantum tunneling problem for 2-dimensional systems, including electron gas and graphene.In spite of the one-dimensional scattering problems, in two dimensions, we observe phenomenon of tunneling at energies above the barrier.This effect is an analogue to the total internal reflection in optics.The scattering amplitudes inside the barrier region exhibit decaying behavior corresponding to optical evanescentwave coupling, not only in energies below barrier height, but also above barrier.Velocity-selecting transmission, corresponding to angle-resolved beam filtering effect is one of the achievements of the paper.The famous Hartman effect which occurs normally at sub-barrier energies and has previously been studied for graphene is also addressed.The results manifest occurrence of the Hartman effect for over-barrier energies, as well.
We introduce a two-dimensional model of spin-1/2 Dirac fermions in graphene subjected to a highly tunable electric field, which exhibits super-Klein tunneling. The electric field can be continuously interpolated between two limiting configurations: a uniform electrostatic Lorentzian barrier with translational invariance and a chain of well-separated electrostatic scatterers. We demonstrate that super-Klein tunneling arises naturally as a direct consequence of the intrinsic connection of the model to free-particle dynamics, a relation that is established through methods of supersymmetric quantum mechanics, which provide an elegant and analytically tractable framework. Besides the mentioned super-Klein tunneling, scale invariance of the model and invisibility of the potential for particles of specific energy are revealed, and possible routes toward experimental realization are discussed.
We have analyzed the influence of the wave packet size in the relativistic tunnelling time τ and its uncertainty �τ when it traverses a given potential barrier. The analytical expressions obtained for both magnitudes confirm that the size of the incident pulse has a significant effect on the tunnelling process. This effect is greater for short pulses, compared with the length of the barrier. For the evanescent zone, we have derived an analytical expression for τ with a good limit of validity. This expression constitutes a value tool to calculate the relativistic tunnelling time as a function of the incident wave packet with a good limit of validity. Superluminal propagation is found in this region but with a large value of the uncertainty �τ compared with the tunnelling time itself. We can conclude that the probability of superluminal propagation is practically negligible in the evanescent region. In respect to the Klein zone, we have derived an analytical expression for τ that depends on the size of the incident
This work investigates the Floquet dynamics of electrons and excitons (particle-hole pairs) in a Dirac material referred to as Kekulé-distorted graphene. Specifically, we examine the role played by a high frequency driving electromagnetic field on the tunneling and blocking by a potential barrier on both the charged single particles as well as the neutral composite particles. We demonstrate that the small effective masses of the electron and hole for the energy spectrum of this Kekulé distorted graphene leads to practically almost perfect transmission across a symmetric potential barrier for any angle of incidence of impinging excitons. However, this unexpected Klein paradox for excitons does not hold for the single-particle electrons. The reduced total transmission of electron due to Kekulé distortion is more suppressed due to irradiation. Additionally, we calculate and investigate the exciton binding energy since the quantum tunneling of a bound electron-hole pair across a potential barrier is governed by its mass measured in the center of mass and binding energy of the composite pair. Thus, irradiation with circularly polarized light fundamentally modifies exciton formation, coherence and transport properties, thereby producing unusual topological behaviors. These behaviors are unlike conventional Dirac materials. Possible technical applications of the results arising from our investigation include valleytronics due to the folding of the valleys, thereby making intervalley coupling feasible. Other practical applications include optoelectronics due to Floquet tuning of energy spectrum and transport properties.