Super-Klein tunneling of Klein-Gordon particles

Kim, Kihong

doi:10.1016/j.rinp.2019.01.029

Cited by 14 publications

(13 citation statements)

References 24 publications

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“…there is no time-delay or time-advance observed for the particle density. Interestingly, in the stationary dispersion problems, the incidence condition |E| = V /2 (or incidence at E = V /2) gives rise to the so-called super-Klein tunneling [42].…”

Section: B Klein-tunneling Regimementioning

confidence: 99%

Zitterbewegung and Klein-tunneling phenomena for transient quantum waves

Nieto-Guadarrama

Villavicencio

2020

Phys. Rev. A

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We explore the dynamics of relativistic quantum waves in a potential step by using an exact solution to the Klein-Gordon equation with a point source initial condition. We show that in both the propagation, and Klein-tunneling regimes, the Zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit. We demonstrate that the beating phenomenon is characterized by the Zitterbewegung frequency, and that the amplitude of these oscillations decays as t −3/2 . We show that beating effect also manifests itself in the free Klein-Gordon and Dirac equations within a quantum shutter setup, which involve the dynamics of cut-off quantum states. We also find a time-domain where the particle density of the point source is governed by the propagation of a main wavefront, exhibiting an oscillating pattern similar to the diffraction in time phenomenon observed in non-relativistic systems. The relative positions of these wavefronts are used to investigate the time-delay of quantum waves in the Klein-tunneling regime. We show that, depending on the energy difference, E, between the source and the potential step, the time-delay can be positive, negative or zero. The latter case corresponds to a super-Klein-tunneling configuration, where E equals to half the energy of the potential step.

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Section: B Klein-tunneling Regimementioning

confidence: 99%

Zitterbewegung and Klein-tunneling phenomena for transient quantum waves

Nieto-Guadarrama

Villavicencio

2020

Phys. Rev. A

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“…In contrast with the original, free-particle system (7), the new system possesses two solutions which are localized in space-time. The vectors v 1 and v 2 , see (6), satisfy…”

Section: Model Amentioning

confidence: 99%

“…It was theoretically predicted for quasi-particles of spin-1 in Dice lattices [1], in line-centered square lattices formed by ultracold atoms [2], in optics [3], or in the systems with spin-orbit interaction [4]. It was also analyzed for the spin-1/2 Dirac fermions in graphene [5] with an inhomogeneous Fermi velocity as well as for the spin-less particles described by the Klein-Gordon equation [6]. Omnidirectional Klein tunneling occurs exclusively for a specific energy.…”

Section: Introductionmentioning

confidence: 99%

Super-Klein tunneling of Dirac fermions through electrostatic gratings in graphene

Contreras-Astorga,

Correa,

Jakubsky

2020

Preprint

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“…Though we can solve the invariant imbedding equations, Eqs. (24), (27), (30) and (35), numerically for general parameter values, it is highly instructive to apply the perturbation theory to them to derive analytical expressions for the localization length in some limiting cases.…”

Section: Analytical Expressions For the Localization Length In Thmentioning

confidence: 99%

Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a correlated random one-dimensional scalar potential

Kim

2019

Phys. Rev. B

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We study theoretically Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a random one-dimensional scalar potential. We focus explicitly on the effect of disorder correlations, considering a short-range correlated dichotomous random potential at all strengths of disorder. We also consider a δ-function correlated random potential at weak disorder. Using the invariant imbedding method, we calculate the localization length in a numerically precise way and analyze its dependencies on incident angle, disorder correlation length, disorder strength, energy, wavelength and average potential over a wide range of parameter values. In addition, we derive analytical formulas for the localization length, which are very accurate in the weak and strong disorder regimes. From the Dirac equation, we obtain an expression for the effective wave impedance, using which we explain several conditions for delocalization. We also deduce a condition under which the localization length vanishes. For all cases considered, the localization length depends non-monotonically on the disorder correlation length and diverges as θ −4 as the incident angle θ goes to zero. As the disorder strength is varied from zero to infinity, we find that there appear three different scaling regimes. As the energy or wavelength is varied from zero to infinity, there appear three or four different scaling regimes with different exponents, depending on the value of the average potential. The crossovers between different scaling regimes are explained in terms of the disorder correlation effect.

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Super-Klein tunneling of Klein-Gordon particles

Cited by 14 publications

References 24 publications

Zitterbewegung and Klein-tunneling phenomena for transient quantum waves

Zitterbewegung and Klein-tunneling phenomena for transient quantum waves

Super-Klein tunneling of Dirac fermions through electrostatic gratings in graphene

Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a correlated random one-dimensional scalar potential

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