2010
DOI: 10.1088/0031-8949/81/02/025010
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Tunneling and transmission resonances of a Dirac particle by a double barrier

Abstract: Abstract. We calculate the tunneling process of a Dirac particle across two square barriers separated a distance d, as well as the scattering by a double cusp barrier where the centers of the cusps are separated a distance larger than their screening lengths. Using the scattering matrix formalism, we obtain the transmission and reflection amplitudes for the scattering processes of both configurations. We show that, the presence of transmission resonances modifies the Lorentizian shape of the energy resonances … Show more

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Cited by 10 publications
(13 citation statements)
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“…We would like to mention a related recent work by Villalba and Gonzales-Arraga [18] who considered the resonant tunneling through a double square barrier and double cusp potentials. Our problem differs from that in [18] by the choice of an elevated floor of the potential well, which gives rise to two Klein energy zones of resonance. This potential design gave rise to a peculiar energy dependence of the transmission with three resonance regions; one is due to the conventional quantum tunneling and two others are due to Klein tunneling.…”
Section: Resultsmentioning
confidence: 99%
“…We would like to mention a related recent work by Villalba and Gonzales-Arraga [18] who considered the resonant tunneling through a double square barrier and double cusp potentials. Our problem differs from that in [18] by the choice of an elevated floor of the potential well, which gives rise to two Klein energy zones of resonance. This potential design gave rise to a peculiar energy dependence of the transmission with three resonance regions; one is due to the conventional quantum tunneling and two others are due to Klein tunneling.…”
Section: Resultsmentioning
confidence: 99%
“…[9]. After these pioneering studies, the transmission resonance and supercriticality for the relativistic/non-relativistic particles in an external potentials have been extensively discussed [3,11,12,13,14,15,16,17,18]. In one of these studies [13], the authors showed that the transmission coefficient obtained for the Klein-Gordon particle displays a behavior similar to that of the one obtained for the Dirac particle [8].…”
Section: Introductionmentioning
confidence: 86%
“…The alternative geometry of transmission through potential barriers has also been a subject of extensive research, with the majority of studies utilizing "sharp but smooth potentials", i.e., potentials which are step-like or have kinks but are assumed to be smooth on the scale of the lattice constant, so that the effects of inter-valley scattering are neglected. Supercritical transmission [50][51][52][53][54][55][56][57][58] and tunneling through barriers has been studied for a variety of one-dimensional (1D) model potentials in both massless and massive 2D Dirac systems [25,27,49,[59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75] including square barrier structures such as the double barrier [76][77][78], inverted double well [79,80], asymmetric waveguides [34,43] and various other step-like structures [41,42,80]. A variety of approaches ranging from the transfer matrix method through to the WKB method have been used.…”
Section: Introductionmentioning
confidence: 99%