Tunneling through Fibonacci barriers

Kiang, D.; Ochiai, T.; Date, S. K.

doi:10.1119/1.16252

Cited by 7 publications

(4 citation statements)

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“…Wc show that this coefficient can be cast in the form of a simple recurrence relationship that can be readily evaluated for any particular quasi periodic or even random lattice. At a subsequent stage, we select the Fibonacci chain as a concretc example, in view of thc broad current knowledge on electron transmission through it [1][2][3][4][5][6][7][8][9][10]. Instead of doing an exhaustive study of all of the electron propagation characteristics, we concern ourselves with several points trying to clarify what are the main new features arising from the inclusion of relativistic effects and different from the already known ones of non-relativistic systems.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, a large amount of work has been devoted to the one-dimensional (ID) Fibonacci chain. as a suitable model for quasicryslals [1][2][3][4][5][6][7][8][9][10] which in addition can be physically realized in the form of supcriattices manufactured by molecular beam epitaxy [11]. This and other quasi periodic systems are of greal interest in solid state physics because they are structures being intermediate betwecn periodic and fully disordered (random) ones.…”

Section: Introductionmentioning

confidence: 99%

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Relativistic effects in Kronig-Penney models on quasiperiodic lattices

Domı́nguez-Adame

Sánchez

1991

Physics Letters A

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Relativistic effects in Kronig-Penney models on quasiperiodic lattices

Domı́nguez-Adame

Sánchez

1991

Physics Letters A

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“…This derivation, the two examples, and the related codes would greatly assist new researchers in their understanding of the basic principles of molecular electronics. In addition to our introductory article, we enthusiastically recommend a good number of valuable references that offer a brilliant start and meaningful discussions [22][23][24][25][26][27][28].…”

Section: Discussionmentioning

confidence: 99%

Transmission of a single impurity system: a comprehensive pedagogical tutorial

Mijbil

2019

Eur. J. Phys.

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We have derived a straightforward and flexible analytical formula to calculate the electronic transmission of a system with a single impurity. Furthermore, two easy-to-follow subderived examples combined with two corresponding FORTRAN codes have been clearly presented. The formula can be employed for more sophisticated systems owing to the allocation of specific parameters, namely onsite energy and coupling elements, for the corresponding part of the system, such as left lead, impurity, and right lead. Moreover, the formula is well defined so that it can easily be formulated with other programming languages such as C++ or Python. We believe that the current work would greatly help new students and researchers in the field of molecular electronics.

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“…It is well known [24] that the transmission coefficient t (k) for an incident plane wave with wave number k has the expression…”

Section: Non-zero Transmission Coefficient Of Critical Fibonacci Chai...mentioning

confidence: 99%

Critical points for finite Fibonacci chains of point delta-interactions and orthogonal polynomials

Prunelé¹

2011

J. Phys. A: Math. Theor.

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For a one-dimensional Schrödinger operator with a finite number n of point delta-interactions with a common intensity, the parameters are the intensity, the n − 1 intercenter distances and the mass. Critical points are points in the parameters space of the Hamiltonian where one bound state appears or disappears. The study of critical points for Hamiltonians with point delta-interactions arranged along a Fibonacci chain is shown to be closely related to the study of the so-called Fibonacci operator, a discrete one-dimensional Schrödinger-type operator, which occurs in the context of tight binding Hamiltonians. These critical points are the zeros of orthogonal polynomials previously studied in the context of special diatomic linear chains with elastic nearest-neighbor interaction. Properties of the zeros (location, asymptotic behavior, gaps, …) are investigated. The perturbation series from the solvable periodic case is determined. The measure which yields orthogonality is investigated numerically from the zeros. It is shown that the transmission coefficient at zero energy can be expressed in terms of the orthogonal polynomials and their associated polynomials. In particular, it is shown that when the number of point delta-interactions is equal to a Fibonacci number minus 1, i.e. when the intervals between point delta-interactions form a palindrome, all the Fibonacci chains at critical points are completely transparent at zero energy.

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Tunneling through Fibonacci barriers

Cited by 7 publications

References 0 publications

Relativistic effects in Kronig-Penney models on quasiperiodic lattices

Relativistic effects in Kronig-Penney models on quasiperiodic lattices

Transmission of a single impurity system: a comprehensive pedagogical tutorial

Critical points for finite Fibonacci chains of point delta-interactions and orthogonal polynomials

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