Überstruktur und magnetische Suszeptibilität im System Kupfer‐Gold

Seemann, H. J.; Vogt, E.

doi:10.1002/andp.19293940804

Cited by 41 publications

(3 citation statements)

References 14 publications

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“…Finally, new semiconductor SLs have become much more appealing than metallic alloy SLs that had, already, a long history. [16][17][18][19][20][21][22][23][24][25][26] The growth techniques of semiconductor structures have long ago reached the level of atomic-layer precision.…”

Section: Introductionmentioning

confidence: 99%

The Transfer Matrix Method and the Theory of Finite Periodic Systems. From Heterostructures to Superlattices

Pereyra

2021

Physica Status Solidi (b)

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Historically, the physics, energy spectrum, and wave functions of superlattices have had different levels of understanding. Unlike the standard approaches, based on theorems for infinite systems, the theory of finite periodic systems (TFPS) constitutes a genuine quantum approach, with closed analytical results. In this theory the finitene number of unit‐cells is an essential condition, while the number of propagating modes, as well as, the potential profiles (or refractive indices) are arbitrary. In this work, the transfer matrix definitions, symmetry properties, group representations, and relations with the scattering amplitudes are reviewed. The derivation of multichannel matrix polynomials (which reduce to Chebyshev polynomials in the one‐propagating mode limit), analytical formulas for resonant states, energy eigenvalues, eigenfunctions, parity symmetries, and discrete dispersion relations for superlattices with different confinement characteristics are reviewed. After showing the inconsistencies and limitations of hybrid approaches that combine the transfer‐matrix method with Floquet's theorem, some applications of the TFPS to multichannel negative resistance, ballistic transistors, coupled channels transport, spintronics, superluminal, and optical antimatter effects are revisited. Two high‐resolution superlattice related experiments are reviewed: the tunneling time in photonic band‐gap and the optical response of blue‐emitting diodes. It is shown that the TFPS accurately predicts the experimental results.

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Section: Introductionmentioning

confidence: 99%

The Transfer Matrix Method and the Theory of Finite Periodic Systems. From Heterostructures to Superlattices

Pereyra

2021

Physica Status Solidi (b)

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“…The development of growing techniques of semiconductor structures such as the metallorganic chemical vapor deposition (MOCVD) and molecular beam epitaxy (MBE), 6 reached in the 70s the ability to produce heterolayered structures (first suggested by H. Kroemer 7 ), quantum wells (QWs), multiple quantum wells and superlattices, [8][9][10] and opened up an intense race in search of better optical devices, [11][12][13][14][15] and a new era of artificial and endless growing family of heterostructures, with new properties and a new spectrum of application possibilities, which settled and expanded the research universe of physics, and the new semiconductor superlattices become much more appealing than the metallic alloys superlattices, which have a longer history. [16][17][18][19][20][21][22][23][24][25][26] The explosive field of semiconductor superlattices originated in the seminal research papers published in the 1970s, studying a variety of basic properties, including, among others, the electron tunneling, 9,27 semiconductor lasers, 14,[29][30][31][32][33][34][35][36][37][38] injection current thresholds, 12,39,40 the temperature effect in growing process, 41 enhancement of charge carries mobility, 42,…”

Section: Introductionmentioning

confidence: 99%

The Transfer Matrix Method and The Theory of Finite Periodic Systems. From Heterostructures to Superlattices

Pereyra

2021

Preprint

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Long-period systems and superlattices, with additional periodicity, have new effects on the energy spectrum and wave functions. Most of the theoretical approaches adjust theories that are acceptable for systems with large number of unit-cells n, but questionable for small n. Lately, a theory of finite periodic systems based entirely on transfer matrices and their mathematical and physical properties, valid for any number of propagation modes, any n, and arbitrary potential profile or refractive indices, was developed. In this review, we focus on this approach where finiteness is an essential condition. We also comment on the widely used hybrid approach that combines transfer matrices with Floquet's theorem, and show that Floquet's theorem implies transfer matrices of the compact subgroup. We review the transfer matrix definitions, symmetry properties, group representations, and relations with the scattering amplitudes. We summarize the derivation of the recurrence relation of matrix polynomials, which in the scalar limit are the Chebyshev polynomials, the analytical formulas for resonant states, energy eigenvalues, eigenfunctions, parity symmetries, and discrete dispersion relations, for superlattices with different confinement characteristics. We review two high-resolution experiments using superlattices: tunneling time in photonic band-gap and optical response of blue-emitting diodes, and show extremely accurate theoretical predictions.

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“…The superlattices (SLs), introduced in the early days of the quantum theory to describe 'peculiar' metallic crystals, 13 has had a large evolution, [14][15][16][17] and many properties, among them the electronic states in long-period SL alloys and the propagation of electromagnetic waves through periodic media, have been studied. [18][19][20][21][22][23][24][25][26][27][28][29][30] The development of techniques to grow semiconductor heterolayers, first suggested by Kroemer 31 and intensively pursued in the race to achieve better optical devices, [32][33][34][35][36] reached in the 70's the ability to produce semiconductor SLs.…”

Section: Introductionmentioning

confidence: 99%

Theory of finite periodic systems: The eigenfunctions symmetries

Pereyra¹

2017

Annals of Physics

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Using the analytical expressions for the genuine eigenfunctions $\varphi_{\mu\nu}(z)$ and eigenvalues $E_{\mu,\nu}$, of open, bounded and quasi-bounded finite periodic systems, we derive the eigenfunctions space-inversion symmetry relations. The superlattice eigenfunctions symmetries, closely related with the symmetries and zeros of the Chebyshev polynomials of the second kind $U_n$, are fully written in terms of the number of unit cells $n$, the subband index $\mu$ and the intra-subband index $\nu$.Comment: 10 pages, 14 figure

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Überstruktur und magnetische Suszeptibilität im System Kupfer‐Gold

Cited by 41 publications

References 14 publications

The Transfer Matrix Method and the Theory of Finite Periodic Systems. From Heterostructures to Superlattices

The Transfer Matrix Method and the Theory of Finite Periodic Systems. From Heterostructures to Superlattices

The Transfer Matrix Method and The Theory of Finite Periodic Systems. From Heterostructures to Superlattices

Theory of finite periodic systems: The eigenfunctions symmetries

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