One-dimensional disordered wires with Pöschl-Teller potentials

Rodríguez, Alejandra; Cerveró, José M.

doi:10.1103/physrevb.74.104201

Cited by 15 publications

(7 citation statements)

References 56 publications

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“…55 This technique has been applied to obtain the spectral properties in the thermodynamic limit of different quantum-wire models with correlated and uncorrelated disorder. [72][73][74][75] Here we give a brief overview of the formalism applied to 1D tight-binding models with diagonal disorder, described by the equation (E − ε x )φ x = φ x+1 − φ x−1 , where the on-site energies are obtained randomly from a continuous distribution P(ε). For such a system, the functional equation reads,…”

Section: Appendix A: Functional Equation Formalismmentioning

confidence: 99%

Controlled engineering of extended states in disordered systems

2012

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We describe how to engineer wavefunction delocalization in disordered systems modelled by tightbinding Hamiltonians in d > 1 dimensions. We show analytically that a simple product structure for the random onsite potential energies, together with suitably chosen hopping strengths, allows a resonant scattering process leading to ballistic transport along one direction, and a controlled coexistence of extended Bloch states and anisotropically localized states in the spectrum. We demonstrate that these features persist in the thermodynamic limit for a continuous range of the system parameters. Numerical results support these findings and highlight the robustness of the extended regime with respect to deviations from the exact resonance condition for finite systems. The localization and transport properties of the system can be engineered almost at will and independently in each direction. This study gives rise to the possibility of designing disordered potentials that work as switching devices and band-pass filters for quantum waves, such as matter waves in optical lattices.

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Section: Appendix A: Functional Equation Formalismmentioning

confidence: 99%

Controlled engineering of extended states in disordered systems

2012

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“…Apart from the interest these systems have in themselves, they could also serve as a starting point to gain more understanding about the inclusion of chemical complexity effects in the electronic structure of periodic lattices, as well as of quasi-periodic, fractal and amorphous atomic or molecular sequences. Various quantum chain models, which are studied in the context of low-dimensional systems, have been treated with the transfer matrix method [28][29][30][31][32]. Here, we use the transfer matrix method [33,34] to solve the TB system of equations and determine expressions for its eigenvalues, for both cyclic and fixed boundary conditions, by combining the spectral duality relations [35,36] with the connection of the elements of the powers of a 2×2 unimodular matrix to the Chebyshev polynomials of the second kind [37,38].…”

Section: Introductionmentioning

confidence: 99%

Spectral and transmission properties of periodic 1D tight-binding lattices with a generic unit cell: an analysis within the transfer matrix approach

Lambropoulos

Simserides

2018

J. Phys. Commun.

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We report on the electronic structure, density of states and transmission properties of the periodic one-dimensional tight-binding (TB) lattice with a single orbital per site and nearest-neighbor hoppings, with a generic unit cell of u sites. The determination of the eigenvalues is equivalent to the diagonalization of a real tridiagonal symmetric u-Toeplitz matrix with (cyclic boundaries) or without (fixed boundaries) perturbed upper right and lower left corners. We solve the TB equations via the Transfer Matrix Method, producing analytical solutions and recursive relations for its eigenvalues, closely related to the Chebyshev polynomials. We examine the density of states and provide relevant analytical relations. We attach semi-infinite leads, determine and discuss the transmission coefficient at zero bias and investigate the peaks number and position, and the effect of the coupling strength and asymmetry as well as of the lead properties on the transmission profiles. We introduce a generic optimal coupling condition and demonstrate its physical meaning.

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“…To end this part of the discussion we would like to mention that resonant (extended) eigenstates arising out of the commutivity of transfer matrices has been addressed also in relation to an array of quantum wells [32], and a distribution of potentials of Pöschl-Teller type [33] using a continuous version of the Schrödinger equation. The difference with the present case is that, here one can have commutators independent of the energy of the electron.…”

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Complete absence of localization in a family of disordered lattices

Pal¹,

Maiti²,

Chakrabarti³

2013

EPL

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Metal-insulator transitions and other electronic transitions PACS 72.15.Rn -Localization effects (Anderson or weak localization) PACS 03.75.-b -Matter wavesAbstract -We present analytically exact results to show that, certain quasi one-dimensional lattices where the building blocks are arranged in a random fashion, can have an absolutely continuous part in the energy spectrum when special correlations are introduced among some of the parameters describing the corresponding Hamiltonians. We explicitly work out two prototype cases, one being a disordered array of a simple diamond network and isolated dots, and the other an array of triangular plaquettes and dots. In the latter case, a magnetic flux threading each plaquette plays a crucial role in converting the energy spectrum into an absolutely continuous one. A flux controlled enhancement in the electronic transport is an interesting observation in the triangle-dot system that may be useful while considering prospective devices. The analytical findings are comprehensively supported by extensive numerical calculations of the density of states and transmission coefficient in each case.

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One-dimensional disordered wires with Pöschl-Teller potentials

Cited by 15 publications

References 56 publications

Controlled engineering of extended states in disordered systems

Controlled engineering of extended states in disordered systems

Spectral and transmission properties of periodic 1D tight-binding lattices with a generic unit cell: an analysis within the transfer matrix approach

Complete absence of localization in a family of disordered lattices

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