Ladder network as a mesoscopic switch: An exact result

Sil, Shreekantha; Maiti, Santanu K.; Chakrabarti, Abhijit

doi:10.1103/physrevb.78.113103

Cited by 44 publications

(62 citation statements)

References 30 publications

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“…Bloch like eigenstates, extended over the entire lattice were observed at certain discrete energy eigenvalues rendering the lattice completely transparent to an incoming electron possessing such an energy. Such a situation was also observed with long range positional correlation in one dimension [25], or in quasi-one dimensional ladder networks with specially correlated potentials where, the existence of even a continuous band of extended states was shown to be possible [26,27].…”

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confidence: 90%

“…The existence of continuous bands is reported recently in quasi-one dimensional or two dimensional systems with diagonal disorder [26,27]. Correlation between the numerical values of the hopping integrals in a class of topologically disordered quasi-one dimensional closed looped systems has also been shown to produce absolutely continuous bands of eigenfunctions recently [28,29].…”

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confidence: 99%

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Tight-binding chains with off-diagonal disorder: Bands of extended electronic states induced by minimal quasi–one-dimensionality

Nandy

Pal

Chakrabarti

2016

EPL

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-It is shown that, an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight binding model can be tailored to generate absolutely continuous energy bands. It can be achieved if linear atomic clusters of an appropriate size are side-coupled to a suitable subset of sites in the backbone, and if the nearest neighbor hopping integrals, in the backbone and in the side-coupled cluster bear a certain ratio. We work out the precise relationship between the number of atoms in one of the building blocks in the backbone, and that in the side-attachment. In addition, we also evaluate the definite correlation between the numerical values of the hopping integrals at different subsections of the chain, that can convert an otherwise point spectrum (or, a singular continuous one for deterministically disordered lattices) with exponentially (or power law) localized eigenfunctions to an absolutely continuous spectrum comprising one or more bands (subbands) populated by extended, totally transparent eigenstates. The results, which are analytically exact, put forward a non-trivial variation of the Anderson localization [P. W. Anderson, Phys. Rev. 109, 1492 (1958)], pointing towards its unusual sensitivity to the numerical values of the system parameters and, go well beyond the other related models such as the Random Dimer Model (RDM) [Dunlap et al., Phys. Rev. Lett. 65, 88 (1990)].Introduction. -Single particle states localize exponentially in a disordered system [1][2][3]. The effect is strongest in one dimension, where there is a complete absence of diffusion irrespective of the strength of disorder [1]. In two dimensions the states retain their exponential decay of amplitude, while in three dimensions a possibility of a metal-insulator transition arises. The results get adequate support from the calculations of the localization length [4,5], density of states [6] and the multi-fractality of the spectra and wave functions of spinless, non-interacting fermionic systems [7][8][9].The path breaking observation by Anderson [1], over the years, has extended its realm well beyond the electronic properties of disordered solid materials, and has been found out to be ubiquitous in a wide variety of systems. For example, one can refer to the field of localization of light, an idea pioneered about three decades ago

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confidence: 90%

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confidence: 99%

Tight-binding chains with off-diagonal disorder: Bands of extended electronic states induced by minimal quasi–one-dimensionality

Nandy

Pal

Chakrabarti

2016

EPL

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“…The backbone of our analytical attempt is an exact mapping of a coupled, quasi-one dimensional multistrand ladder network into a set of totally decoupled linear chains describing the quantum mechanics of a class of pseudoparticles. Such an exact mapping has previously been described in the literature in the context of de-localization of single particle states in a ladder-like geometry [14,15] modelling a DNA-like double chain [14] or a quasi-two dimensional mesh with correlated disorder [15].…”

Section: Introductionmentioning

confidence: 99%

“…The last example has gained momentum and aroused interest recently after the development of the idea of light localization using path-entangled photons [10] and the tailoring of partially coherent light [11]. The variants of the phenomenon, beginning with the concept of geometrically correlated disorder in the distribution of the potentials, the so called random dimer model (RDM) [12], or in the overlap integrals in a tight binding description [13], and moving over to the engineering of continuous bands of extended Bloch-like functions [14][15][16][17][18] in quasi one dimensional disordered or quasiperiodic systems, thus offer exciting physics and the prospects of designing novel devices.…”

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confidence: 99%

Controlled delocalization of electronic states in a multi-strand quasiperiodic lattice

2017

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Finite strips, composed of a periodic stacking of infinite quasiperiodic Fibonacci chains, have been investigated in terms of their electronic properties. The system is described by a tight binding Hamiltonian. The eigenvalue spectrum of such a multi-strand quasiperiodic network is found to be sensitive on the mutual values of the intra-strand and inter-strand tunnel hoppings, whose distribution displays a unique three-subband self-similar pattern in a parameter subspace. In addition, it is observed that special numerical correlations between the nearest and the next-nearest neighbor hopping integrals can render a substantial part of the energy spectrum absolutely continuous. Extended, Bloch like functions populate the above continuous zones, signalling a complete delocalization of single particle states even in such a non-translationally invariant system, and more importantly, a phenomenon that can be engineered by tuning the relative strengths of the hopping parameters. A commutation relation between the potential and the hopping matrices enables us to work out the precise correlation which helps to engineer the extended eigenfunctions and determine the band positions at will.

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“…Eventually, the possibility of a controlled engineering of spectral continuum populated by extended single particle states and even a metal-insulator transition in one, or quasi-one dimensional discrete systems have also been discussed in the literature [34][35][36]. But, on the whole, the general exponentially localized character of the eigenfunctions prevails, and the possibility of having a mixed spectrum of localized and extended states in a disordered system (under some special positional correlations) is now well established.…”

Section: Introductionmentioning

confidence: 99%

Engineering bands of extended electronic states in a class of topologically disordered and quasiperiodic lattices

Pal

Chakrabarti

2014

Physics Letters A

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We show that a discrete tight-binding model representing either a random or a quasiperiodic array of bonds, can have the entire energy spectrum or a substantial part of it absolutely continuous, populated by extended eigenfunctions only, when atomic sites are coupled to the lattice locally, or non-locally from one side. The event can be fine-tuned by controlling only the host-adatom coupling in one case, while in two other cases cited here an additional external magnetic field is necessary. The delocalization of electronic states for the group of systems presented here is sensitive to a subtle correlation between the numerical values of the Hamiltonian parameters -a fact that is not common in the conventional cases of Anderson localization. Our results are analytically exact, and supported by numerical evaluation of the density of states and electronic transmission coefficient.

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Ladder network as a mesoscopic switch: An exact result

Cited by 44 publications

References 30 publications

Tight-binding chains with off-diagonal disorder: Bands of extended electronic states induced by minimal quasi–one-dimensionality

Tight-binding chains with off-diagonal disorder: Bands of extended electronic states induced by minimal quasi–one-dimensionality

Controlled delocalization of electronic states in a multi-strand quasiperiodic lattice

Engineering bands of extended electronic states in a class of topologically disordered and quasiperiodic lattices

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