Landauer resistance of Thue-Morse and Fibonacci lattices and some related issues

Roy, C.L.; Khan, Arif

doi:10.1103/physrevb.49.14979

Cited by 29 publications

(23 citation statements)

References 21 publications

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“…This is not trivial because fluctuations in the values of the matrix elements of Z N used to calcuate the LR and the band spectra become extremely rapid and extreme at higher values of N and lower values of γ. For example, even for N = 18 and γ = 0.999 or N = 8 and γ = 0.9, T rZ N and the LR fluctuate rapidly between ±10 M with M taking values of 200-300 or more for some values of k. Also these fluctuations occur over extremely small intervals of k. In many ways the results obtained here, which are similar to those obtained by Roy and Khan [20,21], are unexpected. The LR fluctuates rapidly with many spikes down to extremely low values over the momentum range examined.…”

Section: Discussionsupporting

confidence: 84%

“…The peaks in log LR appear to be associated with gaps, with the higher peaks associated with wider gaps. This effect [14] was also found for calculations with the Kronig-Penney model with potential distributions corresponding to the Fibonacci and Thue-Morse substitution sequences [20,21]. The minima in log LR which show as downward pointing spikes appear to be associated also with narrow gaps.…”

Section: Landauer Resistance Band Spectrasupporting

confidence: 66%

“…5 (the associated periodic system). As is well known [23,20,21] the band and gap distribution is obtained from a plot of |T rZ|/2 as a function of momentum or energy. Regions in which |T rZ|/2 ≤ 1 correspond to bands; regions with |T rZ|/2 > 1 correspond to gaps.…”

Section: Transfer Matrixmentioning

confidence: 99%

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The Landauer resistance and band spectra for the counting quantum turing machine

Benioff

1998

Physica D: Nonlinear Phenomena

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In other work, the generalized counting quantum Turing machine (GCQTM) was studied. For any N this machine enumerates the first 2 N integers in succession as binary strings. The generalization consists of associating a potential with read 1 steps only. The Landauer Resistance (LR) and band spectra were determined for the tight binding Hamiltonians associated with the GCQTM for energies below the potential height. Here these calculations are extended to energies both above and below the barrier height. For parameters and potentials in the electron region, The LR fluctuates rapidly between very high and very low values as a function of momentum. The rapidity and extent of the fluctuations increases rapidly with increasing N . For N = 18, the largest value considered, the LR shows good transmission probability as a function of momentum with numerous holes of very high LR values present. This is true for energies both above and below the potential height. It is suggested that the main features of the LR can be explained by coherent superposition of the component waves reflected from or transmitted through or across the 2 N −1 potentials present in the distribution. If this explanation is correct, it provides a dramatic illustration of the effects of quantum nonlocality.

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Section: Discussionsupporting

confidence: 84%

Section: Landauer Resistance Band Spectrasupporting

confidence: 66%

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The Landauer resistance and band spectra for the counting quantum turing machine

Benioff

1998

Physica D: Nonlinear Phenomena

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“…The electromagnetic driven approach is achieved by using the Lorentz force, the driven force is large and driven mode is mainly the slide-film damping, so the driven amplitude and Q are high 4 . According to the different application function, the nano resonant tunneling film is also called as resonant tunneling diode (RTD), which is a new type nanometer-devices based on the quantum tunneling effect 5 , and its core structure is the double-barrier with the different band gap materials 6 . Researchers found that RTD based on the resonant tunneling effect has piezoresistance effect 7 , and verify that the static piezoresistance sensitivity is one order higher than piezoresistance sensitivity of the Silicon 8 .…”

Section: Introductionmentioning

confidence: 99%

Research of electromagnetic drive micromechanical gyroscope based on tunneling effect of multi-barrier nano thin films

Wang

et al. 2010

SPIE Proceedings

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Multi-barrier nano-thin films device is a new device based on the quantum tunneling effect. This kind of device has piezoresistive effect and the piezoresistive sensitivity is about one order than that of silicon piezoresistive device. Thin film device fabricated by using molecular beam epitaxy (MBE) has the advantages of small temperature drift compared with the doped devices. Comparing with the electrostatic comb-drive mode, the electromagnetic driving approach is not only with simple structure and easy to fabrication, but also can achieve large displacement-driven. These two methods applied to the study of gyroscope can improve the sensitivity in essence. In this paper, a novel gyroscope structure with folding-type orthogonal beams is designed which is not only meet the drive approach, but also meet the detection conditions. The nano thin films device and gyroscope structure are fabricated by the GaAs surface micromachining and GaAs bulk micromachining processes respectively. The preliminary measurement results prove that the gyroscope design is feasible.

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“…Recent study [9] on Fibonacci multibarrier systems (FMS) also suggests the use of such quasi-periodic systems in perfect bandpass or band-eliminator (of extremely low width) filter circuitry. It is worth mentioning that most researches have considered FMSs as the archetype of quasiperiodic heterostructures with the studies on electron dynamics [10], Landauer resistance [11], dc conductance [12,13]. The importance of another quasiperiodic system, Thue-Morse multibarrier system (TMS), over FMS lies in the fact that TMS exhibits better transport properties than FMS in presence of the same degree of growth fluctuations [14].…”

Section: Introductionmentioning

confidence: 99%

Efficient band-pass and stop-band filtering by GaAs–Al_cGa₁₋_cAs generalized Thue–Morse multibarrier systems

Panchadhyayee¹

2013

Philosophical Magazine

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The influence of Al concentration and barrier width on the transmission spectra in GaAs-Al c Ga 1Àc As heterostructure is studied for two different kinds of the generalized Thue-Morse multibarrier systems (GTMS). These structures provide interesting filter properties with regard to effective band-pass or stopband (of extremely low width) circuitry. The first kind of GTMS is suitable for application as a band-pass electronic filter, while the second kind as stopband filter. High Al concentration and large barrier width result in sharp resonances in the transmission spectrum. IntroductionSince the experimental realization of Fibonacci [1] and Thue-Morse [2] quasiperiodic superlattices (SL), their fascinating physical properties have been a subject of growing interest both from the fundamental point of view as well as for their potential device applications. The competition between localization and delocalization arising out of quasiperiodicity leads to many intriguing features affecting electron conduction like the occurrence of a highly fragmented, self-similar spectrum [3-6] and the tuning of the tunneling current [7]. The fragmentation of the SL minibands could serve as a basis for electronic filters. Fibonacci SL is reported [8] as a good electronic filter because the Fourier spectrum of the transmitted part of a Gaussian wave packet passing through the SL clearly indicates many prominent and sharp peaks. These peaks correspond to the allowed subminibands of the energy spectrum. Recent study [9] on Fibonacci multibarrier systems (FMS) also suggests the use of such quasi-periodic systems in perfect bandpass or band-eliminator (of extremely low width) filter circuitry. It is worth mentioning that most researches have considered FMSs as the archetype of quasiperiodic heterostructures with the studies on electron dynamics [10], Landauer resistance [11], dc conductance [12,13]. The importance of another quasiperiodic system, Thue-Morse multibarrier system (TMS), over FMS lies in the fact that TMS exhibits better transport

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Landauer resistance of Thue-Morse and Fibonacci lattices and some related issues

Cited by 29 publications

References 21 publications

The Landauer resistance and band spectra for the counting quantum turing machine

The Landauer resistance and band spectra for the counting quantum turing machine

Research of electromagnetic drive micromechanical gyroscope based on tunneling effect of multi-barrier nano thin films

Efficient band-pass and stop-band filtering by GaAs–Al_cGa₁₋_cAs generalized Thue–Morse multibarrier systems

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Landauer resistance of Thue-Morse and Fibonacci lattices and some related issues

Cited by 29 publications

References 21 publications

The Landauer resistance and band spectra for the counting quantum turing machine

The Landauer resistance and band spectra for the counting quantum turing machine

Research of electromagnetic drive micromechanical gyroscope based on tunneling effect of multi-barrier nano thin films

Efficient band-pass and stop-band filtering by GaAs–AlcGa1−cAs generalized Thue–Morse multibarrier systems

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Efficient band-pass and stop-band filtering by GaAs–Al_cGa₁₋_cAs generalized Thue–Morse multibarrier systems