Self-similarity appearance conditions for electronic transmission probability and Landauer resistance in a Fibonacci array of T stubs

Nomata, Atsushi; Horie, Shinkichi

doi:10.1103/physrevb.76.235113

Cited by 7 publications

(6 citation statements)

References 34 publications

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“…The transmission spectra and the control of their properties in aperiodic, inhomogeneous media is a field of intense study among a large class of wave scattering systems [39][40][41]. The design of our experimental setup has been based on the (lossless) construction rules [29,30] for perfect transmission resonances, which provide the technique for the design of setups which are transparent at preselected frequencies.…”

Section: Acoustic Waveguide With Complete Local Symmetry a Constructi...mentioning

confidence: 99%

Invariant currents in lossy acoustic waveguides with complete local symmetry

et al. 2015

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We study the effect of discrete symmetry breaking in inhomogeneous scattering media within the framework of generic wave propagation. Our focus is on one-dimensional scattering potentials exhibiting local symmetries. We find a class of spatially invariant nonlocal currents, emerging when the corresponding generalized potential exhibits symmetries in arbitrary spatial domains. These invariants characterize the wave propagation and provide a spatial mapping of the wave function between any symmetry related domains. This generalizes the Bloch and parity theorems for broken reflection and translational symmetries, respectively. Their nonvanishing values indicate the symmetry breaking, whereas a zero value denotes the restoration of the global symmetry where the well-known forms of the two theorems are recovered. These invariants allow for a systematic treatment of systems with any local symmetry combination, providing a tool for the investigation of

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Section: Acoustic Waveguide With Complete Local Symmetry a Constructi...mentioning

confidence: 99%

Invariant currents in lossy acoustic waveguides with complete local symmetry

et al. 2015

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“…Transmission properties and their control in inhomogeneous media with complex geometric structure has developed into a field of intense study with applications to electronic [1][2][3], photonic [4][5][6], acoustic [7] and magnonic [8] systems. Aperiodic systems possess a central role both in understanding the fundamental concepts which govern the transitions from perfectly periodic order to randomness, and in the development and design of devices with controllable transport properties.…”

Section: Introductionmentioning

confidence: 99%

Local symmetries and perfect transmission in aperiodic photonic multilayers

et al. 2013

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We develop a classification of perfectly transmitting resonances occurring in effectively one-dimensional optical media which are decomposable into locally reflection symmetric parts. The local symmetries of the medium are shown to yield piecewise translation-invariant quantities, which are used to distinguish resonances with arbitrary field profile from resonances following the medium symmetries. Focusing on light scattering in aperiodic multilayer structures, we demonstrate this classification for representative setups, providing insight into the origin of perfect transmission. We further show how local symmetries can be utilized for the design of optical devices with perfect transmission at prescribed energies. Providing a link between resonant scattering and local symmetries of the underlying medium, the proposed approach may contribute to the understanding of optical response in complex systems

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“…Orellana, et al in 2003 [97], while engineering Fano resonances in discrete arrays were proposed by A. E. Miroshnichenko and Y. S. Kivshar in 2005 [98]. During the next decade, more detailed studies using RSRM were carried out for the transmission coefficient [99][100][101][102][103][104][105], Landauer resistance [106], Lyapunov exponent [100], local DOS [101][102][103], and Kubo conductivity [107]. Moreover, the ballistic AC conductivity of periodic lattices has been surpassed through quasiperiodicity [108] or Fano resonances [109].…”

Section: Multidimensional Aperiodic Latticesmentioning

confidence: 99%

Real Space Theory for Electron and Phonon Transport in Aperiodic Lattices via Renormalization

Sánchez

Wang

2020

Symmetry

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Structural defects are inherent in solids at a finite temperature, because they diminish free energies by growing entropy. The arrangement of these defects may display long-range orders, as occurring in quasicrystals, whose hidden structural symmetry could greatly modify the transport of excitations. Moreover, the presence of such defects breaks the translational symmetry and collapses the reciprocal lattice, which has been a standard technique in solid-state physics. An alternative to address such a structural disorder is the real space theory. Nonetheless, solving 1023 coupled Schrödinger equations requires unavailable yottabytes (YB) of memory just for recording the atomic positions. In contrast, the real-space renormalization method (RSRM) uses an iterative procedure with a small number of effective sites in each step, and exponentially lessens the degrees of freedom, but keeps their participation in the final results. In this article, we review aperiodic atomic arrangements with hierarchical symmetry investigated by means of RSRM, as well as their consequences in measurable physical properties, such as electrical and thermal conductivities.

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Self-similarity appearance conditions for electronic transmission probability and Landauer resistance in a Fibonacci array of T stubs

Cited by 7 publications

References 34 publications

Invariant currents in lossy acoustic waveguides with complete local symmetry

Invariant currents in lossy acoustic waveguides with complete local symmetry

Local symmetries and perfect transmission in aperiodic photonic multilayers

Real Space Theory for Electron and Phonon Transport in Aperiodic Lattices via Renormalization

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