Wannier functions and the calculation of localized modes in one-dimensional photonic crystals

Romano, Maria Cecilia; Gomes, A. da S.; Bruno-Alfonso, Alexys

doi:10.1364/josab.35.000826

Cited by 10 publications

(7 citation statements)

References 46 publications

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“…The previous statements are supported by the fact that coupling engineering in structured mechanical systems is flexible enough to introduce length deformations that generalize simple periodic configurations. The realization of evanescent couplings extends well beyond the mathematical abstraction of Wannier functions [26,27] and the limitations of electronic transport in traditional solids. allow us to identify the locations of the global maximum and minimum of the torsional vibrations to excite and detect spectrum efficiently; they are located at the edges of the resonators.…”

Section: Mainmentioning

confidence: 99%

Emulating tightly bound electrons in crystalline solids using mechanical waves

Ramírez-Ramírez

Flores-Olmedo

Báez

et al. 2019

Preprint

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Solid state physics deals with systems composed of atoms with strongly bound electrons. The tunneling probability of each electron is determined by interactions that typically extend to neighboring sites, as their corresponding wave amplitudes decay rapidly away from an isolated atomic core. This kind of description is essential to material science, and it rules the electronic transport properties of metals, insulators and other condensed matter systems. The corresponding phenomenology is well captured by tight-binding models, where the electronic band structure emerges from atomic orbitals of isolated atoms plus their coupling to neighboring sites in a cristal.In this work, a mechanical system that emulates dynamically a tightly bound electron is built. This is done by connecting mechanical resonators via locally periodic aluminum bars acting as couplers. When the frequency of a particular resonator lies within the frequency gap of a coupler, the vibrational wave amplitude imitates a bound electron orbital. The localization of the wave at the resonator site and its

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Section: Mainmentioning

confidence: 99%

Emulating tightly bound electrons in crystalline solids using mechanical waves

Ramírez-Ramírez

Flores-Olmedo

Báez

et al. 2019

Preprint

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“…The coupling engineering also allows to tune in the coupling with the distance since the model in the site basis is tridiagonal. The realization of evanescent couplings extends well beyond the mathematical abstraction of Wannier functions 36,37 and the limitations of electronic transport in traditional solids.…”

mentioning

confidence: 99%

Emulating tightly bound electrons in crystalline solids using mechanical waves

Ramírez-Ramírez

Flores-Olmedo

Báez

et al. 2020

Sci Rep

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Solid state physics deals with systems composed of atoms with strongly bound electrons. The tunneling probability of each electron is determined by interactions that typically extend to neighboring sites, as their corresponding wave amplitudes decay rapidly away from an isolated atomic core. This kind of description is essential in condensed-matter physics, and it rules the electronic transport properties of metals, insulators and many other solid-state systems. The corresponding phenomenology is well captured by tight-binding models, where the electronic band structure emerges from atomic orbitals of isolated atoms plus their coupling to neighboring sites in a crystal. In this work, a mechanical system that emulates dynamically a quantum tightly bound electron is built. This is done by connecting mechanical resonators via locally periodic aluminum bars acting as couplers. When the frequency of a particular resonator lies within the frequency gap of a coupler, the vibrational wave amplitude imitates a bound electron orbital. The localization of the wave at the resonator site and its exponential decay along the coupler are experimentally verified. The quantum dynamical tight-binding model and frequency measurements in mechanical structures show an excellent agreement. Some applications in atomic and condensed matter physics are suggested.

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“…Under an inversion-symmetric choice of unit cell, the Berry phase is quantized to 0 or 𝜋. This quantization has an intuitive interpretation: in 1D, all photonic bands admit maximally localized Wannier functions whose centers are gauge invariant quantities [68][69][70][71][72][73][74]. Due to inversion symmetry, a single Wannier center (per unit cell) can only be located in two distinct positions in the unit cell, as shown in Fig.…”

Section: A Classification Due To Inversion Symmetrymentioning

confidence: 99%

Topological Phases of Photonic Crystals under Crystalline Symmetries

Vaidya¹,

Ghorashi²,

Christensen³

et al. 2023

Preprint

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Photonic crystals (PhCs) have emerged as a popular platform for realizing various topological phases due to their flexibility and potential for device applications. In this article, we present a comprehensive classification of topological bands in one-and two-dimensional photonic crystals, with and without time-reversal symmetry. Our approach exploits the symmetry representations of field eigenmodes at high-symmetry points in momentum space, allowing for the efficient design of a wide range of topological PhCs. In particular, we show that the complete classification provided here is useful for diagnosing photonic crystal analogs of obstructed atomic limits, fragile phases, and stable topological phases that include bands with Dirac points and Chern numbers.

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Wannier functions and the calculation of localized modes in one-dimensional photonic crystals

Cited by 10 publications

References 46 publications

Emulating tightly bound electrons in crystalline solids using mechanical waves

Emulating tightly bound electrons in crystalline solids using mechanical waves

Emulating tightly bound electrons in crystalline solids using mechanical waves

Topological Phases of Photonic Crystals under Crystalline Symmetries

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