Selective enhancement of topologically induced interface states in a dielectric resonator chain

Poli, Charles; Bellec, Matthieu; Kuhl, Ulrich; Mortessagne, Fabrice; Schomerus, Henning

doi:10.1038/ncomms7710

Cited by 534 publications

(474 citation statements)

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“…Lattice bands with a non vanishing imaginary part could be realized in synthetic temporal optical crystals, waveguide lattices, coupled-resonator optical waveguides, microwave resonator chains, etc. as discussed in several recent works [42,44,48,52,[54][55][56]. In this work we aim to investigate the onset of BOs in non-Hermitian lattices with a non vanishing imaginary part of the band dispersion curve.…”

Section: Introductionmentioning

confidence: 99%

Bloch oscillations in non-Hermitian lattices with trajectories in the complex plane

Longhi

2015

Phys. Rev. A

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Bloch oscillations (BOs), i.e. the oscillatory motion of a quantum particle in a periodic potential, are one of the most striking effects of coherent quantum transport in the matter. In the semiclassical picture, it is well known that BOs can be explained owing to the periodic band structure of the crystal and the so-called 'acceleration' theorem: since in the momentum space the particle wave packet drifts with a constant speed without being distorted, in real space the probability distribution of the particle undergoes a periodic motion following a trajectory which exactly reproduces the shape of the lattice band. In non-Hermitian lattices with a complex (i.e. not real) energy band, extension of the semiclassical model is not intuitive. Here we show that the acceleration theorem holds for non-Hermitian lattices with a complex energy band only on average, and that the periodic wave packet motion of the particle in the real space is described by a trajectory in complex plane, i.e. it generally corresponds to reshaping and breathing of the wave packet in addition to a transverse oscillatory motion. The concept of BOs involving complex trajectories is exemplified by considering two examples of non-Hermitian lattices with a complex band dispersion relation, including the Hatano-Nelson tight-binding Hamiltonian describing the hopping motion of a quantum particle on a linear lattice with an imaginary vector potential and a tight-binding lattice with imaginary hopping rates.

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Section: Introductionmentioning

confidence: 99%

Bloch oscillations in non-Hermitian lattices with trajectories in the complex plane

Longhi

2015

Phys. Rev. A

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“…1. It has also been realized in acoustics, photonics and ultracold atomic gases [14][15][16][17]. The system is obviously invariant under time and space inversions.…”

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confidence: 99%

Geometrical phase shift in Friedel oscillations

Dutreix

Delplace

2017

Phys. Rev. B

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This work addresses the problem of elastic scattering through a localized impurity in a one-dimensional crystal with sublattice freedom degrees. The impurity yields long-range interferences in the local density of states known as Friedel oscillations. Here, we show that the internal degrees of freedom of Bloch waves are responsible for a geometrical phase shift in Friedel oscillations. The Fourier transform of the energy-resolved interference pattern reveals a topological property of this phase shift, which is intrinsically related to the Bloch band structure topology in the absence of impurity. Therefore, Friedel oscillations in the local density of states can be regarded as a probe of wave topological properties in a broad class of classical and quantum systems, such as acoustic and photonic crystals, ultracold atomic gases in optical lattices, and electronic compounds.Electric screening in metals arises as a collective response of the conduction electrons to the Coulomb potential of a charged impurity. A long wavelength description of the problem captures the exponential screening of the impurity by the surrounding electrons, in agreement with the classical picture that depicts electrons as point charges. In quantum mechanics, however, particles are described by wavefunctions and may interfere. In the 1950s, J. Friedel actually understood that a charged impurity additionally yields a long-range interference pattern in the electronic density [1]. It consists of algebraically decaying 2k F -wavevector oscillations, and results from Fermi surface nesting associated to twice the Fermi momentum k F . Thus, these oscillations reported by Friedel for charges in metals rely on wave features, and they have subsequently been revisited in other contexts, such as magnetic interactions [2][3][4][5] and noninteracting electrons [6][7][8]. In particular, Friedel oscillations have been observed in nonrelativistic electron gases via scanning tunnelling microscopy (STM); an experimental technique that images the local density of states (LDOS), i.e., the electronic density with atomic-scale and energy resolutions [9][10][11]. These experiments have confirmed that backscattering was the most efficient process involved in the elastic scattering through short-range impurities. For noninteracting electrons in a one-dimensional crystal, backscattering is indeed responsible for 2k 0 -wavevector Friedel oscillations that behave asHere δρ denotes the correction to the LDOS induced by a localized impurity, m labels the distance to the impurity in units of the Bravais lattice vector, V(ω) is some real function, and wavevector 2k 0 refers to the elastic backscattering between the time-reversed states −k 0 and k 0 at energy ω ( = 1). Such backscattering wavevectors are illustrated in Fig. 1 by the double arrows. The reader may find the details of the derivation of Eq. (1) in Supplemental Material (SM) [12]. In this letter, we would like to highlight the effects of internal degrees of freedom on the long-range interference pattern induced b...

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“…Towards mechanical lasers.-This phenomenon is the acoustic analog of selective enhancement of microwave modes realized in Ref. [44]. Just as selective enhancement for light waves may lead to the design of novel parity-timesymmetric [45,46] and topological [8] lasers, analogously, selective enhancement of sound waves may be useful in the design of sound amplification by stimulated emission of radiation (SASER), i.e., the acoustic analog of lasers, acoustic couplers, and rectifiers.…”

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Sonic Landau Levels and Synthetic Gauge Fields in Mechanical Metamaterials

et al. 2017

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Mechanical strain can lead to a synthetic gauge field that controls the dynamics of electrons in graphene sheets as well as light in photonic crystals. Here, we show how to engineer an analogous synthetic gauge field for lattice vibrations. Our approach relies on one of two strategies: shearing a honeycomb lattice of masses and springs or patterning its local material stiffness. As a result, vibrational spectra with discrete Landau levels are generated. Upon tuning the strength of the gauge field, we can control the density of states and transverse spatial confinement of sound in the metamaterial. We also show how this gauge field can be used to design waveguides in which sound propagates with robustness against disorder as a consequence of the change in topological polarization that occurs along a domain wall. By introducing dissipation, we can selectively enhance the domain-wall-bound topological sound mode, a feature that may potentially be exploited for the design of sound amplification by stimulated emission of radiation (SASER, the mechanical analogs of lasers). DOI: 10.1103/PhysRevLett.119.195502 Electronic systems subject to a uniform magnetic field experience a wealth of fascinating phenomena such as topological states [1] in the integer quantum Hall effect [2] and anyons associated with the fractional quantum Hall effect [3]. Recently, it has been shown that in a strained graphene sheet, electrons experience external potentials that can mimic the effects of a magnetic field, which results in the formation of Landau levels and edge states [4,5]. Working in direct analogy with this electronic setting, pseudomagnetic fields have been engineered by arranging CO molecules on a gold surface [6] and in photonic honeycomb-lattice metamaterials [7,8].In this Letter, we apply insights about wave propagation in the presence of a gauge field to acoustic phenomena in a nonuniform phononic crystal, using the appropriate mechanisms of strain-phonon coupling and frictional dissipation, in contrast to those present in electronic and photonic cases. The acoustic metamaterial context in which we implement gauge fields provides us with significant control [9-11] over frequency, wavelength, and attenuation scales unavailable in the analogous electronic realizations. For example, a metamaterial composed of stiff (e.g., metallic) components of micron-scale length may be suitable for control over ultrasound with gigahertz-scale frequencies, whereas cm-scale metamaterials may provide control over kHz-scale sound waves. We develop two strategies for realizing a uniform pseudomagnetic field in a metamaterial based on the honeycomb lattice, i.e., "mechanical graphene" [12]. In the first strategy, we apply stress at the boundary to obtain nonuniform strain in the bulk, which leads to a Landau-level spectrum, whereas in the second strategy, we exploit builtin, nonuniform patterning of the local metamaterial stiffness. This second strategy shows how the unique controllability of metamaterials can lead to novel designs inaccessibl...

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Selective enhancement of topologically induced interface states in a dielectric resonator chain

Cited by 534 publications

References 41 publications

Bloch oscillations in non-Hermitian lattices with trajectories in the complex plane

Bloch oscillations in non-Hermitian lattices with trajectories in the complex plane

Geometrical phase shift in Friedel oscillations

Sonic Landau Levels and Synthetic Gauge Fields in Mechanical Metamaterials

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