Double Dirac cones in phononic crystals

Li, Yan; Wu, Ying; Mei, Jun

doi:10.1063/1.4890304

Cited by 116 publications

(102 citation statements)

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“…Actually, such special dispersions at point D are the result of accidental degeneracy of the monopolar state and dipolar states. By 'accidental degeneracy', [3][4][5][6][7][8][9][10][11][12][13] we mean that these three eigenstates occur at exactly the same frequency only when the geometrical and/or material parameters satisfy certain conditions. For our 2D system of honey-coated-air cylinders placed in a water host, the condition is that R and r take a particular set of values, i.e., R = 0.249986a and r = 0.158276a, as specified in Figs.…”

Section: Fig 1 (A)mentioning

confidence: 99%

“…Is there any interesting property associated with this special point? To answer these questions, we develop a ⇀ k · ⇀ p perturbation method [3][4][5][6] to study the behaviors of the dispersion relations near point D. In short words, the essence of the perturbation method is to take the degenerate Bloch eigenstates at D as a basis to expand the Bloch functions at ⇀ k point that is close to D in the ⇀ k space. If we are interested in the linear slopes of the dispersions, we only need to consider the degenerate eigenstates atω D as the expansion basis, because the eigenstates away fromω D contribute only to higher orders of ⇀ k in the dispersions.…”

Section: Fig 1 (A)mentioning

confidence: 99%

“…1,2 Such special dispersion relations were also found in classical waves systems such as photonic and acoustic crystals. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] Like in the electronic systems, a lot of intriguing wave manipulating phenomena were discovered at the Dirac point in classical systems, including pseudo-diffusive transmission, Zitterbewegung effect, Klein tunneling and anti-localization. In recent years, not only Dirac point at the corner of the BZ, but also Dirac-like point, 3,[6][7][8][9][13][14][15] semi-Dirac point 4 and double Dirac point 5,10 at the BZ center have been found.…”

Section: Introductionmentioning

confidence: 99%

“…Our study shows that the triply degeneracy at the Γ point is a result of the accidental degeneracy. With the help of a perturbation method, [3][4][5][6] predict the linear slopes of the bands from first-principles, and immediately justify the existence of a Dirac-like point by checking the spatial symmetry of the eigenstates. We also develop an effective medium theory, and find that the AC can be characterized by a near-zero refractive index (NZRI) material.…”

Section: Introductionmentioning

confidence: 99%

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Flat band degeneracy and near-zero refractive index materials in acoustic crystals

Mei

2016

AIP Advances

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A Dirac-like cone is formed by utilizing the flat bands associated with localized modes in an acoustic crystal (AC) composed of a square array of core-shell-structure cylinders in a water host. Although the triply-degeneracy seems to arise from two almost-overlapping flat bands touching another curved band, the enlarged view of the band structure around the degenerate point reveals that there are actually two linear bands intersecting each other at the Brillouin zone center, with another flat band passing through the same crossing point. The linearity of dispersion relations is achieved by tuning the geometrical parameters of the cylindrical scatterers. A perturbation method is used to not only accurately predict the linear slopes of the dispersions, but also confirm the linearity of the bands from first principles. An effective medium theory based on coherent potential approximation is developed, and it shows that a slab made of the AC carries a near-zero refractive index around the Dirac-like point. Full-wave simulations are performed to unambiguously demonstrate the wave manipulating properties of the AC structures such as perfect transmission, unidirectional transmission and wave front shaping.

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Section: Fig 1 (A)mentioning

confidence: 99%

Section: Fig 1 (A)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Flat band degeneracy and near-zero refractive index materials in acoustic crystals

Mei

2016

AIP Advances

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“…Interestingly, the edge wave modes in phononic crystals are important in many scenarios [59][60][61][62] Lett. 61, 2015Lett.…”

Section: H Y S I C a L R E V I E W L E T T E R S Week Ending 4 Septemmentioning

confidence: 99%

Topological Phononic Crystals with One-Way Elastic Edge Waves

2015

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We report a new type of phononic crystals with topologically nontrivial band gaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum (anomalous) Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern numbers of 1 and 2, indicating that these structures support single and multimode edge elastic waves immune to backscattering. These robust one-way phononic waveguides could potentially lead to the design of a novel class of surface wave devices that are widely used in electronics, telecommunication, and acoustic imaging. DOI: 10.1103/PhysRevLett.115.104302 PACS numbers: 46.40.Cd, 46.40.Ff, 73.43.-f Topological states in electronic materials, including the quantum Hall effect [1] and topological insulators [2,3], have inspired a number of recent developments in photonics [4,5], phononics [6][7][8][9], and mechanical metamaterials [10][11][12][13]. In particular, in analogy to the quantum anomalous Hall effect [14], one-way electromagnetic waveguides in two-dimensional systems have been realized by breaking time-reversal symmetry [15][16][17][18].Very recently, unidirectional edge channels have been proposed for elastic waves using Coriolis force in a noninertial reference frame [19], but such a rotating frame is very difficult to implement in solid state devices. Moreover, one-way propagation of scalar acoustic waves has also been proposed by introducing rotating fluids [20][21][22]. However, it is important to recognize that elastic waves in solids have both transverse and longitudinal polarizations, while acoustic waves in fluids are purely longitudinal. As a result, it is challenging to achieve topological protection for elastic waves on an integrated platform.Here, we present a robust strategy to create topologically nontrivial edge modes for both longitudinal and transverse polarizations in a solid medium. In particular, we introduce gyroscopic phononic crystals, where each lattice site is coupled with a spinning gyroscope that breaks timereversal symmetry in a well-controlled manner. In both hexagonal and square lattices, gyroscopic coupling opens band gaps that are characterized by Chern numbers of 1 and 2. As a result, at the edge of these lattices both single-mode and multimode one-way elastic waves are observed to propagate around arbitrary defects without backscattering.To start, we consider a hexagonal phononic crystal with equal masses (m 2 ¼ m 1 ) connected by linear springs [red and black rods in Figs. 1(a) and 1(b)]. The resulting unit cell has 4 degrees of freedom specified by the displacements of m 1 and m 2 (U ¼ ½u for wave vectors μ within the first Brillouin zone. Here, ω denotes the angular frequency of the propagating wave and M ¼ diagfm 1 ; m 1 ; m 2 ; m 2 g is the mass matrix. Moreover, K is the 4 × 4 stiffness matrix and is a functi...

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Various topological phases and their abnormal effects of topological acoustic metamaterials

Chen

et al. 2023

Interdisciplinary Materials

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The last 20 years have witnessed growing impacts of the topological concept on the branches of physics, including materials, electronics, photonics, and acoustics. Topology describes objects with some global invariant property under continuous deformation, which in mathematics could date back to the 17th century and mature in the 20th century. In physics, it successfully underpinned the physics of the Quantum Hall effect in 1984. To date, topology has been extensively applied to describe topological phases in acoustic metamaterials. As artificial structures, acoustic metamaterials could be well theoretically analyzed, on‐demand designed, and easily fabricated by modern techniques, such as three‐dimensional printing. Some new theoretical topological models were first discovered in acoustic metamaterials analogous to electronic counterparts, associated with novel effects for acoustics closer to applications. In this review, we focused on the concept of topology and its realization in airborne acoustic crystals, solid elastic phononic crystals, and surface acoustic wave systems. We also introduced emerging concepts of non‐Hermitian, higher‐order, and Floquet topological insulators in acoustics. It has been shown that the topology theory has such a powerful generality that among the disciplines from electron to photon and phonon, from electronic to photonics and acoustics, from acoustic topological theory to acoustic devices, could interact and be analogous to fertilize fantastic new ideas and prototype devices, which might find applications in acoustic engineering and noise‐vibration control engineering in the near future.

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Double Dirac cones in phononic crystals

Cited by 116 publications

References 40 publications

Flat band degeneracy and near-zero refractive index materials in acoustic crystals

Flat band degeneracy and near-zero refractive index materials in acoustic crystals

Topological Phononic Crystals with One-Way Elastic Edge Waves

Various topological phases and their abnormal effects of topological acoustic metamaterials

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