Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states

Ochiai, Tetsuyuki; Onoda, Masaru

doi:10.1103/physrevb.80.155103

Cited by 236 publications

(170 citation statements)

References 36 publications

(36 reference statements)

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“…However, the bandgaps opened by breaking P [24] and T individually are topologically inequivalent [5,25], meaning that the bulk bands in these two cases carry different Chern numbers. The Chern number is the integration of the Berry curvature [F (k) in Table B1] on a closed surface in the wavevector space.…”

Section: From Dirac Cones To Quantum Hall Topological Phasementioning

confidence: 99%

Topological photonics

2014

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The application of topology, the mathematics studying conserved properties through continuous deformations, is creating new opportunities within photonics, bringing with it theoretical discoveries and a wealth of potential applications. This field was inspired by the discovery of topological insulators, in which interfacial electrons transport without dissipation even in the presence of impurities. Similarly, the use of carefully-designed wave-vector space topologies allows the creation of interfaces that support new states of light with useful and interesting properties. In particular, it suggests the realization of unidirectional waveguides that allow light to flow around large imperfections without back-reflection. The present review explains the underlying principles and highlights how topological effects can be realized in photonic crystals, coupled resonators, metamaterials and quasicrystals.Frequency, wavevector, polarization and phase are degrees of freedom that are often used to describe a photonic system. In the last few years, topology -a property of a photonic material that characterizes the quantized global behavior of the wavefunctions on its entire dispersion band-has been emerging as another indispensable ingredient, opening a path forward to the discovery of fundamentally new states of light and possibly revolutionary applications. Possible practical applications of topological photonics include photonic circuitry less dependent on isolators and slow light insensitive to disorder.Topological ideas in photonics branch from exciting developments in solid-state materials, along with the discovery of new phases of matter called topological insulators [1, 2]. Topological insulators, being insulating in their bulk, conduct electricity on their surfaces without dissipation or backscattering, even in the presence of large impurities. The first example was the integer quantum Hall effect, discovered in 1980. In quantum Hall states, two-dimensional (2D) electrons in a uniform magnetic field form quantized cyclotron orbits of discrete eigenvalues called Landau levels. When the electron energy sits within the energy gap between the Landau levels, the measured edge conductance remains constant within the accuracy of about one part in a billion, regardless of sample details like size, composition and impurity levels. In 1988, Haldane proposed a theoretical model to achieve the same phenomenon but in a periodic system without Landau levels [3], the so-called quantum anomalous Hall effect.Posted on arXiv in 2005, Haldane and Raghu transcribed the key feature of this electronic model into photonics [4,5]. They theoretically proposed the photonic analogue of the quantum (anomalous) Hall effect in photonic crystals [6], the periodic variation of optical materials, molding photons the same way as solids modulating electrons. Three years later, the idea was confirmed by Wang et al., who provided realistic material designs [7] and experimental observations [8]. Those studies spurred numerous subsequent theoretical [9...

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Section: From Dirac Cones To Quantum Hall Topological Phasementioning

confidence: 99%

Topological photonics

2014

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“…These modes are well known in electronic graphene, 3,34 as well as in both photonic 6,7,22 and acoustic graphene. 12 In the next section a multiple scattering method is developed for the simulations of waves propagating in ribbons under point source excitation.…”

Section: Dispersion Relation Of Zigzag Ribbonsmentioning

confidence: 99%

“…Thus, Dirac points appear in the band structure of 2D photonic [6][7][8][9][10] and sonic [11][12][13] crystals, showing also extraordinary propagation properties, like Zitterbewegung, 14 a near-zero refraction index, 15 edge states, 16 extraordinary transmission, 11,17,18 or one-way propagation. [19][20][21][22] An elastic analog of graphene has not been fully analyzed, although the effort to create structures to control the propagation of elastic waves in 2D systems has been remarkable.…”

Section: Introductionmentioning

confidence: 99%

Elastic analog of graphene: Dirac cones and edge states for flexural waves in thin plates

2013

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An elastic analog of graphene is introduced and analyzed. The system consists of a honeycomb arrangement of spring-mass resonators attached to a thin elastic layer, and the propagation properties of flexural waves along it is studied. The band-structure calculation shows the presence of Dirac points near the K point of the Brillouin zone. Analytical expressions are found for both Dirac frequency and velocity as a function of the resonator's parameters. Finally, the bounded modes of infinitely long ribbons of this honeycomb arrangement are analyzed. The presence of edge states, which are studied using multiple scattering theory, is shown. It is concluded that these structures can be used to control the propagation of flexural waves in thin plates.

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“…The honeycomb or hexagonal lattice geometry has now been studied theoretically and experimentally in many different photonic systems including metamaterials and photonic crystals [15][16][17], plasmonic nanoparticles [18,19], photonic lattices [20][21][22], and microwave resonator arrays [23][24][25][26], eg. Fig.…”

Section: Designmentioning

confidence: 99%

“…On a more fundamental level, the realization of conical intersections in photonic and matter wave systems allows the direct observation of relativistic quantum analogies not easily visible in systems such as graphene [75], for example the parity anomaly [76], along with the study of surface effects such as edge states that are notoriously hard to control in condensed matter systems [16,17,21,24]. When a conical dispersion is restricted to a finite system, the intersection is replaced by a (small) band gap, due to the vanishing density of states.…”

Section: Applicationsmentioning

confidence: 99%

Conical intersections for light and matter waves

Leykam

Desyatnikov

2016

Advances in Physics: X

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We review the design, theory, and applications of two dimensional periodic lattices hosting conical intersections in their energy-momentum spectrum. The best known example is the Dirac cone, where propagation is governed by an effective Dirac equation, with electron spin replaced by a "fermionic" half-integer pseudospin. However, in many systems such as metamaterials, modal symmetries result in the formation of higher order conical intersections with integer or "bosonic" pseudospin. The ability to engineer lattices with these qualitatively different singular dispersion relations opens up many applications, including superior slab lasers, generation of orbital angular momentum, zeroindex metamaterials, and quantum simulation of exotic phases of relativistic matter.

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Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states

Cited by 236 publications

References 36 publications

Topological photonics

Topological photonics

Elastic analog of graphene: Dirac cones and edge states for flexural waves in thin plates

Conical intersections for light and matter waves

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