Proposed method for detection of the pseudospin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mstyle scriptlevel="1"><mml:mfrac bevelled="false"><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mstyle></mml:mrow></mml:math>Berry phase in a photonic crystal with a Dirac spectrum

Sepkhanov, R. A.; Nilsson, Johan; Beenakker, C. W. J.

doi:10.1103/physrevb.78.045122

Cited by 56 publications

(46 citation statements)

References 21 publications

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“…In such crystals, the unusual transmission properties near a Dirac point [23][24][25] were predicted and observed experimentally.…”

Section: Confining Photonsmentioning

confidence: 96%

“…Current methods of design and synthesis include i) nanopatterning of ultra-high-mobility 2D electron gases (EGs) [13][14][15][16][17][18], ii) molecule-by-molecule assembly on metal surfaces by scanning probe methods [19], iii) trapping ultracold fermionic and bosonic atoms in honeycomb optical lattices [20][21][22], and iv) confining photons in honeycomb photonic crystals [23][24][25][26]. Figure 1 summarizes these four different approaches and the relevant tunable parameters.…”

Section: Introductionmentioning

confidence: 99%

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Artificial honeycomb lattices for electrons, atoms and photons

et al. 2013

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Artificial honeycomb lattices offer a tunable platform to study massless Dirac quasiparticles and their topological and correlated phases. Here we review recent progress in the design and fabrication of such synthetic structures focusing on nanopatterning of two-dimensional electron gases in semiconductors, molecule-by-molecule assembly by scanning probe methods, and optical trapping of ultracold atoms in crystals of light. We also discuss photonic crystals with Dirac cone dispersion and topologically protected edge states. We emphasize how the interplay between single-particle band structure engineering and cooperative effects leads to spectacular manifestations in tunneling and optical spectroscopies.

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“…In such crystals, the unusual transmission properties near a Dirac point [23][24][25] were predicted and observed experimentally.…”

Section: Confining Photonsmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Artificial honeycomb lattices for electrons, atoms and photons

et al. 2013

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“…By performing an experiment with samples with ideal edges of a well-defined configuration we were able to observe an oscillation with sample thickness related to the excitation of different K valleys; an effect that has not been observed for electrons in graphene. This holds promise for other experiments that probe the intriguing properties of these two-dimensional materials, such as the detection of the pseudospin 1 2 -Berry phase in a photonic crystal [17] or a valley-polarized beam splitter [12]. In the latter case, the photonic version of graphene holds promise to observe an effect which may not be possible in an electronic structure.…”

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confidence: 95%

Experimental Observation of Strong Edge Effects on the Pseudodiffusive Transport of Light in Photonic Graphene

2010

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Photonic graphene is a two-dimensional photonic crystal structure that is analogous to graphene. We use 5 mm diameter Al 2 O 3 rods placed on a triangular lattice with a lattice constant a ¼ 8 mm to create an isolated conical singularity in the photonic band structure at a microwave frequency of 17.6 GHz. At this frequency, the measured transmission of microwaves through a perfectly ordered structure enters a pseudodiffusive regime where the transmission scales inversely with the thickness L of the crystal (L=a * 5). The transmission depends critically on the configuration of the edges: distinct oscillations with an amplitude comparable to the transmission are observed for structures terminated with zigzag edges, while these oscillations are absent for samples with a straight edge configuration. DOI: 10.1103/PhysRevLett.104.043903 PACS numbers: 42.25.Gy, 42.25.Bs, 42.70.Qs The experimental realization of graphene [1], a single layer of carbon atoms arranged in a two-dimensional hexagonal structure, has attracted a lot of attention. The interest in this gapless semiconductor is due to the conical singularities in the electronic band structure [2] that create a linear dispersion for electrons, leading to interesting physical phenomena such as an anomalous quantum Hall effect and the absence of Anderson localization [3,4]. Since the dispersion around these points is linear, the motion of electrons resembles that of massless particles and can be described by the relativistic Dirac equation. These singularities have been aptly named ''Dirac points'' and are entirely due to the geometry of the underlying triangular lattice.As a consequence, similar conical singularities can be identified in the band structure of electromagnetic waves in two-dimensional photonic crystals with a triangular lattice [5][6][7], acoustic waves in a sonic crystal [8], and electrons in a two-dimensional electron gas [9]. Of these analogous systems, only the propagation of acoustic waves was studied experimentally, and an acoustic analogue to the Zitterbewegung of relativistic electrons was identified [8]. The analogy between graphene and these structures strengthens our understanding of the physics common to these two-dimensional structures. In particular, the analogy with optics has already inspired researchers to predict known optical effects, such as negative refraction [10] and a Goos-Hänchen shift for electrons in graphene [11].Despite the success of graphene, the observation of effects predicted by theory often require samples with perfect edges of a well-defined configuration that can only be obtained by atomic scale engineering. In this Letter, we experimentally investigate a photonic crystal structure for microwave frequencies that is analogous to graphene and realize samples with ideal edges on a much more accessible millimeter length scale. The transmission at the Dirac point of this perfectly ordered structure enters a pseudodiffusive transport regime and becomes inversely proportional to the thickness of the sample, as predic...

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“…Dirac cones are protected, in the whole 2D Brillouin zone, by PT symmetry, the product of time-reversal symmetry (T , in Box 2) and parity (P) inversion. Every Dirac cone has a quantized Berry phase (Box 1) of π looped around it [17,18]. Protected Dirac cones generate and annihilate in pairs [19][20][21][22][23].…”

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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Proposed method for detection of the pseudospin-12Berry phase in a photonic crystal with a Dirac spectrum

Cited by 56 publications

References 21 publications

Artificial honeycomb lattices for electrons, atoms and photons

Artificial honeycomb lattices for electrons, atoms and photons

Experimental Observation of Strong Edge Effects on the Pseudodiffusive Transport of Light in Photonic Graphene

Topological photonics

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