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Register a new userSurface density-of-states on semi-infinite topological photonic and acoustic crystals
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Iterative Greens function, based on cyclic reduction of block tridiagonal matrices, has been the ideal algorithm, through tight-binding models, to compute the surface density-of-states of semi-infinite topological electronic materials. In this paper, we apply this method to photonic and acoustic crystals, using finite-element discretizations and a generalized eigenvalue formulation, to calculate the local density-of-states on a single surface of semi-infinite lattices. The three-dimensional (3D) examples of gapless helicoidal surface states in Weyl and Dirac crystals are shown and the computational cost, convergence and accuracy are analyzed.
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Photonic topological states have revolutionized our understanding on the propagation and scattering of light. Recent discovery of higher-order photonic topological insulators opens an emergent horizon for zero-dimensional topological corner states. However, the previous realizations of higher-order photonic topological insulators suffer from either a limited operational frequency range due to the lumped components involved or a bulky structure with a large footprint, which are unfavorable for future integrated photonics. To overcome these limitations, we hereby experimentally demonstrate a planar surface-wave photonic crystal realization of two-dimensional higher-order topological insulators. The surface-wave photonic crystals exhibit a very large bulk bandgap (a bandwidth of 28%) due to multiple Bragg scatterings and host one-dimensional gapped edge states described by massive Dirac equations. The topology of those higher-dimensional photonic bands leads to the emergence of zero-dimensional corner states, which provide a route toward robust cavity modes for scalable, integrated photonic chips and an interface for the control of light-matter interaction.
Topological states in photonics offer novel prospects for guiding and manipulating photons and facilitate the development of modern optical components for a variety of applications. Over the past few years, photonic topology physics has evolved and unveiled various unconventional optical properties in these topological materials, such as silicon photonic crystals. However, the design of such topological states still poses a significant challenge. Conventional optimization schemes often fail to capture their complex high dimensional design space. In this manuscript, we develop a deep learning framework to map the design space of topological states in the photonic crystals. This framework overcomes the limitations of existing deep learning implementations. Specifically, it reconciles the dimension mismatch between the input (topological properties) and output (design parameters) vector spaces and the non-uniqueness that arises from one-to-many function mappings. We use a fully connected deep neural network (DNN) architecture for the forward model and a cyclic convolutional neural network (cCNN)for the inverse model. The inverse architecture contains the pre-trained forward model in tandem, thereby reducing the prediction error significantly.
Topological manipulation of waves is at the heart of the cutting-edge metamaterial researches. Quadrupole topological insulators were recently discovered in two-dimensional (2D) flux-threading lattices which exhibit higher-order topological wave trapping at both the edges and corners. Photonic crystals (PhCs), lying at the boundary between continuous media and discrete lattices, however, are incompatible with the present quadrupole topological theory. Here, we unveil quadrupole topological PhCs triggered by a twisting degree-of-freedom. Using a topologically trivial PhC as the motherboard, we show that twisting induces quadrupole topological PhCs without flux-threading. The twisting-induced crystalline symmetry enriches the Wannier polarizations and lead to the anomalous quadrupole topology. Versatile edge and corner phenomena are observed by controlling the twisting angles in a lateral heterostructure of 2D PhCs. Our study paves the way toward topological twist-photonics as well as the quadrupole topology in the quasi-continuum regime for phonons and polaritons.
Bi2Te3 is a member of a new class of materials known as topological insulators which are supposed to be insulating in the bulk and conducting on the surface. However experimental verification of the surface states has been difficult in electrical transport measurements due to a conducting bulk. We report low temperature magnetotransport measurements on single crystal samples of Bi2Te3. We observe metallic character in our samples and large and linear magnetoresistance from 1.5 K to 290 K with prominent Shubnikov-de Haas (SdH) oscillations whose traces persist upto 20 K. Even though our samples are metallic we are able to obtain a Berry phase close to the value of {pi} expected for Dirac fermions of the topological surface states. This indicates that we might have obtained evidence for the topological surface states in metallic single crystals of Bi2Te3. Other physical quantities obtained from the analysis of the SdH oscillations are also in close agreement with those reported for the topological surface states. The linear magnetoresistance observed in our sample, which is considered as a signature of the Dirac fermions of the surface states, lends further credence to the existence of topological surface states.
Gapless surface states on topological insulators are protected from elastic scattering on non-magnetic impurities which makes them promising candidates for low-power electronic applications. However, for wide-spread applications, these states should remain coherent and significantly spin polarized at ambient temperatures. Here, we studied the coherence and spin-structure of the topological states on the surface of a model topological insulator, Bi2Se3, at elevated temperatures in spin and angle-resolved photoemission spectroscopy. We found an extremely weak broadening and essentially no decay of spin polarization of the topological surface state up to room temperature. Our results demonstrate that the topological states on surfaces of topological insulators could serve as a basis for room temperature electronic devices.
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