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Relevant bibliographies by topics / Higher order topological insulators

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Academic literature on the topic 'Higher order topological insulators'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Higher order topological insulators"

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Schindler, Frank, Ashley M. Cook, Maia G. Vergniory, Zhijun Wang, Stuart S. P. Parkin, B. Andrei Bernevig, and Titus Neupert. "Higher-order topological insulators." Science Advances 4, no. 6 (June 2018): eaat0346. http://dx.doi.org/10.1126/sciadv.aat0346.

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Kirsch, Marco S., Yiqi Zhang, Mark Kremer, Lukas J. Maczewsky, Sergey K. Ivanov, Yaroslav V. Kartashov, Lluis Torner, Dieter Bauer, Alexander Szameit, and Matthias Heinrich. "Nonlinear second-order photonic topological insulators." Nature Physics 17, no. 9 (July 1, 2021): 995–1000. http://dx.doi.org/10.1038/s41567-021-01275-3.

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AbstractHigher-order topological insulators are a novel topological phase beyond the framework of conventional bulk–boundary correspondence1,2. In these peculiar systems, the topologically non-trivial boundary modes are characterized by a co-dimension of at least two3,4. Despite several promising preliminary considerations regarding the impact of nonlinearity in such systems5,6, the flourishing field of experimental higher-order topological insulator research has thus far been confined to the linear evolution of topological states. As such, the observation of the interplay between nonlinearity and the dynamics of higher-order topological phases in conservative systems remains elusive. Here we experimentally demonstrate nonlinear higher-order topological corner states. Our photonic platform enables us to observe nonlinear topological corner states as well as the formation of solitons in such topological structures. Our work paves the way towards the exploration of topological properties of matter in the nonlinear regime, and may herald a new class of compact devices that harnesses the intriguing features of topology in an on-demand fashion.

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Zhang, Baile. "Acoustic higher-order topological insulators." Journal of the Acoustical Society of America 146, no. 4 (October 2019): 2914. http://dx.doi.org/10.1121/1.5137110.

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Peterson, Christopher W., Tianhe Li, Wladimir A. Benalcazar, Taylor L. Hughes, and Gaurav Bahl. "A fractional corner anomaly reveals higher-order topology." Science 368, no. 6495 (June 4, 2020): 1114–18. http://dx.doi.org/10.1126/science.aba7604.

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Spectral measurements of boundary-localized topological modes are commonly used to identify topological insulators. For high-order insulators, these modes appear at boundaries of higher codimension, such as the corners of a two-dimensional material. Unfortunately, this spectroscopic approach is only viable if the energies of the topological modes lie within the bulk bandgap, which is not required for many topological crystalline insulators. The key topological feature in these insulators is instead fractional charge density arising from filled bulk bands, but measurements of such charge distributions have not been accessible to date. We experimentally measure boundary-localized fractional charge density in rotationally symmetric two-dimensional metamaterials and find one-fourth and one-third fractionalization. We then introduce a topological indicator that allows for the unambiguous identification of higher-order topology, even without in-gap states, and we demonstrate the associated higher-order bulk-boundary correspondence.

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Yan, Zhong-Bo. "Higher-order topological insulators and superconductors." Acta Physica Sinica 68, no. 22 (2019): 226101. http://dx.doi.org/10.7498/aps.68.20191101.

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Schindler, Frank. "Dirac equation perspective on higher-order topological insulators." Journal of Applied Physics 128, no. 22 (December 14, 2020): 221102. http://dx.doi.org/10.1063/5.0035850.

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Zhang, Yiqi, Y. V. Kartashov, L. Torner, Yongdong Li, and A. Ferrando. "Nonlinear higher-order polariton topological insulator." Optics Letters 45, no. 17 (August 19, 2020): 4710. http://dx.doi.org/10.1364/ol.396039.

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8

Chen, Kai, Matthew Weiner, Mengyao Li, Xiang Ni, Andrea Alù, and Alexander B. Khanikaev. "Nonlocal topological insulators: Deterministic aperiodic arrays supporting localized topological states protected by nonlocal symmetries." Proceedings of the National Academy of Sciences 118, no. 34 (August 19, 2021): e2100691118. http://dx.doi.org/10.1073/pnas.2100691118.

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The properties of topological systems are inherently tied to their dimensionality. Indeed, higher-dimensional periodic systems exhibit topological phases not shared by their lower-dimensional counterparts. On the other hand, aperiodic arrays in lower-dimensional systems (e.g., the Harper model) have been successfully employed to emulate higher-dimensional physics. This raises a general question on the possibility of extended topological classification in lower dimensions, and whether the topological invariants of higher-dimensional periodic systems may assume a different meaning in their lower-dimensional aperiodic counterparts. Here, we demonstrate that, indeed, for a topological system in higher dimensions one can construct a one-dimensional (1D) deterministic aperiodic counterpart which retains its spectrum and topological characteristics. We consider a four-dimensional (4D) quantized hexadecapole higher-order topological insulator (HOTI) which supports topological corner modes. We apply the Lanczos transformation and map it onto an equivalent deterministic aperiodic 1D array (DAA) emulating 4D HOTI in 1D. We observe topological zero-energy zero-dimensional (0D) states of the DAA—the direct counterparts of corner states in 4D HOTI and the hallmark of the multipole topological phase, which is meaningless in lower dimensions. To explain this paradox, we show that higher-dimension invariant, the multipole polarization, retains its quantization in the DAA, yet changes its meaning by becoming a nonlocal correlator in the 1D system. By introducing nonlocal topological phases of DAAs, our discovery opens a direction in topological physics. It also unveils opportunities to engineer topological states in aperiodic systems and paves the path to application of resonances associates with such states protected by nonlocal symmetries.

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Xue, Haoran, Yahui Yang, Fei Gao, Yidong Chong, and Baile Zhang. "Acoustic higher-order topological insulator on a kagome lattice." Nature Materials 18, no. 2 (December 31, 2018): 108–12. http://dx.doi.org/10.1038/s41563-018-0251-x.

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Huang, Huaqing, Jiahao Fan, Dexin Li, and Feng Liu. "Generic Orbital Design of Higher-Order Topological Quasicrystalline Insulators with Odd Five-Fold Rotation Symmetry." Nano Letters 21, no. 16 (August 5, 2021): 7056–62. http://dx.doi.org/10.1021/acs.nanolett.1c02661.

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Dissertations / Theses on the topic "Higher order topological insulators"

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Radha, Santosh Kumar. "Knitting quantum knots-Topological phase transitions in Two-Dimensional systems." Case Western Reserve University School of Graduate Studies / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=case1595870012750826.

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Mazumdar, Saikat. "Équations polyharmoniques sur les variétés et études asymptotiques dans une équation de Hardy-Sobolev." Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0047/document.

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Ce mémoire est divisé en deux parties : Partie 1 : Nous obtenons des résultats d'existence pour des problèmes au limite mettant en jeu des opérateurs polyharmoniques conformément invariants. Nous nous plaçons indifféremment dans le cas d'une variété riemannienne avec ou sans bord. En particulier, nous montrons que la meilleure constante de Sobolev sur les variétés est exactement la constante euclidienne. En conséquence, nous montrons l'existence d'une solution d'énergie minimale lorsque la fonctionnelle descend en-dessous d'un seuil quantifié. Puis nous montrons l'existence de solutions de haute énergie en utilisant la méthode topologique de Coron. Nous généralisons la décomposition des suites de Palais-Smale comme somme de bulles sur une variété avec ou sans bord : il s'agit d'un résultat dans l'esprit du célèbre théorème de Struwe en 1984. Nous obtenons aussi une version du lemme de compacité-concentration de Pierre-Louis Lions sur les variétés. Partie 2 : Dans cette partie, nous effectuons une analyse de blow-up pour une équation de Hardy-Sobolev à croissance critique et à singularité évanescente au bord. En supposant que l'équation limite n'admet pas de solution minimisante, nous étudions le comportement asymptotique d’une suite de solutions de l'équation perturbée. Ici, la perturbation est la singularité à l'origine. Dans un premier temps, nous obtenons un contrôle ponctuel optimal de la suite de solutions. Dans un second temps, nous obtenons des informations précises sur le point d'explosion en utilisant une identité de Pohozaev
This memoir can be divided into two parts: Part 1: In this part we obtain some existence results for conformally invariant polyharmonic boundary value problems on a compact Riemannian manifold with or without boundary. In particular we show that the best constant of the Sobolev embedding on manifolds is same as the euclidean one, and as a consequence prove the existence of minimum energy solutions when the energy functionnal goes below a quantified threshold. Next we show the existence of high energy solution using the topological method of Coron. We generalize the decomposition of Palais Smale sequences as a sum of bubble on manifolds with or without boundary, a result in the spirit of Struwe's celebrated 1984 result and also an extension of PL Lions concentration compactness result on manifolds. Part2: In this part we do a blow-up analysis of the nonlinear elliptic Hardy-Sobolev equation with critical growth and vanishing boundary singularity. We assume that our equation does not admit minimising solutions, and study the asymptotic behaviour of a sequence of solution to the perturbed equation. Here the perturbation is the singularity at the origin. First we obtain optimal pointwise controlon the sequence and then obtain more precise informations on the localization of the blow-up point using the Pohozaev identity

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Zhang, Shaofei. "Endogenous gypsy insulators mediate higher order chromatin organization and repress gene expression in Drosophila." 2011. http://trace.tennessee.edu/utk_graddiss/1150.

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Chromatin insulators play a role in gene transcription regulation by defining chromatinboundaries. Genome-wide studies in Drosophila have shown that a large proportion of insulator sites are found in intergenic DNA sequences, supporting a role for these elements as boundaries. However, approximately 40% of insulator sites are also found in intragenic sequences, where they can potentially perform as yet unidentified functions. Here we show that multiple Su(Hw) insulator sites map within the 110 kb sequence of the muscleblind gene (mbl), which also forms a highly condensed chromatin structure in polytene chromosomes. Chromosome Conformation Capture assays indicate that Su(Hw) insulators mediate the organization of higher-order chromatin structures at the mbl locus, resulting in a barrier for the progression of RNA polymeraseII (PolII ), and producing a repressive effect on basal and active transcription. The interference of intragenic insulators in PolII progression suggests a role for insulators in the elongation process. Supporting this interpretation, we found that mutations in su(Hw) and mod(mdg4) also result in changes in the relative abundance of the mblD isoform, by promoting early transcription termination. These results provide experimental evidence for a new role ofintragenic Su(Hw) insulators in higher-order chromatin organization, repression of transcription, and RNA processing.

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Books on the topic "Higher order topological insulators"

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Alestalo, Pekka. Uniform domains of higher order. Helsinki: Suomalainen Tiedeakatemia, 1994.

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2

Denzler, Jochen. Higher-order time asymptotics of fast diffusion in Euclidean space: A dynamical systems methods. Providence, Rhode Island: American Mathematical Society, 2014.

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3

Murakami, S., and T. Yokoyama. Quantum spin Hall effect and topological insulators. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198787075.003.0017.

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This chapter begins with a description of quantum spin Hall systems, or topological insulators, which embody a new quantum state of matter theoretically proposed in 2005 and experimentally observed later on using various methods. Topological insulators can be realized in both two dimensions (2D) and in three dimensions (3D), and are nonmagnetic insulators in the bulk that possess gapless edge states (2D) or surface states (3D). These edge/surface states carry pure spin current and are sometimes called helical. The novel property for these edge/surface states is that they originate from bulk topological order, and are robust against nonmagnetic disorder. The following sections then explain how topological insulators are related to other spin-transport phenomena.

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Book chapters on the topic "Higher order topological insulators"

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Bakker, J. W., and F. Breugel. "Topological models for higher order control flow." In Lecture Notes in Computer Science, 122–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-58027-1_6.

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Berger, Mitchell A. "Topological Quantities: Calculating Winding, Writhing, Linking, and Higher Order Invariants." In Lecture Notes in Mathematics, 75–97. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00837-5_2.

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"13. Quantum Hall Effect and Chern Insulators in Higher Dimensions." In Topological Insulators and Topological Superconductors, 164–76. Princeton: Princeton University Press, 2013. http://dx.doi.org/10.1515/9781400846733-013.

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4

"TOPOLOGICAL METHODS." In Boundary Value Problems from Higher Order Differential Equations, 235–42. WORLD SCIENTIFIC, 1986. http://dx.doi.org/10.1142/9789814415477_0019.

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Nguyen, Dong Quan Ngoc, Lin Xing, and Lizhen Lin. "Community Detection, Pattern Recognition, and Hypergraph-Based Learning: Approaches Using Metric Geometry and Persistent Homology." In Fuzzy Systems and Data Mining VI. IOS Press, 2020. http://dx.doi.org/10.3233/faia200724.

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Hypergraph data appear and are hidden in many places in the modern age. They are data structure that can be used to model many real data examples since their structures contain information about higher order relations among data points. One of the main contributions of our paper is to introduce a new topological structure to hypergraph data which bears a resemblance to a usual metric space structure. Using this new topological space structure of hypergraph data, we propose several approaches to study community detection problem, detecting persistent features arising from homological structure of hypergraph data. Also based on the topological space structure of hypergraph data introduced in our paper, we introduce a modified nearest neighbors methods which is a generalization of the classical nearest neighbors methods from machine learning. Our modified nearest neighbors methods have an advantage of being very flexible and applicable even for discrete structures as in hypergraphs. We then apply our modified nearest neighbors methods to study sign prediction problem in hypegraph data constructed using our method.

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Conference papers on the topic "Higher order topological insulators"

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Safaei, Alireza, Nayan E. Myerson-Jain, Md Farhadul Haque, Taylor L. Hughes, and Gaurav Bahl. "Higher-Order Topological Insulators in Nanophotonic Smart-Patterns." In Frontiers in Optics. Washington, D.C.: OSA, 2020. http://dx.doi.org/10.1364/fio.2020.fth5c.8.

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Bisharat, Dia'aaldin J., and Dan Sievenpiper. "Higher-order photonic topological insulator metasurfaces." In Photonic and Phononic Properties of Engineered Nanostructures X, edited by Ali Adibi, Shawn-Yu Lin, and Axel Scherer. SPIE, 2020. http://dx.doi.org/10.1117/12.2547285.

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Yan, Wenchao, Shiqi Xia, Xiuying Liu, Yuqing Xie, Liqin Tang, Daohong Song, Jingjun Xu, and Zhigang Chen. "Demonstration of corner states in photonic square-root higher-order topological insulators." In CLEO: Applications and Technology. Washington, D.C.: OSA, 2021. http://dx.doi.org/10.1364/cleo_at.2021.jtu3a.38.

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Gladstone, Ran Gladstein, Minwoo Jung, and Gennady Shvets. "Spinful Photonic Higher Order Topological Insulators in the Presence of Spin Orbit Coupling." In CLEO: QELS_Fundamental Science. Washington, D.C.: OSA, 2021. http://dx.doi.org/10.1364/cleo_qels.2021.ftu1m.6.

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Kirsch, M. S., Y. Zhang, L. J. Maczewsky, S. K. Ivanov, Y. V. Kartashov, L. Torner, D. Bauer, A. Szameit, and M. Heinrich. "Observation of nonlinear corner states in a higher-order photonic topological insulator." In CLEO: QELS_Fundamental Science. Washington, D.C.: OSA, 2021. http://dx.doi.org/10.1364/cleo_qels.2021.fth4h.2.

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Shvets, Gennady B. "Higher-order topological photonics across temporal and spatial scales." In Active Photonic Platforms XIII, edited by Ganapathi S. Subramania and Stavroula Foteinopoulou. SPIE, 2021. http://dx.doi.org/10.1117/12.2595189.

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Vakulenko, Anton, Svetlana Kiriushechkina, Mingsong Wang, Mengyao Li, Dmitriy Zhirihin, Xiang Ni, Sriram Guddala, Dmitriy Korobkin, Andrea Alù, and Alexander B. Khanikaev. "Visualization of topological transitions and imaging of higher-order topological states in photonic metasurfaces." In Active Photonic Platforms XII, edited by Ganapathi S. Subramania and Stavroula Foteinopoulou. SPIE, 2020. http://dx.doi.org/10.1117/12.2569324.

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Vakulenko, A., S. Kiriushechkina, M. Li, D. Zhirihin, X. Ni, S. Guddala, D. Korobkin, A. Alu, and A. B. Khanikaev. "Experimental demonstration of higher-order topological states in photonic metasurfaces." In CLEO: Applications and Technology. Washington, D.C.: OSA, 2020. http://dx.doi.org/10.1364/cleo_at.2020.jm3a.3.

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Li, Mengyao, Dmitry Zhirihin, Maxim Gorlach, Xiang Ni, Dmitry Filonov, Alexey Slobozhanyuk, Andrea Alù, and Alexander B. Khanikaev. "Photonic higher-order topological states induced by long-range interactions." In Metamaterials, Metadevices, and Metasystems 2020, edited by Nader Engheta, Mikhail A. Noginov, and Nikolay I. Zheludev. SPIE, 2020. http://dx.doi.org/10.1117/12.2569326.

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Ning, Xin, Weijun Li, Weijuan Tian, and Yueyue Lu. "Topological Higher-Order Neuron Model Based on Homology-Continuity Principle." In 2019 2nd China Symposium on Cognitive Computing and Hybrid Intelligence (CCHI). IEEE, 2019. http://dx.doi.org/10.1109/cchi.2019.8901920.

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