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Journal articles on the topic 'Higher order topological insulators'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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9

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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10

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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11

Schindler, Frank. "Erratum: “Dirac equation perspective on higher-order topological insulators” [J. Appl. Phys. 128, 221102 (2020)]." Journal of Applied Physics 129, no. 4 (January 28, 2021): 049901. http://dx.doi.org/10.1063/5.0042685.

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12

Zhang, Zhiwang, Ying Cheng, and Xiaojun Liu. "Subwavelength higher-order topological insulator based on stereo acoustic networks." Journal of Applied Physics 129, no. 13 (April 7, 2021): 135101. http://dx.doi.org/10.1063/5.0041928.

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13

Nayak, Abhay Kumar, Jonathan Reiner, Raquel Queiroz, Huixia Fu, Chandra Shekhar, Binghai Yan, Claudia Felser, Nurit Avraham, and Haim Beidenkopf. "Resolving the topological classification of bismuth with topological defects." Science Advances 5, no. 11 (November 2019): eaax6996. http://dx.doi.org/10.1126/sciadv.aax6996.

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The growing diversity of topological classes leads to ambiguity between classes that share similar boundary phenomenology. This is the status of bulk bismuth. Recent studies have classified it as either a strong or a higher-order topological insulator, both of which host helical modes on their boundaries. We resolve the topological classification of bismuth by spectroscopically mapping the response of its boundary modes to a screw-dislocation. We find that the one-dimensional mode, on step-edges, extends over a wide energy range and does not open a gap near the screw-dislocations. This signifies that this mode binds to the screw-dislocation, as expected for a material with nonzero weak indices. We argue that the small energy gap, at the time reversal invariant momentum L, positions bismuth within the critical region of a topological phase transition between a higher-order topological insulator and a strong topological insulator with nonzero weak indices.

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14

Kempkes, S. N., M. R. Slot, J. J. van den Broeke, P. Capiod, W. A. Benalcazar, D. Vanmaekelbergh, D. Bercioux, I. Swart, and C. Morais Smith. "Robust zero-energy modes in an electronic higher-order topological insulator." Nature Materials 18, no. 12 (September 23, 2019): 1292–97. http://dx.doi.org/10.1038/s41563-019-0483-4.

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15

Wang, Zhen, and Qi Wei. "An elastic higher-order topological insulator based on kagome phononic crystals." Journal of Applied Physics 129, no. 3 (January 21, 2021): 035102. http://dx.doi.org/10.1063/5.0031377.

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16

Hsu, Chuang-Han, Xiaoting Zhou, Tay-Rong Chang, Qiong Ma, Nuh Gedik, Arun Bansil, Su-Yang Xu, Hsin Lin, and Liang Fu. "Topology on a new facet of bismuth." Proceedings of the National Academy of Sciences 116, no. 27 (June 13, 2019): 13255–59. http://dx.doi.org/10.1073/pnas.1900527116.

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Bismuth-based materials have been instrumental in the development of topological physics, even though bulk bismuth itself has been long thought to be topologically trivial. A recent study has, however, shown that bismuth is in fact a higher-order topological insulator featuring one-dimensional (1D) topological hinge states protected by threefold rotational and inversion symmetries. In this paper, we uncover another hidden facet of the band topology of bismuth by showing that bismuth is also a first-order topological crystalline insulator protected by a twofold rotational symmetry. As a result, its (11¯0) surface exhibits a pair of gapless Dirac surface states. Remarkably, these surface Dirac cones are “unpinned” in the sense that they are not restricted to locate at specific k points in the (11¯0) surface Brillouin zone. These unpinned 2D Dirac surface states could be probed directly via various spectroscopic techniques. Our analysis also reveals the presence of a distinct, previously uncharacterized set of 1D topological hinge states protected by the twofold rotational symmetry. Our study thus provides a comprehensive understanding of the topological band structure of bismuth.

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17

Song, Lingling, Huanhuan Yang, Yunshan Cao, and Peng Yan. "Realization of the Square-Root Higher-Order Topological Insulator in Electric Circuits." Nano Letters 20, no. 10 (September 17, 2020): 7566–71. http://dx.doi.org/10.1021/acs.nanolett.0c03049.

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18

Meng, Fei, Yafeng Chen, Weibai Li, Baohua Jia, and Xiaodong Huang. "Realization of multidimensional sound propagation in 3D acoustic higher-order topological insulator." Applied Physics Letters 117, no. 15 (October 12, 2020): 151903. http://dx.doi.org/10.1063/5.0023033.

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19

Wang, Zhen, Qi Wei, Heng-Yi Xu, and Da-Jian Wu. "A higher-order topological insulator with wide bandgaps in Lamb-wave systems." Journal of Applied Physics 127, no. 7 (February 21, 2020): 075105. http://dx.doi.org/10.1063/1.5140553.

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20

Arai, Nobuhiro, and Shuichi Murakami. "Anisotropic Penetration Depths of Corner States in a Higher-Order Topological Insulator." Journal of the Physical Society of Japan 90, no. 7 (July 15, 2021): 074711. http://dx.doi.org/10.7566/jpsj.90.074711.

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21

Khokhriakov, Dmitrii, Aron W. Cummings, Kenan Song, Marc Vila, Bogdan Karpiak, André Dankert, Stephan Roche, and Saroj P. Dash. "Tailoring emergent spin phenomena in Dirac material heterostructures." Science Advances 4, no. 9 (September 2018): eaat9349. http://dx.doi.org/10.1126/sciadv.aat9349.

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Dirac materials such as graphene and topological insulators (TIs) are known to have unique electronic and spintronic properties. We combine graphene with TIs in van der Waals heterostructures to demonstrate the emergence of a strong proximity-induced spin-orbit coupling in graphene. By performing spin transport and precession measurements supported by ab initio simulations, we discover a strong tunability and suppression of the spin signal and spin lifetime due to the hybridization of graphene and TI electronic bands. The enhanced spin-orbit coupling strength is estimated to be nearly an order of magnitude higher than in pristine graphene. These findings in graphene-TI heterostructures could open interesting opportunities for exploring exotic physical phenomena and new device functionalities governed by topological proximity effects.

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22

Melnikova, L. S., M. V. Kostyuchenko, V. V. Molodina, P. G. Georgiev, and A. K. Golovnin. "Functional properties of the Su(Hw) complex are determined by its regulatory environment and multiple interactions on the Su(Hw) protein platform." Vavilov Journal of Genetics and Breeding 23, no. 2 (March 30, 2019): 168–73. http://dx.doi.org/10.18699/vj19.477.

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The Su(Hw) protein was first identified as a DNA-binding component of an insulator complex in Drosophila. Insulators are regulatory elements that can block the enhancer-promoter communication and exhibit boundary activity. Some insulator complexes contribute to the higher-order organization of chromatin in topologically associated domains that are fundamental elements of the eukaryotic genomic structure. The Su(Hw)-dependent protein complex is a unique model for studying the insulator, since its basic structural components affecting its activity are already known. However, the mechanisms involving this complex in various regulatory processes and the precise interaction between the components of the Su(Hw) insulators remain poorly understood. Our recent studies reveal the fine mechanism of formation and function of the Su(Hw) insulator. Our results provide, for the first time, an example of a high complexity of interactions between the insulator proteins that are required to form the (Su(Hw)/Mod(mdg4)-67.2/CP190) complex. All interactions between the proteins are to a greater or lesser extent redundant, which increases the reliability of the complex formation. We conclude that both association with CP190 and Mod(mdg4)-67.2 partners and the proper organization of the DNA binding site are essential for the efficient recruitment of the Su(Hw) complex to chromatin insulators. In this review, we demonstrate the role of multiple interactions between the major components of the Su(Hw) insulator complex (Su(Hw)/Mod(mdg4)-67.2/CP190) in its activity. It was shown that Su(Hw) may regulate the enhancer–promoter communication via the newly described insulator neutralization mechanism. Moreover, Su(Hw) participates in direct regulation of activity of vicinity promoters. Finally, we demonstrate the mechanism of organization of “insulator bodies” and suggest a model describing their role in proper binding of the Su(Hw) complex to chromatin.

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23

Su, Zixian, Yanzhuo Kang, Bofeng Zhang, Zhiqiang Zhang, and Hua Jiang. "Disorder induced phase transition in magnetic higher-order topological insulator: A machine learning study." Chinese Physics B 28, no. 11 (October 2019): 117301. http://dx.doi.org/10.1088/1674-1056/ab4582.

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24

Bhat, Ruchira V., and Soumya Bera. "Out of equilibrium chiral higher order topological insulator on a π -flux square lattice." Journal of Physics: Condensed Matter 33, no. 16 (April 20, 2021): 164005. http://dx.doi.org/10.1088/1361-648x/abf0c3.

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25

Martín-Ruiz, A., M. Cambiaso, and L. F. Urrutia. "The magnetoelectric coupling in electrodynamics." International Journal of Modern Physics A 34, no. 28 (October 10, 2019): 1941002. http://dx.doi.org/10.1142/s0217751x19410021.

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We explore a model akin to axion electrodynamics in which the axion field [Formula: see text] rather than being dynamical is a piecewise constant effective parameter [Formula: see text] encoding the microscopic properties of the medium inasmuch as its permittivity or permeability, defining what we call a [Formula: see text]-medium. This model describes a large class of phenomena, among which we highlight the electromagnetic response of materials with topological order, like topological insulators for example. We pursue a Green’s function formulation of what amounts to typical boundary-value problems of [Formula: see text]-media, when external sources or boundary conditions are given. As an illustration of our methods, which we have also extended to ponderable media, we interpret the constant [Formula: see text] as a novel topological property of vacuum, a so called [Formula: see text]-vacuum, and restrict our discussion to the cases where the permittivity and the permeability of the media is one. In this way we concentrate upon the effects of the additional [Formula: see text] coupling which induce remarkable magnetoelectric effects. The issue of boundary conditions for electromagnetic radiation is crucial for the occurrence of the Casimir effect, therefore we apply the methods described above as an alternative way to approach the modifications to the Casimir effect by the inclusion of topological insulators.

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26

Li, Zhixiong, Yunshan Cao, Peng Yan, and Xiangrong Wang. "Higher-order topological solitonic insulators." npj Computational Materials 5, no. 1 (November 12, 2019). http://dx.doi.org/10.1038/s41524-019-0246-4.

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Abstract Pursuing topological phase and matter in a variety of systems is one central issue in current physical sciences and engineering. Motivated by the recent experimental observation of corner states in acoustic and photonic structures, we theoretically study the dipolar-coupled gyration motion of magnetic solitons on the two-dimensional breathing kagome lattice. We calculate the phase diagram and predict both the Tamm–Shockley edge modes and the second-order corner states when the ratio between alternate lattice constants is greater than a critical value. We show that the emerging corner states are topologically robust against both structure defects and moderate disorders. Micromagnetic simulations are implemented to verify the theoretical predictions with an excellent agreement. Our results pave the way for investigating higher-order topological insulators based on magnetic solitons.

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27

Kudo, Koji, Tsuneya Yoshida, and Yasuhiro Hatsugai. "Higher-Order Topological Mott Insulators." Physical Review Letters 123, no. 19 (November 7, 2019). http://dx.doi.org/10.1103/physrevlett.123.196402.

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28

Yang, Yan-Bin, Kai Li, L. M. Duan, and Yong Xu. "Higher-order topological Anderson insulators." Physical Review B 103, no. 8 (February 4, 2021). http://dx.doi.org/10.1103/physrevb.103.085408.

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29

Matsugatani, Akishi, and Haruki Watanabe. "Connecting higher-order topological insulators to lower-dimensional topological insulators." Physical Review B 98, no. 20 (November 16, 2018). http://dx.doi.org/10.1103/physrevb.98.205129.

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30

Wang, Yao, Bi-Ye Xie, Yong-Heng Lu, Yi-Jun Chang, Hong-Fei Wang, Jun Gao, Zhi-Qiang Jiao, et al. "Quantum superposition demonstrated higher-order topological bound states in the continuum." Light: Science & Applications 10, no. 1 (August 30, 2021). http://dx.doi.org/10.1038/s41377-021-00612-8.

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AbstractHigher-order topological insulators, as newly found non-trivial materials and structures, possess topological phases beyond the conventional bulk-boundary correspondence. In previous studies, in-gap boundary states such as the corner states were regarded as conclusive evidence for the emergence of higher-order topological insulators. Here, we present an experimental observation of a photonic higher-order topological insulator with corner states embedded into the bulk spectrum, denoted as the higher-order topological bound states in the continuum. Especially, we propose and experimentally demonstrate a new way to identify topological corner states by exciting them separately from the bulk states with photonic quantum superposition states. Our results extend the topological bound states in the continuum into higher-order cases, providing an unprecedented mechanism to achieve robust and localized states in a bulk spectrum. More importantly, our experiments exhibit the advantage of using the time evolution of quantum superposition states to identify topological corner modes, which may shed light on future exploration between quantum dynamics and higher-order topological photonics.

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31

Fang, Yuan, and Jennifer Cano. "Higher-order topological insulators in antiperovskites." Physical Review B 101, no. 24 (June 1, 2020). http://dx.doi.org/10.1103/physrevb.101.245110.

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32

Chen, Rui, Chui-Zhen Chen, Jin-Hua Gao, Bin Zhou, and Dong-Hui Xu. "Higher-Order Topological Insulators in Quasicrystals." Physical Review Letters 124, no. 3 (January 22, 2020). http://dx.doi.org/10.1103/physrevlett.124.036803.

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33

Huang, Huaqing, and Feng Liu. "Structural buckling induced higher-order topology." National Science Review, September 9, 2021. http://dx.doi.org/10.1093/nsr/nwab170.

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ABSTRACT The higher-order topological insulator (HOTI) states, such as two-dimension (2D) HOTI featured with topologically protected corner modes at the intersection of two gapped crystalline boundaries, have attracted much recent interest. However, physical mechanism underlying the formation of HOTI states is not fully understood, which has hindered our fundamental understanding and discovery of HOTI materials. Here we propose a mechanistic approach to induce higher-order topological phases via structural buckling of 2D topological crystalline insulators (TCIs). While in-plane mirror symmetry is broken by structural buckling, which destroys the TCI state, the combination of mirror and rotation symmetry preserves in the buckled system, which gives rise to the HOTI state. We demonstrate that this approach is generally applicable to various 2D lattices with different symmetries and buckling patterns, opening a horizon of possible materials to realize 2D HOTIs. The HOTIs so generated are also shown to be robust against buckling height fluctuation and in-plane displacement. A concrete example is given for the buckled $\beta $-Sb monolayer from first-principles calculations. Our finding not only enriches our fundamental understanding of higher-order topology, but also opens a new route to discovering HOTI materials.

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34

Di Liberto, M., N. Goldman, and G. Palumbo. "Non-Abelian Bloch oscillations in higher-order topological insulators." Nature Communications 11, no. 1 (November 23, 2020). http://dx.doi.org/10.1038/s41467-020-19518-x.

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AbstractBloch oscillations (BOs) are a fundamental phenomenon by which a wave packet undergoes a periodic motion in a lattice when subjected to a force. Observed in a wide range of synthetic systems, BOs are intrinsically related to geometric and topological properties of the underlying band structure. This has established BOs as a prominent tool for the detection of Berry-phase effects, including those described by non-Abelian gauge fields. In this work, we unveil a unique topological effect that manifests in the BOs of higher-order topological insulators through the interplay of non-Abelian Berry curvature and quantized Wilson loops. It is characterized by an oscillating Hall drift synchronized with a topologically-protected inter-band beating and a multiplied Bloch period. We elucidate that the origin of this synchronization mechanism relies on the periodic quantum dynamics of Wannier centers. Our work paves the way to the experimental detection of non-Abelian topological properties through the measurement of Berry phases and center-of-mass displacements.

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35

Lin, Kuan-Sen, and Barry Bradlyn. "Simulating higher-order topological insulators in density wave insulators." Physical Review B 103, no. 24 (June 2, 2021). http://dx.doi.org/10.1103/physrevb.103.245107.

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36

Costa, Marcio, Gabriel R. Schleder, Carlos Mera Acosta, Antonio C. M. Padilha, Frank Cerasoli, Marco Buongiorno Nardelli, and Adalberto Fazzio. "Discovery of higher-order topological insulators using the spin Hall conductivity as a topology signature." npj Computational Materials 7, no. 1 (April 12, 2021). http://dx.doi.org/10.1038/s41524-021-00518-4.

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AbstractThe discovery and realization of topological insulators, a phase of matter which hosts metallic boundary states when the d-dimension insulating bulk is confined to (d − 1)-dimensions, led to several potential applications. Recently, it was shown that protected topological states can manifest in (d − 2)-dimensions, such as hinge and corner states for three- and two-dimensional systems, respectively. These nontrivial materials are named higher-order topological insulators (HOTIs). Here we show a connection between spin Hall effect and HOTIs using a combination of ab initio calculations and tight-binding modeling. The model demonstrates how a non-zero bulk midgap spin Hall conductivity (SHC) emerges within the HOTI phase. Following this, we performed high-throughput density functional theory calculations to find unknown HOTIs, using the SHC as a criterion. We calculated the SHC of 693 insulators resulting in seven stable two-dimensional HOTIs. Our work guides novel experimental and theoretical advances towards higher-order topological insulator realization and applications.

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37

Dutt, Avik, Momchil Minkov, Ian A. D. Williamson, and Shanhui Fan. "Higher-order topological insulators in synthetic dimensions." Light: Science & Applications 9, no. 1 (July 20, 2020). http://dx.doi.org/10.1038/s41377-020-0334-8.

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38

Agarwala, Adhip, Vladimir Juričić, and Bitan Roy. "Higher-order topological insulators in amorphous solids." Physical Review Research 2, no. 1 (March 17, 2020). http://dx.doi.org/10.1103/physrevresearch.2.012067.

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39

Li, Heqiu, and Kai Sun. "Pfaffian Formalism for Higher-Order Topological Insulators." Physical Review Letters 124, no. 3 (January 22, 2020). http://dx.doi.org/10.1103/physrevlett.124.036401.

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40

Li, Heqiu, and Kai Sun. "Topological insulators and higher-order topological insulators from gauge-invariant one-dimensional lines." Physical Review B 102, no. 8 (August 4, 2020). http://dx.doi.org/10.1103/physrevb.102.085108.

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41

Hsu, Chen-Hsuan, Peter Stano, Jelena Klinovaja, and Daniel Loss. "Majorana Kramers Pairs in Higher-Order Topological Insulators." Physical Review Letters 121, no. 19 (November 6, 2018). http://dx.doi.org/10.1103/physrevlett.121.196801.

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42

Otaki, Yuria, and Takahiro Fukui. "Higher-order topological insulators in a magnetic field." Physical Review B 100, no. 24 (December 5, 2019). http://dx.doi.org/10.1103/physrevb.100.245108.

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43

Chen, Yafeng, Fei Meng, Yuri Kivshar, Baohua Jia, and Xiaodong Huang. "Inverse design of higher-order photonic topological insulators." Physical Review Research 2, no. 2 (May 1, 2020). http://dx.doi.org/10.1103/physrevresearch.2.023115.

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44

Queiroz, Raquel, Ion Cosma Fulga, Nurit Avraham, Haim Beidenkopf, and Jennifer Cano. "Partial Lattice Defects in Higher-Order Topological Insulators." Physical Review Letters 123, no. 26 (December 27, 2019). http://dx.doi.org/10.1103/physrevlett.123.266802.

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45

Hu, Haiping, Biao Huang, Erhai Zhao, and W. Vincent Liu. "Dynamical Singularities of Floquet Higher-Order Topological Insulators." Physical Review Letters 124, no. 5 (February 3, 2020). http://dx.doi.org/10.1103/physrevlett.124.057001.

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46

Zhang, Weixuan, Deyuan Zou, Qingsong Pei, Wenjing He, Jiacheng Bao, Houjun Sun, and Xiangdong Zhang. "Experimental Observation of Higher-Order Topological Anderson Insulators." Physical Review Letters 126, no. 14 (April 6, 2021). http://dx.doi.org/10.1103/physrevlett.126.146802.

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47

You, Yizhi, F. J. Burnell, and Taylor L. Hughes. "Multipolar topological field theories: Bridging higher order topological insulators and fractons." Physical Review B 103, no. 24 (June 16, 2021). http://dx.doi.org/10.1103/physrevb.103.245128.

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48

Queiroz, Raquel, and Ady Stern. "Splitting the Hinge Mode of Higher-Order Topological Insulators." Physical Review Letters 123, no. 3 (July 16, 2019). http://dx.doi.org/10.1103/physrevlett.123.036802.

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Zou, Jinyu, Zhuoran He, and Gang Xu. "Higher-order topological insulators in a crisscross antiferromagnetic model." Physical Review B 100, no. 23 (December 23, 2019). http://dx.doi.org/10.1103/physrevb.100.235137.

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Huang, Biao, and W. Vincent Liu. "Floquet Higher-Order Topological Insulators with Anomalous Dynamical Polarization." Physical Review Letters 124, no. 21 (May 28, 2020). http://dx.doi.org/10.1103/physrevlett.124.216601.

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