Статті в журналах: "Topological physics"

1

Ota, Yasutomo, Kenta Takata, Tomoki Ozawa, Alberto Amo, Zhetao Jia, Boubacar Kante, Masaya Notomi, Yasuhiko Arakawa, and Satoshi Iwamoto. "Active topological photonics." Nanophotonics 9, no. 3 (January 28, 2020): 547–67. http://dx.doi.org/10.1515/nanoph-2019-0376.

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AbstractTopological photonics emerged as a novel route to engineer the flow of light. Topologically protected photonic edge modes, which are supported at the perimeters of topologically nontrivial insulating bulk structures, are of particular interest as they may enable low-loss optical waveguides immune to structural disorder. Very recently, there has been a sharp rise of interest in introducing gain materials into such topological photonic structures, primarily aiming at revolutionizing semiconductor lasers with the aid of physical mechanisms existing in topological physics. Examples of remarkable realizations are topological lasers with unidirectional light output under time-reversal symmetry breaking and topologically protected polariton and micro/nanocavity lasers. Moreover, the introduction of gain and loss provides a fascinating playground to explore novel topological phases, which are in close relevance to non-Hermitian and parity-time symmetric quantum physics and are, in general, difficult to access using fermionic condensed matter systems. Here, we review the cutting-edge research on active topological photonics, in which optical gain plays a pivotal role. We discuss recent realizations of topological lasers of various kinds, together with the underlying physics explaining the emergence of topological edge modes. In such demonstrations, the optical modes of the topological lasers are determined by the dielectric structures and support lasing oscillation with the help of optical gain. We also address recent research on topological photonic systems in which gain and loss, themselves, essentially influence topological properties of the bulk systems. We believe that active topological photonics provides powerful means to advance micro/nanophotonics systems for diverse applications and topological physics, itself, as well.

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2

Cho, Y. M., Seung Hun Oh, and Pengming Zhang. "Knots in physics." International Journal of Modern Physics A 33, no. 07 (March 8, 2018): 1830006. http://dx.doi.org/10.1142/s0217751x18300065.

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After Dirac introduced the monopole, topological objects have played increasingly important roles in physics. In this review we discuss the role of the knot, the most sophisticated topological object in physics, and related topological objects in various areas in physics. In particular, we discuss how the knots appear in Maxwell’s theory, Skyrme theory, and multicomponent condensed matter physics.

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3

Kim, Ki-Seok, and Akihiro Tanaka. "Emergent gauge fields and their nonperturbative effects in correlated electrons." Modern Physics Letters B 29, no. 16 (June 20, 2015): 1540054. http://dx.doi.org/10.1142/s0217984915400540.

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The history of modern condensed matter physics may be regarded as the competition and reconciliation between Stoner’s and Anderson’s physical pictures, where the former is based on momentum–space descriptions focusing on long wave-length fluctuations while the latter is based on real-space physics emphasizing emergent localized excitations. In particular, these two view points compete with each other in various nonperturbative phenomena, which range from the problem of high [Formula: see text] superconductivity, quantum spin liquids in organic materials and frustrated spin systems, heavy-fermion quantum criticality, metal-insulator transitions in correlated electron systems such as doped silicons and two-dimensional electron systems, the fractional quantum Hall effect, to the recently discussed Fe-based superconductors. An approach to reconcile these competing frameworks is to introduce topologically nontrivial excitations into the Stoner’s description, which appear to be localized in either space or time and sometimes both, where scattering between itinerant electrons and topological excitations such as skyrmions, vortices, various forms of instantons, emergent magnetic monopoles, and etc. may catch nonperturbative local physics beyond the Stoner’s paradigm. In this review paper, we discuss nonperturbative effects of topological excitations on dynamics of correlated electrons. First, we focus on the problem of scattering between itinerant fermions and topological excitations in antiferromagnetic doped Mott insulators, expected to be relevant for the pseudogap phase of high [Formula: see text] cuprates. We propose that nonperturbative effects of topological excitations can be incorporated within the perturbative framework, where an enhanced global symmetry with a topological term plays an essential role. In the second part, we go on to discuss the subject of symmetry protected topological states in a largely similar light. While we do not introduce itinerant fermions here, the nonperturbative dynamics of topological excitations is again seen to be crucial in classifying topologically nontrivial gapped systems. We point to some hidden links between several effective field theories with topological terms, starting with one-dimensional physics, and subsequently finding natural generalizations to higher dimensions.

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4

Hafezi, Mohammad, and Jacob M. Taylor. "Topological physics with light." Physics Today 67, no. 5 (May 2014): 68–69. http://dx.doi.org/10.1063/pt.3.2394.

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5

Shuo, LIU, ZHANG Shuang, and CUI Tie-jun. "Topological circuit: a playground for exotic topological physics." Chinese Optics 14, no. 4 (2021): 736–53. http://dx.doi.org/10.37188/co.2021-0095.

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6

Shen, Yuanyuan, Shengguo Guan, and Chunyin Qiu. "Topological valley transport of spoof surface acoustic waves." Journal of Applied Physics 133, no. 11 (March 21, 2023): 114305. http://dx.doi.org/10.1063/5.0137591.

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In recent years, topological physics has attracted broad attention in condensed matter systems. Here, we report an experimental study on topological valley transport of spoof surface acoustic waves (SAWs). Specifically, we realize valley pseudospins and a valley Hall phase transition by tuning the structural size of adjacent grooves. In addition to a direct visualization of the vortex chirality-locked beam splitting for the bulk valley states, valley-projected edge states are observed in straight and bent interface channels formed by two topologically distinct valley Hall insulating phases. The experimental data agree well with our numerical predictions. The topological transport of spoof SAWs, encoded with valley information, provides more possibilities in design novel acoustic devices based on the valley-contrasting physics.

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7

HAN, Jung Hoon. "Solid State Physics, Condensed Matter Physics, and Topological Physics!" Physics and High Technology 25, no. 12 (December 30, 2016): 2–6. http://dx.doi.org/10.3938/phit.25.060.

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8

Novitsky, Denis V., and Andrey V. Novitsky. "Bound States in the Continuum versus Fano Resonances: Topological Argument." Photonics 9, no. 11 (November 20, 2022): 880. http://dx.doi.org/10.3390/photonics9110880.

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There is a recent surge of interest to the bound states in the continuum (BICs) due to their ability to provide high-quality resonances in open photonic systems. They are usually observed in perturbed systems possessing Fano resonances in their spectra. We argue that, generally speaking, the Fano resonances should not be considered as a proxy for BICs (as it is often done) due to their fundamentally different topological properties. This difference is illustrated with the non-Hermitian layered structure supporting both topologically nontrivial quasi-BIC and topologically trivial Fano resonances. Non-Hermiticity can also be a source of additional topological features of these resonant responses. Moreover, the lasing mode associated with BIC in this structure also possesses nonzero topological charge that can be useful for producing unconventional states of light. This paper contributes to the discussion of BIC physics and raises new questions concerning topological properties of non-Hermitian systems.

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9

Liu, Shuo, Wenlong Gao, Qian Zhang, Shaojie Ma, Lei Zhang, Changxu Liu, Yuan Jiang Xiang, Tie Jun Cui, and Shuang Zhang. "Topologically Protected Edge State in Two-Dimensional Su–Schrieffer–Heeger Circuit." Research 2019 (February 5, 2019): 1–8. http://dx.doi.org/10.34133/2019/8609875.

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Topological circuits, an exciting field just emerged over the last two years, have become a very accessible platform for realizing and exploring topological physics, with many of their physical phenomena and potential applications as yet to be discovered. In this work, we design and experimentally demonstrate a topologically nontrivial band structure and the associated topologically protected edge states in an RF circuit, which is composed of a collection of grounded capacitors connected by alternating inductors in the x and y directions, in analogy to the Su–Schrieffer–Heeger model. We take full control of the topological invariant (i.e., Zak phase) as well as the gap width of the band structure by simply tuning the circuit parameters. Excellent agreement is found between the experimental and simulation results, both showing obvious nontrivial edge state that is tightly bound to the circuit boundaries with extreme robustness against various types of defects. The demonstration of topological properties in circuits provides a convenient and flexible platform for studying topological materials and the possibility for developing flexible circuits with highly robust circuit performance.

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10

Liu, Shuo, Wenlong Gao, Qian Zhang, Shaojie Ma, Lei Zhang, Changxu Liu, Yuan Jiang Xiang, Tie Jun Cui, and Shuang Zhang. "Topologically Protected Edge State in Two-Dimensional Su–Schrieffer–Heeger Circuit." Research 2019 (February 5, 2019): 1–8. http://dx.doi.org/10.1155/2019/8609875.

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Topological circuits, an exciting field just emerged over the last two years, have become a very accessible platform for realizing and exploring topological physics, with many of their physical phenomena and potential applications as yet to be discovered. In this work, we design and experimentally demonstrate a topologically nontrivial band structure and the associated topologically protected edge states in an RF circuit, which is composed of a collection of grounded capacitors connected by alternating inductors in the x and y directions, in analogy to the Su–Schrieffer–Heeger model. We take full control of the topological invariant (i.e., Zak phase) as well as the gap width of the band structure by simply tuning the circuit parameters. Excellent agreement is found between the experimental and simulation results, both showing obvious nontrivial edge state that is tightly bound to the circuit boundaries with extreme robustness against various types of defects. The demonstration of topological properties in circuits provides a convenient and flexible platform for studying topological materials and the possibility for developing flexible circuits with highly robust circuit performance.

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11

Hatsugai, Y. "Topological aspect of graphene physics." Journal of Physics: Conference Series 334 (December 28, 2011): 012004. http://dx.doi.org/10.1088/1742-6596/334/1/012004.

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12

Mavromatos, Nick E. "Topological avatars of new physics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2161 (November 11, 2019): 20190393. http://dx.doi.org/10.1098/rsta.2019.0393.

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13

Anselmi, Damiano. "Topological field theory and physics." Classical and Quantum Gravity 14, no. 1 (January 1, 1997): 1–20. http://dx.doi.org/10.1088/0264-9381/14/1/005.

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14

Liu, Yizhou, Yong Xu, and Wenhui Duan. "Three-Dimensional Topological States of Phonons with Tunable Pseudospin Physics." Research 2019 (July 31, 2019): 1–8. http://dx.doi.org/10.34133/2019/5173580.

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Efficient control of phonons is crucial to energy-information technology, but limited by the lacking of tunable degrees of freedom like charge or spin. Here we suggest to utilize crystalline symmetry-protected pseudospins as new quantum degrees of freedom to manipulate phonons. Remarkably, we reveal a duality between phonon pseudospins and electron spins by presenting Kramers-like degeneracy and pseudospin counterparts of spin-orbit coupling, which lays the foundation for “pseudospin phononics”. Furthermore, we report two types of three-dimensional phononic topological insulators, which give topologically protected, gapless surface states with linear and quadratic band degeneracies, respectively. These topological surface states display unconventional phonon transport behaviors attributed to the unique pseudospin-momentum locking, which are useful for phononic circuits, transistors, antennas, etc. The emerging pseudospin physics offers new opportunities to develop future phononics.

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15

PALUMBO, GIANDOMENICO, ROBERTO CATENACCI, and ANNALISA MARZUOLI. "TOPOLOGICAL EFFECTIVE FIELD THEORIES FOR DIRAC FERMIONS FROM INDEX THEOREM." International Journal of Modern Physics B 28, no. 01 (December 11, 2013): 1350193. http://dx.doi.org/10.1142/s0217979213501932.

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Dirac fermions have a central role in high energy physics but it is well-known that they emerge also as quasiparticles in several condensed matter systems supporting topological order. We present a general method for deriving the topological effective actions of (3+1)-massless Dirac fermions living on general backgrounds and coupled with vector and axial-vector gauge fields. The first step of our strategy is standard (in the Hermitian case) and consists in connecting the determinants of Dirac operators with the corresponding analytical indices through the zeta-function regularization. Then, we introduce a suitable splitting of the heat kernel that naturally selects the purely topological part of the determinant (i.e., the topological effective action). This topological effective action is expressed in terms of gauge fields using the Atiyah–Singer index theorem which computes the analytical index in topological terms. The main new result of this paper is to provide a consistent extension of this method to the non-Hermitian case, where a well-defined determinant does not exist. Quantum systems supporting relativistic fermions can thus be topologically classified on the basis of their response to the presence of (external or emergent) gauge fields through the corresponding topological effective field theories (TEFTs).

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16

Xiao, Meng, Liping Ye, Chunyin Qiu, Hailong He, Zhengyou Liu, and Shanhui Fan. "Experimental demonstration of acoustic semimetal with topologically charged nodal surface." Science Advances 6, no. 8 (February 2020): eaav2360. http://dx.doi.org/10.1126/sciadv.aav2360.

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Weyl points are zero-dimensional band degeneracy in three-dimensional momentum space that has nonzero topological charges. The presence of the topological charges protects the degeneracy points against perturbations and enables a variety of fascinating phenomena. It is so far unclear whether such charged objects can occur in higher dimensions. Here, we introduce the concept of charged nodal surface, a two-dimensional band degeneracy surface in momentum space that is topologically charged. We provide an effective Hamiltonian for this charged nodal surface and show that such a Hamiltonian can be implemented in a tight-binding model. This is followed by an experimental realization in a phononic crystal. The measured topologically protected surface arc state of such an acoustic semimetal reproduces excellently the full-wave simulations. Creating high-dimensional charged geometric objects in momentum space promises a broad range of unexplored topological physics.

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17

Liu, Wenjie, Yongguan Ke, Zhoutao Lei, and Chaohong Lee. "Magnon boundary states tailored by longitudinal spin–spin interactions and topology." New Journal of Physics 25, no. 9 (September 1, 2023): 093042. http://dx.doi.org/10.1088/1367-2630/acf8ea.

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Abstract Since longitudinal spin–spin interaction is ubiquitous in magnetic materials, it is very interesting to explore the interplay between topology and longitudinal spin–spin interaction. Here, we examine the role of longitudinal spin–spin interaction on topological magnon excitations. Remarkably, even for single-magnon excitations, we discover topological edge states and defect edge states of magnon excitations in a dimerized Heisenberg XXZ chain and their topological properties can be distinguished via adiabatic quantum transport. We uncover topological phase transitions induced by longitudinal spin–spin interactions whose boundary is analytically obtained via the transfer matrix method. For multi-magnon excitations, even-magnon bound states are found to be always topologically trivial, but odd-magnon bound states may be topologically nontrivial due to the interplay between the transverse dimerization and the longitudinal spin–spin interaction. For two-dimensional spin systems, the longitudinal spin–spin interaction contributes to the coexistence of defect corner states, second-order topological corner states and first-order topological edge states. We propose an experimental scheme to realize and measure the magnon boundary states in superconducting qubits. Our work opens an avenue for exploring topological magnon excitations and has potential applications in topological magnon devices.

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18

Deng, Jinfeng, Hang Dong, Chuanyu Zhang, Yaozu Wu, Jiale Yuan, Xuhao Zhu, Feitong Jin, et al. "Observing the quantum topology of light." Science 378, no. 6623 (December 2, 2022): 966–71. http://dx.doi.org/10.1126/science.ade6219.

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Topological photonics provides a powerful platform to explore topological physics beyond traditional electronic materials and shows promising applications in light transport and lasers. Classical degrees of freedom are routinely used to construct topological light modes in real or synthetic dimensions. Beyond the classical topology, the inherent quantum nature of light provides a wealth of fundamentally distinct topological states. Here we implement experiments on topological states of quantized light in a superconducting circuit, with which one- and two-dimensional Fock-state lattices are constructed. We realize rich topological physics including topological zero-energy states of the Su-Schrieffer-Heeger model, strain-induced pseudo-Landau levels, valley Hall effect, and Haldane chiral edge currents. Our study extends the topological states of light to the quantum regime, bridging topological phases of condensed-matter physics with circuit quantum electrodynamics, and offers a freedom in controlling the quantum states of multiple resonators.

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Lei, Lin-Lin, Ling-Juan He, Wen-Xing Liu, Qing-Hua Liao, and Tian-Bao Yu. "Coexistence of photonic and phononic corner states in a second-order topological phoxonic crystal." Applied Physics Letters 121, no. 19 (November 7, 2022): 193103. http://dx.doi.org/10.1063/5.0127301.

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Recently, higher-order topological insulators (HOTIs) have been extended from the electronic system to classical wave systems. Beyond the conventional bulk-boundary correspondence, HOTIs can host zero-dimensional topologically protected corner states, which show the strong field localization and robustness against fabrication flaws. Here, we propose a second-order topological phoxonic crystal (PXC) based on a two-dimensional (2D) square lattice, of which different unit cell choices can show either a topologically trivial or non-trivial band structure characterized by the 2D Zak phase. The proposed PXC supports the coexistence of photonic and phononic topological corner states, and their robustness to disorders and defects is numerically demonstrated. Our work opens a venue for achieving simultaneous confinement of photons and phonons, which is potentially useful for exploring the interaction of photonic and phononic second-order topological states and for designing novel topological optomechanical devices.

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20

Tan, Rui, Qi Qi, Peng Wang, Yanqiang Cao, Rongrong Si, Maoxiang Wang та Xiaoxiong Wang. "Reorganization of the topological surface mode of topological insulating α-Sn". Journal of Physics: Condensed Matter 34, № 9 (9 грудня 2021): 095501. http://dx.doi.org/10.1088/1361-648x/ac3c65.

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Abstract α-Sn is a topologically nontrivial semimetal in its natural structure. Upon compressively strained in plane, it transforms into a topological insulator. But, up to now, a clear and systematic understanding of the topological surface mode of topological insulating α-Sn is still lacking. In the present work, first-principle simulations are employed to investigate the electronic structure evolution of Ge1−x Sn x alloys aiming at understanding the band reordering, topological phase transition and topological surface mode of α-Sn in detail. Progressing from Ge to Sn with increasing Sn content in Ge1−x Sn x , the conduction band inverts with the first valence band (VB) and then with the second VB sequentially, rather than inverting with the latter directly. Correspondingly, a topologically nontrivial surface mode arises in the first inverted band gap. Meanwhile, a fragile Dirac cone appears in the second inverted band gap as a result of the reorganization of the topological surface mode caused by the first VB. The reorganization of the topological surface mode in α-Sn is very similar to the HgTe case. The findings of the present work are helpful for understanding and utilizing of the topological surface mode of α-Sn.

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21

Ball, Philip. "Making the world from topological order." National Science Review 6, no. 2 (November 6, 2018): 227–30. http://dx.doi.org/10.1093/nsr/nwy116.

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Abstract Topology used to be a term confined to a branch of pure mathematics, where it referred to an invariant property of shape. The classic example was the way objects containing a single hole, like a torus and a coffee cup with handle, can be smoothly moulded into one another without tearing. But topological considerations have long played a role in the physics of matter, where for example they might dictate particular arrangements of component parts that can’t be erased from the system. The classic example here is the fact that a ‘hairy ball’ can’t be combed flat without having at least two pointy tufts. Such ‘defects’ in organization can be considered ‘topologically protected’, since they are robust against any recombing of the hair. They are universal features that don’t depend on the material specifics of the system: topological defects in liquid crystals are analogous to defects in spacetime called cosmic strings. In the past several decades in particular, properties of matter arising from topological considerations have become a major theme, reflected for example in the award of the 1985 and 1998 Nobel Prizes in Physics for discoveries involving the quantum Hall effect. Here the ‘Hall conductance’, quantifying the passage of electrical current in a 2D conductor in the presence of a transverse magnetic field, takes precise integral or fractional multiples of a particular quantized value related to the electron charge. This behaviour persists regardless of how we modify the material, for example by adding impurities. Topological phases and transitions were also a feature of the work that won the 2016 Nobel Prize. It has become recognized that the topological properties of the quantum-mechanical electronic structures of certain materials can give them unusual and perhaps useful properties. Some researchers think, for example, that ‘topological matter’ might supply quantum bits for quantum computation that resist the randomizing effects of noise. Xiao-Gang Wen of the Massachusetts Institute of Technology has been developing ideas about ‘topological order’ in fundamental physics for several decades. His notions of how topology in the underlying structure of spacetime might give rise to fundamental particles and forces make a connection to the topological phases recognized in condensed matter, revealing a new unifying principle in physics. National Science Review spoke to him about his work.

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22

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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23

Zhou, Longwen. "Entanglement Phase Transitions in Non-Hermitian Kitaev Chains." Entropy 26, no. 3 (March 20, 2024): 272. http://dx.doi.org/10.3390/e26030272.

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The intricate interplay between unitary evolution and projective measurements could induce entanglement phase transitions in the nonequilibrium dynamics of quantum many-particle systems. In this work, we uncover loss-induced entanglement transitions in non-Hermitian topological superconductors. In prototypical Kitaev chains with onsite particle losses and varying hopping and pairing ranges, the bipartite entanglement entropy of steady states is found to scale logarithmically versus the system size in topologically nontrivial phases and become independent of the system size in the trivial phase. Notably, the scaling coefficients of log-law entangled phases are distinguishable when the underlying system resides in different topological phases. Log-law to log-law and log-law to area-law entanglement phase transitions are further identified when the system switches between different topological phases and goes from a topologically nontrivial to a trivial phase, respectively. These findings not only establish the relationships among spectral, topological and entanglement properties in a class of non-Hermitian topological superconductors but also provide an efficient means to dynamically reveal their distinctive topological features.

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24

Thouless, D. J. "Topological Quantum Numbers in Nonrelativistic Physics." International Journal of Modern Physics B 11, no. 28 (November 10, 1997): 3319–27. http://dx.doi.org/10.1142/s0217979297001623.

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Voltage measurements using the ac Josephson effect and electrical resistance measurements using the quantum Hall effect are capable of very high precision, despite the relatively poor control of details of the devices. Such measurements rely on topological quantum numbers, which, unlike symmetry-based quantum numbers, are insensitive to deviations of the system from ideality. The circulation in superfluid 4 He , flux quantization in superconductors and quantized Hall conductance are all examples of topological quantum numbers, but only the last two are known to be very precise. Vinen's early measurement of quantized circulation was based on measurement of the resulting Magnus force, and we (Ping Ao, Qian Niu and I) have recently shown that the strength of the Magnus force can itself be determined by an argument that shares common features with topological arguments.

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25

Parker, Jeffrey B. "Topological phase in plasma physics." Journal of Plasma Physics 87, no. 2 (April 2021). http://dx.doi.org/10.1017/s0022377821000301.

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Recent discoveries have demonstrated that matter can be distinguished on the basis of topological considerations, giving rise to the concept of topological phase. Introduced originally in condensed matter physics, the physics of topological phase can also be fruitfully applied to plasmas. Here, the theory of topological phase is introduced, including a discussion of Berry phase, Berry connection, Berry curvature and Chern number. One of the clear physical manifestations of topological phase is the bulk-boundary correspondence, the existence of localized unidirectional modes at the interface between topologically distinct phases. These concepts are illustrated through examples, including the simple magnetized cold plasma. An outlook is provided for future theoretical developments and possible applications.

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26

Kumar, Ranjith R., and Sujit Sarkar. "Physics of emergence beyond Berezinskii–Kosterlitz–Thouless transition for interacting topological quantum matter." Scientific Reports 12, no. 1 (July 13, 2022). http://dx.doi.org/10.1038/s41598-022-15834-y.

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AbstractAn attempt is made to find different emergent quantum phases for interacting topological state of quantum matter. Our study is based on the quantum field theoretical renormalization group (RG) calculations. The behaviour of the RG flow lines give the emergence of different quantum phases for non-interacting and interacting topological state of quantum matter. We show explicitly electron-electron interaction can turn a topologically trivial phase into a topologically nontrivial one and also topologically nontrivial phase to topologically trivial phase. We show that physics of emergence goes beyond the quantum Berezinskii–Kosterlitz–Thouless transition. We also present the analysis of fixed point and show the behaviour of fixed point changes in presence and absence of interaction. This work provides a new perspective not only from the topological state of interacting quantum matter and but also for the correlated quantum many -body physics.

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27

Xie, Boyang, Hui Liu, Haonan Wang, Hua Cheng, Jianguo Tian, and Shuqi Chen. "A Review of Topological Semimetal Phases in Photonic Artificial Microstructures." Frontiers in Physics 9 (November 16, 2021). http://dx.doi.org/10.3389/fphy.2021.771481.

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In the past few years, the concept of topological matter has inspired considerable research in broad areas of physics. In particular, photonic artificial microstructures like photonic crystals and metamaterials provide a unique platform to investigate topologically non-trivial physics in spin-1 electromagnetic fields. Three-dimensional (3D) topological semimetal band structures, which carry non-trivial topological charges, are fundamental to 3D topological physics. Here, we review recent progress in understanding 3D photonic topological semimetal phases and various approaches for realizing them, especially with photonic crystals or metamaterials. We review topological gapless band structures and topological surface states aroused from the non-trivial bulk topology. Weyl points, 3D Dirac points, nodal lines, and nodal surfaces of different types are discussed. We also demonstrate their application in coupling spin-polarized electromagnetic waves, anomalous reflection, vortex beams generation, bulk transport, and non-Hermitian effects.

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28

Liu En-Ke. "Coupling of magnetism and topology: From the fundamental physics to topological magneto-electronics." Acta Physica Sinica, 2024, 0. http://dx.doi.org/10.7498/aps.73.20231711.

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Magnetism and topological physics are both well-developed disciplines, and their combination is a demand and foundation for the development of next-generation magneto-electronics. Magnetic topological materials, which arise from the coupling between magnetic order and topological physics, serve as significant platforms with controlled degrees of freedom for novel topological physics. Magnetic Weyl semimetals enable the realization of Weyl fermion states with time-reversal symmetry breaking, leading to a host of novel magnetic, electric, thermal, and optical effects through enhanced Berry curvature originating from topology. The interaction between Weyl electrons and magnetic order also establishes topological electronic physics as a new principle and driving force for magneto-electronic applications. At present, the primary task and characteristic of the first development stage of magnetic topological materials is to discover new states and effects, while attention has been drawn towards understanding the interaction between topologically nontrivial electrons in momentum space and magnetic order in real space. The comprehensive advancement of these two stages will accumulate the physical foundation and application explorations for topological magneto-electronics. This paper focuses on the two development stages of magnetic topological materials and discusses three aspects: (i) proposal and realization strategies for magnetic topological materials; (ii) exploration of electronic states with nontrivial topology under uniform magnetic order and their associated novel physical properties; (iii) the interaction between localized magnetic states and topological electrons. It provides an in-depth discussion on current hot topics and development trends in the field, anticipates future developments in topological magneto-electronics, and contributes to the advancement of future topological spin quantum devices.

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29

Juzeliūnas, Gediminas, and Ian Spielman. "Seeing Topological Order." Physics 4 (November 28, 2011). http://dx.doi.org/10.1103/physics.4.99.

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30

Anonymous. "Topological catalysis." Physics 4 (July 28, 2011). http://dx.doi.org/10.1103/physics.4.s111.

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31

Anonymous. "Topological Origami." Physics 9 (March 30, 2016). http://dx.doi.org/10.1103/physics.9.s36.

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32

Karki, Ravi Karki. "Topological Order in Physics." Himalayan Physics, October 12, 2017, 108–11. http://dx.doi.org/10.3126/hj.v6i0.18372.

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In general, we know that there are four states of matter solid, liquid, gas and plasma. But there are much more states of matter. For e. g. there are ferromagnetic states of matter as revealed by the phenomenon of magnetization and superfluid states defined by the phenomenon of zero viscosity. The various phases in our colorful world are so rich that it is amazing that they can be understood systematically by the symmetry breaking theory of Landau. Topological phenomena define the topological order at macroscopic level. Topological order need new mathematical framework to describe it. More recently it is found that at microscopic level topological order is due to the long range quantum entanglement, just like the fermions fluid is due to the fermion-pair condensation. Long range quantum entanglement leads to many amazing emergent phenomena, such as fractional quantum numbers, non- Abelian statistics ad perfect conducting boundary channels. It can even provide a unified origin of light and electron i.e. gauge interactions and Fermi statistics. Light waves (gauge fields) are fluctuations of long range entanglement and electron (fermion) are defect of long range entanglements.The Himalayan Physics Vol. 6 & 7, April 2017 (108-111)

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33

Walker, Helen. "Topological Magnetism Turns Elementary." Physics 15 (March 2, 2022). http://dx.doi.org/10.1103/physics.15.30.

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34

Bandres, Miguel A., and Mordechai Segev. "Non-Hermitian Topological Systems." Physics 11 (September 24, 2018). http://dx.doi.org/10.1103/physics.11.96.

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35

Quandt, Alexander. "Quasicrystals, Meet Topological Insulators." Physics 5 (September 4, 2012). http://dx.doi.org/10.1103/physics.5.99.

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36

McCormick, Katie. "Optical Fibers Go Topological." Physics 16 (February 2, 2023). http://dx.doi.org/10.1103/physics.16.16.

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37

Linder, Jacob. "Quantized topological surface states promise a quantum Hall state in topological insulators." Physics 3 (August 9, 2010). http://dx.doi.org/10.1103/physics.3.66.

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38

Wu, Shi-Qiao, Zhi-Kang Lin, Yongyao Li, and Jianing Xie. "Geometry-dependent acoustic higher-order topological phases on a two-dimensional honeycomb lattice." Journal of Applied Physics 135, no. 13 (April 1, 2024). http://dx.doi.org/10.1063/5.0202383.

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Higher-order topological states, as emergent topological phases of matter, originating from condensed matter physics, have sparked a vibrant exploration of topological insulators. Their topologically protected multidimensional localized states are typically associated with nontrivial bulk band topology, and the significant impact of lattice geometry is unconsciously overlooked. Here, we construct coupled acoustic cavities on a two-dimensional honeycomb lattice to investigate the sensitivity of higher-order topological modes to the variations of edge contour. Fractional charge is utilized to accurately predict topological modes with distinct topological orders, in spite of the minimal bulk bandgaps inherent in the honeycomb lattice and bound states in the continuum. It is found that the presence and absence of the first-order and higher-order topological modes in the same topological phase are tightly linked to the sample boundaries, which can be demonstrated by both theoretical analysis and numerical calculation. Our study also discusses potential physical realization of geometry-dependent topological states across different platforms, providing inspiration for the prospective application of topological devices in acoustics.

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39

Tran, Minh-Tien, and Thanh-Mai Thi Tran. "Half topological state in magnetic topological insulators." Journal of Physics: Condensed Matter, April 22, 2022. http://dx.doi.org/10.1088/1361-648x/ac699f.

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Abstract We predict a novel topological state, half-topological state, in magnetic topological insulators. The topological state is characterized by different topologies of electrons with different spin orientations, i.e., electrons with one spin orientation occupy a nontrivial topological insulating state, while electrons with opposite orientation occupy another insulating state with trivial topology. We demonstrate the occurrence of the half-topological state in magnetic topological insulators by employing a minimal model. The minimal model is a combination of the spinful Haldane and the double-exchange models. The double-exchange processes maintain a spontaneous magnetic ordering, while the next-nearest-neighbor hopping in the Haldane model gives rise to a nontrivial topological insulator. The minimal model is studied by applying the dynamical mean field theory. It is found that the long-range antiferromagnetic ordering drives the system from either topological or topologically trivial antiferromagnetic insulator to the half-topological state, and finally to topologically trivial antiferromagnetic insulator. The equations for the topological phase transitions are also explicitly derived.

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40

Cano, Jennifer, and Barry Bradlyn. "Band Representations and Topological Quantum Chemistry." Annual Review of Condensed Matter Physics 12, no. 1 (December 7, 2020). http://dx.doi.org/10.1146/annurev-conmatphys-041720-124134.

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In this article, we provide a pedagogical review of the theory of topological quantum chemistry and topological crystalline insulators. We begin with an overview of the properties of crystal symmetry groups in position and momentum space. Next, we introduce the concept of a band representation, which quantifies the symmetry of topologically trivial band structures. By combining band representations with symmetry constraints on the connectivity of bands in momentum space, we show how topologically nontrivial bands can be cataloged and classified. We present several examples of new topological phases discovered using this paradigm and conclude with an outlook toward future developments. Expected final online publication date for the Annual Review of Condensed Matter Physics, Volume 12 is March 10, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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41

Yi, F., M. Q. Liu, N. N. Wang, B. X. Wang, and C. Y. Zhao. "Near-field observation of mid-infrared edge modes in topological photonic crystals." Applied Physics Letters 123, no. 8 (August 21, 2023). http://dx.doi.org/10.1063/5.0157868.

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Topological photonic crystals inherit the unique properties of topological insulators, including topologically protected energy transfer and unidirectional propagation, which offer an excellent platform for exploring exotic physics and developing photonic devices. However, topological photonic crystals possessing mid-infrared edge modes that have potential applications in infrared imaging, biosensing, thermal radiation energy transfer, etc., are seldom brought into focus. In this work, we study the topological properties of a photonic crystal slab (PCS) consisting of silicon square veins in the mid-infrared, which is intended to mimic the two-dimensional Su–Schrieffer–Heeger model. By interfacing topologically trivial and nontrivial PCSs, mid-infrared edge modes can appear at domain wall, according to the principle of bulk-edge correspondence. It is also demonstrated high-efficiency mid-infrared light transport can be achieved by these edge modes. In addition, adjusting the vertical offset near the interface can manipulate the bandwidth for various applications and turns the connected PCS structure to a photonic realization of Rice–Mele model. We further fabricate the PCS and provide an experimental observation of transverse-electric-like edge modes in mid-infrared by using the scattering-type scanning near-field optical microscope. Additionally, we integrate it with phase change material of nanoscale thickness, Ge2Sb2Te5, to realize an ultrafast and switchable topological waveguide with zero static power. This work not only enriches the fundamental understanding of topological physics in mid-infrared optical settings, but also shows promising prospects in compact devices for energy transfer and information processing for light sources in these wavelengths, for instance, thermal radiation.

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42

Huang, Z., W. L. Liu, H. Y. Wang, Y. L. Su, Z. T. Liu, X. B. Shi, S. Y. Gao, et al. "Dual topological states in the layered titanium-based oxypnictide superconductor BaTi2Sb2O." npj Quantum Materials 7, no. 1 (June 28, 2022). http://dx.doi.org/10.1038/s41535-022-00477-z.

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AbstractTopological superconductors have long been predicted to host Majorana zero modes which obey non-Abelian statistics and have potential for realizing non-decoherence topological quantum computation. However, material realization of topological superconductors is still a challenge in condensed matter physics. Utilizing high-resolution angle-resolved photoemission spectroscopy and first-principles calculations, we predict and then unveil the coexistence of topological Dirac semimetal and topological insulator states in the vicinity of Fermi energy (EF) in the titanium-based oxypnictide superconductor BaTi2Sb2O. Further spin-resolved measurements confirm its spin-helical surface states around EF, which are topologically protected and give an opportunity for realization of Majorana zero modes and Majorana flat bands in one material. Hosting dual topological states, the intrinsic superconductor BaTi2Sb2O is expected to be a promising platform for further investigation of topological superconductivity.

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43

Lee, Myung-Joon, and Il-Kwon Oh. "Robust separation of topological in-plane and out-of-plane waves in a phononic crystal." Communications Physics 5, no. 1 (January 11, 2022). http://dx.doi.org/10.1038/s42005-021-00793-z.

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AbstractValley degree of freedom, associated with the valley topological phase, has propelled the advancement of the elastic waveguide by offering immunity to backscattering against bending and weak perturbations. Despite many attempts to manipulate the wave path and working frequency of the waveguide, internal characteristic of an elastic wave such as rich polarization has not yet been utilized with valley topological phases. Here, we introduce the rich polarization into the valley degree of freedom, to achieve topologically protected in-plane and out-of-plane mode separation of an elastic wave. Accidental degeneracy proves its real worth of decoupling the in-plane and out-of-plane polarized valley Hall phases. We further demonstrate independent and simultaneous control of in-plane and out-of-plane waves, with intact topological protection. The presenting procedure for designing the topologically protected wave separation based on accidental degeneracy will widen the valley topological physics in view of both generation mechanism and application areas.

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44

Anonymous. "Snowflake Topological Insulator." Physics 11 (January 18, 2018). http://dx.doi.org/10.1103/physics.11.s9.

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45

Anonymous. "Optimizing Topological Insulators." Physics 4 (October 6, 2011). http://dx.doi.org/10.1103/physics.4.s147.

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46

Anonymous. "Odd topological superconductor." Physics 4 (June 23, 2011). http://dx.doi.org/10.1103/physics.4.s90.

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47

Rao, Mujie, Fulong Shi, Zhixuan Rao, Jiawei Yang, Changkun Song, Xiaodong Chen, Jianwen Dong, Ying Yu, and Siyuan Yu. "Single photon emitter deterministically coupled to a topological corner state." Light: Science & Applications 13, no. 1 (January 17, 2024). http://dx.doi.org/10.1038/s41377-024-01377-6.

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AbstractIncorporating topological physics into the realm of quantum photonics holds the promise of developing quantum light emitters with inherent topological robustness and immunity to backscattering. Nonetheless, the deterministic interaction of quantum emitters with topologically nontrivial resonances remains largely unexplored. Here we present a single photon emitter that utilizes a single semiconductor quantum dot, deterministically coupled to a second-order topological corner state in a photonic crystal cavity. By investigating the Purcell enhancement of both single photon count and emission rate within this topological cavity, we achieve an experimental Purcell factor of Fp = 3.7. Furthermore, we demonstrate the on-demand emission of polarized single photons, with a second-order autocorrelation function g(2)(0) as low as 0.024 ± 0.103. Our approach facilitates the customization of light-matter interactions in topologically nontrivial environments, thereby offering promising applications in the field of quantum photonics.

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48

Wang, Hongfei, Biye Xie, and Wei Ren. "Coexistence of Chiral and Antichiral Edge States in Photonic Crystals." Laser & Photonics Reviews, October 17, 2023. http://dx.doi.org/10.1002/lpor.202300764.

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AbstractThis study reports a modified Haldane model that supports transitions between valley and Chern topological phases in photonic crystals. Berry curvatures of this system can be flexibly diffused, converged, or flipped by endowing different model parameters, thus exhibiting exotic topological interface/edge behaviors, such as topological bound states with ideally zero dispersion. Importantly, the coexistence of chiral and antichiral edge states preserved simultaneously by valley and Chern topological phases is achieved by splicing together two kinds of topological structures as an entirety. It further employs a honeycomb lattice comprising gyromagnetic and ceramic cylinders at microwave frequencies, where inversion and time‐reversal symmetries can be flexibly manipulated. Topological interface transport is demonstrated, including two opposite signs of group velocities jointly protected by topologically distinct regimes. These results bridge the gap between valley and Chern topological physics and shed light on developing reconfigurable integrated device applications for classical (quantum) information processing and photonic computing.

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49

Ding, Zhong‐Ke, Yu‐Jia Zeng, Wangping Liu, Li‐Ming Tang, and Ke‐Qiu Chen. "Topological Phonons and Thermoelectric Conversion in Crystalline Materials." Advanced Functional Materials, April 5, 2024. http://dx.doi.org/10.1002/adfm.202401684.

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AbstractTopological phononics, a fascinating frontier in condensed matter physics, holds great promise for advancing energy‐related applications. Topologically nontrivial phonons typically possess gapless edge or surface states. These exotic states of lattice vibrations, characterized by their nontrivial topology, offer unique opportunities for manipulating and harnessing energy transport. The exploration of topological phonons opens new avenues in understanding and controlling thermal transport properties, with potential applications in fields such as thermoelectric materials, phononic devices, and waste heat recovery. Here, an overview of concepts such as Berry curvature and topological invariants, along with the applications of phonon tight‐binding method and nonequilibrium Green's function method in the field of topological phononics is provided. This review encompasses the latest research progress of various topological phonon states within crystalline materials, including topological optical phonons, topological acoustical phonons, and higher‐order topological phonons. Furthermore, the study delves into the prospective applications of topological phonons in the realm of thermoelectric conversion, focusing on aspects like size effects and symmetry engineering.

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50

Chen, Jianfei, Chaohua Wu, Jingtao Fan, and Gang Chen. "Characterizing topological phase of superlattices in superconducting circuits." Chinese Physics B, February 17, 2022. http://dx.doi.org/10.1088/1674-1056/ac5612.

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Abstract The recent experimental observation of topological magnon insulator states in a superconducting circuit chain marks a breakthrough for topological physics with qubits. In that study, a dimerized qubit chain was realized. Here, we extend such dimer lattice to superlattice with arbitrary number of qubits in each unit cell in superconducting circuits, which exhibit rich topological properties. Specifically, by considering a quadrimeric superlattice, we show that the topological invariant (winding number) can be effectively characterized by the dynamics of the single-excitation quantum state through a time-dependent quantities. Moreover, we explore the appearance and detection of the topological protected edge states in such multiband qubit system. Finally, we also demonstrate the stable Bloch-like-oscillation of multiple interface states induced by the interference of them. Our proposal can be readily realized in experiment and may pave the way towards the investigation of topological quantum phases and topologically protected quantum information processing.

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