Journal articles: 'Topological state of matter'

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GROVER, TARUN. "ENTANGLEMENT ENTROPY AND STRONGLY CORRELATED TOPOLOGICAL MATTER." Modern Physics Letters A 28, no. 05 (February 6, 2013): 1330001. http://dx.doi.org/10.1142/s0217732313300012.

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Topological ordered phases are gapped states of matter that are characterized by non-local entanglement in their ground state wave functions instead of a local order parameter. In this paper, we review some of the basic results on the entanglement structure of topologically ordered phases. In particular, we focus on the notion and uses of "topological entanglement entropy" in two and higher dimensions, and also briefly review the relation between entanglement spectrum and the spectrum of the physical edge states for chiral topological states. Furthermore, we discuss a curvature expansion for the entanglement entropy which sharpens the nonlocality of topological entanglement entropy.

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Fatemi, Valla, Sanfeng Wu, Yuan Cao, Landry Bretheau, Quinn D. Gibson, Kenji Watanabe, Takashi Taniguchi, Robert J. Cava, and Pablo Jarillo-Herrero. "Electrically tunable low-density superconductivity in a monolayer topological insulator." Science 362, no. 6417 (October 25, 2018): 926–29. http://dx.doi.org/10.1126/science.aar4642.

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Turning on superconductivity in a topologically nontrivial insulator may provide a route to search for non-Abelian topological states. However, existing demonstrations of superconductor-insulator switches have involved only topologically trivial systems. Here we report reversible, in situ electrostatic on-off switching of superconductivity in the recently established quantum spin Hall insulator monolayer tungsten ditelluride (WTe2). Fabricated into a van der Waals field-effect transistor, the monolayer’s ground state can be continuously gate-tuned from the topological insulating to the superconducting state, with critical temperaturesTcup to ~1 kelvin. Our results establish monolayer WTe2as a material platform for engineering nanodevices that combine superconducting and topological phases of matter.

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Luo, M. J. "Quark–gluon plasma and topological quantum field theory." Modern Physics Letters A 32, no. 10 (March 27, 2017): 1750056. http://dx.doi.org/10.1142/s0217732317500560.

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Based on an analogy with topologically ordered new state of matter in condensed matter systems, we propose a low energy effective field theory for a parity conserving liquid-like quark–gluon plasma (QGP) around critical temperature in quantum chromodynamics (QCD) system. It shows that below a QCD gap which is expected several times of the critical temperature, the QGP behaves like topological fluid. Many exotic phenomena of QGP near the critical temperature discovered at Relativistic Heavy Ion Collision (RHIC) are more readily understood by the suggestion that QGP is a topologically ordered state.

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Panagiotou, Eleni. "Following the entangled state of filaments." Science 380, no. 6643 (April 28, 2023): 340–41. http://dx.doi.org/10.1126/science.adh4055.

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Kumar, Abhishek, Manoj Gupta, Prakash Pitchappa, Yi Ji Tan, Nan Wang, and Ranjan Singh. "Topological sensor on a silicon chip." Applied Physics Letters 121, no. 1 (July 4, 2022): 011101. http://dx.doi.org/10.1063/5.0097129.

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An ultrasensitive photonic sensor is vital for sensing matter with absolute specificity. High specificity terahertz photonic sensors are essential in many fields, including medical research, clinical diagnosis, security inspection, and probing molecular vibrations in all forms of matter. Widespread photonic sensing technology detects small frequency shifts due to the targeted specimen, thus requiring ultra-high quality ( Q) factor resonance. However, the existing terahertz waveguide resonating structures are prone to defects, possess limited Q-factor, and lack the feature of chip-scale CMOS integration. Here, inspired by the topologically protected edge state of light, we demonstrate a silicon valley photonic crystal based ultrasensitive, robust on-chip terahertz topological insulator sensor that consists of a topological waveguide critically coupled to a topological cavity with an ultra-high quality ( Q) factor of [Formula: see text]. Topologically protected cavity resonance exhibits strong resilience against disorder and multiple sharp bends. Leveraging on the extremely narrow linewidth (2.3 MHz) of topological cavity resonance, the terahertz sensor shows a record-high figure of merit of [Formula: see text]. In addition to the spectral shift, the intensity modulation of cavity resonance offers an additional sensor metric through active tuning of critical coupling in the waveguide-cavity system. We envision that the ultra-high Q photonic terahertz topological sensor could have chip-scale biomedical applications such as differentiation between normal and cancerous tissues by monitoring the water content.

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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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Semeghini, G., H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, et al. "Probing topological spin liquids on a programmable quantum simulator." Science 374, no. 6572 (December 3, 2021): 1242–47. http://dx.doi.org/10.1126/science.abi8794.

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Synthesizing topological order Topologically ordered matter exhibits long-range quantum entanglement. However, measuring this entanglement in real materials is extremely tricky. Now, two groups take a different approach and turn to synthetic systems to engineer the topological order of the so-called toric code type (see the Perspective by Bartlett). Satzinger et al . used a quantum processor to study the ground state and excitations of the toric code. Semeghini et al . detected signatures of a toric code–type quantum spin liquid in a two-dimensional array of Rydberg atoms held in optical tweezers. —JS

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Satzinger, K. J., Y. J. Liu, A. Smith, C. Knapp, M. Newman, C. Jones, Z. Chen, et al. "Realizing topologically ordered states on a quantum processor." Science 374, no. 6572 (December 3, 2021): 1237–41. http://dx.doi.org/10.1126/science.abi8378.

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Synthesizing topological order Topologically ordered matter exhibits long-range quantum entanglement. However, measuring this entanglement in real materials is extremely tricky. Now, two groups take a different approach and turn to synthetic systems to engineer the topological order of the so-called toric code type (see the Perspective by Bartlett). Satzinger et al . used a quantum processor to study the ground state and excitations of the toric code. Semeghini et al . detected signatures of a toric code–type quantum spin liquid in a two-dimensional array of Rydberg atoms held in optical tweezers. —JS

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LIU, LAN-FENG, and SU-PENG KOU. "TOPOLOGICAL QUANTUM PHASE TRANSITION BETWEEN QUANTUM SPIN HALL STATE AND QUANTUM ANOMALOUS HALL STATE." International Journal of Modern Physics B 25, no. 17 (July 10, 2011): 2323–40. http://dx.doi.org/10.1142/s0217979211100096.

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In this paper, starting from a lattice model of topological insulators, we study the quantum phase transitions among different quantum states, including quantum spin Hall state, quantum anomalous Hall state and normal band insulator state by calculating their topological properties (edge states, quantized spin Hall conductivities, and the number of zero mode on a π-flux). We find that at the topological quantum phase transitions (TQPTs), the topological "order parameter" — spin Chern number will jump. And since the masses of the nodal fermions will change sign, the third derivative of ground-state energy is nonanalytic. In addition, we discuss the finite temperature properties and the stability of the TQPTs.

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Marra, Pasquale, Alessandro Braggio, and Roberta Citro. "A zero-dimensional topologically nontrivial state in a superconducting quantum dot." Beilstein Journal of Nanotechnology 9 (June 8, 2018): 1705–14. http://dx.doi.org/10.3762/bjnano.9.162.

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The classification of topological states of matter in terms of unitary symmetries and dimensionality predicts the existence of nontrivial topological states even in zero-dimensional systems, i.e., systems with a discrete energy spectrum. Here, we show that a quantum dot coupled with two superconducting leads can realize a nontrivial zero-dimensional topological superconductor with broken time-reversal symmetry, which corresponds to the finite size limit of the one-dimensional topological superconductor. Topological phase transitions corresponds to a change of the fermion parity, and to the presence of zero-energy modes and discontinuities in the current–phase relation at zero temperature. These fermion parity transitions therefore can be revealed by the current discontinuities or by a measure of the critical current at low temperatures.

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Lian, Biao, Xiao-Qi Sun, Abolhassan Vaezi, Xiao-Liang Qi, and Shou-Cheng Zhang. "Topological quantum computation based on chiral Majorana fermions." Proceedings of the National Academy of Sciences 115, no. 43 (October 8, 2018): 10938–42. http://dx.doi.org/10.1073/pnas.1810003115.

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The chiral Majorana fermion is a massless self-conjugate fermion which can arise as the edge state of certain 2D topological matters. It has been theoretically predicted and experimentally observed in a hybrid device of a quantum anomalous Hall insulator and a conventional superconductor. Its closely related cousin, the Majorana zero mode in the bulk of the corresponding topological matter, is known to be applicable in topological quantum computations. Here we show that the propagation of chiral Majorana fermions leads to the same unitary transformation as that in the braiding of Majorana zero modes and propose a platform to perform quantum computation with chiral Majorana fermions. A Corbino ring junction of the hybrid device can use quantum coherent chiral Majorana fermions to implement the Hadamard gate and the phase gate, and the junction conductance yields a natural readout for the qubit state.

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Elben, Andreas, Jinlong Yu, Guanyu Zhu, Mohammad Hafezi, Frank Pollmann, Peter Zoller, and Benoît Vermersch. "Many-body topological invariants from randomized measurements in synthetic quantum matter." Science Advances 6, no. 15 (April 2020): eaaz3666. http://dx.doi.org/10.1126/sciadv.aaz3666.

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Many-body topological invariants, as quantized highly nonlocal correlators of the many-body wave function, are at the heart of the theoretical description of many-body topological quantum phases, including symmetry-protected and symmetry-enriched topological phases. Here, we propose and analyze a universal toolbox of measurement protocols to reveal many-body topological invariants of phases with global symmetries, which can be implemented in state-of-the-art experiments with synthetic quantum systems, such as Rydberg atoms, trapped ions, and superconducting circuits. The protocol is based on extracting the many-body topological invariants from statistical correlations of randomized measurements, implemented with local random unitary operations followed by site-resolved projective measurements. We illustrate the technique and its application in the context of the complete classification of bosonic symmetry-protected topological phases in one dimension, considering in particular the extended Su-Schrieffer-Heeger spin model, as realized with Rydberg tweezer arrays.

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Barbachoux, Cécile, and Joseph Kouneiher. "Dark matter as residual of topological changes." International Journal of Geometric Methods in Modern Physics 13, no. 03 (March 2016): 1650027. http://dx.doi.org/10.1142/s0219887816500274.

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We investigate in this paper the possibilities that the observed cold dark matter density can be generated by decays of a heavy scalar field which dominate the universe at the quantum regime. Indeed, we present two approaches based on an extension of quantum field theory to the case when spacetime topology fluctuates (spacetime foam, at the quantum regime). In this extension the number of bosonic fields becomes a variable and the ground state is characterized by a finite particle number density. In the second approach it is the gauge-group parameters which became dynamical. This is tributary on the Centrally Extended Group and Cohomology.

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14

Sinev, Ivan, Mengyao Li, Fedor Benimetskiy, Tatiana Ivanova, Svetlana Kiriushechkina, Anton Vakulenko, Sriram Guddala, Dmitry Krizhanovskii, Anton Samusev, and Alexander Khanikaev. "Strong light-matter coupling in topological metasurfaces integrated with transition metal dichalcogenides." Journal of Physics: Conference Series 2015, no. 1 (November 1, 2021): 012142. http://dx.doi.org/10.1088/1742-6596/2015/1/012142.

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Abstract Strong light-matter interactions enable unique nonlinear and quantum phenomena at moderate light intensities. Within the last years, polaritonic metasurfaces emerged as a viable candidate for realization of such regimes. In particular, planar photonic structures integrated with 2D excitonic materials, such as transition metal dichalcogenides (TMD), can support exciton polaritons – half-light half-matter quasiparticles. Here, we explore topological exciton polaritons which are formed in a suitably engineered all-dielectric topological photonic metasurface coupled to TMD monolayers. We experimentally demonstrate the transition of topological charge from photonic to polaritonic bands with the onset of strong coupling regime and confirm the presence of one-way spin-polarized edge topological polaritons. The proposed system constitutes a promising platform for photonic/solid-state interfaces for valleytronics and spintronics.

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Phat, Tran Huu, and Nguyen Van Thu. "Topological phase transition in asymmetric nuclear matter." International Journal of Modern Physics E 23, no. 05 (May 2014): 1450031. http://dx.doi.org/10.1142/s0218301314500311.

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Starting from an effective model of asymmetric nuclear matter we show that at finite temperature T and baryon chemical potential μB there exists a topological phase transition from state of non-Fermi liquid to that of Fermi liquid which is protected by winding numbers. At low μB the transition is first-order, then extends to a second-order phase transition at larger μB through a tri-critical point. The isospin dependences of the tri-critical point and the phase diagram in the (T, μB)-plane are established. The distinction between this type of phase transition and the similar phenomenon caused by the Silver Blaze property (SBP) at T = 0 is confirmed for isospin varying from 0 to 1. We reveal that the topological phase transition could emerge in a large class of nuclear theories.

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16

Bañados, Máximo. "The ground state of general relativity, topological theories and dark matter." Classical and Quantum Gravity 24, no. 23 (November 21, 2007): 5911–16. http://dx.doi.org/10.1088/0264-9381/24/23/013.

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Zhang, Ming-Ming, Lei Xu, and Jun Zhang. "Topological insulator state in gated bilayer silicene." Journal of Physics: Condensed Matter 27, no. 44 (October 16, 2015): 445301. http://dx.doi.org/10.1088/0953-8984/27/44/445301.

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BANERJEE, DIPTI. "TOPOLOGICAL TRANSPORT IN EDGE STATE OF HIERARCHIES." Modern Physics Letters B 14, no. 05 (February 28, 2000): 181–86. http://dx.doi.org/10.1142/s0217984900000264.

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We have given here a topological approach of edge current flowing through one compressible state at the edge hierarchies. The shift quantum number visualized through deviation of the Berry phase has played a major role in realizing the edge transport theory.

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Zhong, Hua, Yongdong Li, Daohong Song, Yaroslav V. Kartashov, Yiqi Zhang, Yanpeng Zhang, and Zhigang Chen. "Topological Valley Hall Edge State Lasing." Laser & Photonics Reviews 14, no. 7 (June 22, 2020): 2000001. http://dx.doi.org/10.1002/lpor.202000001.

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Hu, M., X. Zong, J. Zheng, J. J. Mann, Z. Li, S. P. Pantazatos, Y. Li, et al. "Risperidone-induced topological alterations of anatomical brain network in first-episode drug-naive schizophrenia patients: a longitudinal diffusion tensor imaging study." Psychological Medicine 46, no. 12 (June 24, 2016): 2549–60. http://dx.doi.org/10.1017/s0033291716001380.

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BackgroundIt remains unclear whether the topological deficits of the white matter network documented in cross-sectional studies of chronic schizophrenia patients are due to chronic illness or to other factors such as antipsychotic treatment effects. To answer this question, we evaluated the white matter network in medication-naive first-episode schizophrenia patients (FESP) before and after a course of treatment.MethodWe performed a longitudinal diffusion tensor imaging study in 42 drug-naive FESP at baseline and then after 8 weeks of risperidone monotherapy, and compared them with 38 healthy volunteers. Graph theory was utilized to calculate the topological characteristics of brain anatomical network. Patients’ clinical state was evaluated using the Positive and Negative Syndrome Scale (PANSS) before and after treatment.ResultsPretreatment, patients had relatively intact overall topological organizations, and deficient nodal topological properties primarily in prefrontal gyrus and limbic system components such as the bilateral anterior and posterior cingulate. Treatment with risperidone normalized topological parameters in the limbic system, and the enhancement positively correlated with the reduction in PANSS-positive symptoms. Prefrontal topological impairments persisted following treatment and negative symptoms did not improve.ConclusionsDuring the early phase of antipsychotic medication treatment there are region-specific alterations in white matter topological measures. Limbic white matter topological dysfunction improves with positive symptom reduction. Prefrontal deficits and negative symptoms are unresponsive to medication intervention, and prefrontal deficits are potential trait biomarkers and targets for negative symptom treatment development.

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Sun, Yun-Lei, and En-Jia Ye. "Linear AC transport in T-stub and crossed silicene nanosystems." International Journal of Modern Physics B 32, no. 03 (January 22, 2018): 1850016. http://dx.doi.org/10.1142/s0217979218500169.

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In this work, we theoretically study the linear AC transport properties in T-stub and crossed zigzag silicene nanosystems. The DC conductance and AC emittance are numerically calculated based on the tight-binding approach and AC transport theory, by considering the nearest-neighbor hopping, second-nearest-neighbor spin-orbit interaction (SOI) and external electric field. The relatively strong SOI of silicene was demonstrated to induce a topological quantum edge state in the nanosystems by the local density of states, which eliminates the AC emittance response at the Dirac point. Further investigations suggest that the SOI-induced AC transport is topologically protected from the changes of geometrical size. Moreover, the AC transport properties of these nanosystems can be tuned by the external electric field, which would open an energy gap and destroy the topological quantum state, making them trivial band insulators.

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Scappucci, G., P. J. Taylor, J. R. Williams, T. Ginley, and S. Law. "Crystalline materials for quantum computing: Semiconductor heterostructures and topological insulators exemplars." MRS Bulletin 46, no. 7 (July 2021): 596–606. http://dx.doi.org/10.1557/s43577-021-00147-8.

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AbstractHigh-purity crystalline solid-state materials play an essential role in various technologies for quantum information processing, from qubits based on spins to topological states. New and improved crystalline materials emerge each year and continue to drive new results in experimental quantum science. This article summarizes the opportunities for a selected class of crystalline materials for qubit technologies based on spins and topological states and the challenges associated with their fabrication. We start by describing semiconductor heterostructures for spin qubits in gate-defined quantum dots and benchmark GaAs, Si, and Ge, the three platforms that demonstrated two-qubit logic. We then examine novel topologically nontrivial materials and structures that might be incorporated into superconducting devices to create topological qubits. We review topological insulator thin films and move onto topological crystalline materials, such as PbSnTe, and its integration with Josephson junctions. We discuss advances in novel and specialized fabrication and characterization techniques to enable these. We conclude by identifying the most promising directions where advances in these material systems will enable progress in qubit technology.

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Xun, Russell Yang Qi. "Emerging Scientists Supplementary Issue II: Topological Circuits - A Stepping Stone in the Topological Revolution." Molecular Frontiers Journal 04, Supp01 (January 1, 2020): 1–6. http://dx.doi.org/10.1142/s2529732520970020.

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The 2016 Nobel prize in physics was awarded to the pioneers who studied topological systems in Condensed Matter Physics such as the Quantum Hall Effect, where edge currents in a material are restricted to discrete values. Topology was developed to study geometric structures where only global properties are of concern (like the number of holes in an object). It has since been applied to physical systems with remarkable success; such as circuit theory. In this project, Kirchhoff ’s Laws are reformulated so that circuits can be analysed using the powerful tool of topology. This sheds light on the properties of exotic real materials such as graphene[1]. The quantum edge effect in a polyacetylene chain happens only when the edge of the chain is conducting. This was recreated experimentally using electrical circuits. Physical laws govern the properties of the bulk in a material to that of the edge. However, dissipation introduced into circuits using voltage controlled current sources was shown to have broken these laws. Results are attributed to boundary conditions affecting all states in the bulk, not just edge states, implying a new state of matter. Studying Condensed matter systems using electrical circuits gives physicists an accessible, scalable and inexpensive way to study real materials.

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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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PAOLA, C. A., and A. M. PLATZECK. "Determination of minimum magnetic energy states in frozen plasmas." Journal of Plasma Physics 69, no. 5 (September 9, 2003): 431–38. http://dx.doi.org/10.1017/s0022377803002344.

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As is known, the minimum magnetic energy state for a frozen plasma, subject to the infinite topological constraints, corresponds to a nonlinear force-free field. The magnetic flux invariance in ideal magnetohydrodynamics is possible in important astrophysical applications. We develop a method for explicitly obtaining a minimum energy state starting from an arbitrary initial state. This method does not require the explicit use of the invariance of the differential magnetic helicities. It is particularly useful when the minimum magnetic energy state for the given topological structure is unique. We show examples of the application of the method for this kind of system.

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Chardac, Amélie, Suraj Shankar, M. Cristina Marchetti, and Denis Bartolo. "Emergence of dynamic vortex glasses in disordered polar active fluids." Proceedings of the National Academy of Sciences 118, no. 10 (March 3, 2021): e2018218118. http://dx.doi.org/10.1073/pnas.2018218118.

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In equilibrium, disorder conspires with topological defects to redefine the ordered states of matter in systems as diverse as crystals, superconductors, and liquid crystals. Far from equilibrium, however, the consequences of quenched disorder on active condensed matter remain virtually uncharted. Here, we reveal a state of strongly disordered active matter with no counterparts in equilibrium: a dynamical vortex glass. Combining microfluidic experiments and theory, we show how colloidal flocks collectively cruise through disordered environments without relaxing the topological singularities of their flows. The resulting state is highly dynamical but the flow patterns, shaped by a finite density of frozen vortices, are stationary and exponentially degenerated. Quenched isotropic disorder acts as a random gauge field turning active liquids into dynamical vortex glasses. We argue that this robust mechanism should shape the collective dynamics of a broad class of disordered active matter, from synthetic active nematics to collections of living cells exploring heterogeneous media.

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de Léséleuc, Sylvain, Vincent Lienhard, Pascal Scholl, Daniel Barredo, Sebastian Weber, Nicolai Lang, Hans Peter Büchler, Thierry Lahaye, and Antoine Browaeys. "Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms." Science 365, no. 6455 (August 1, 2019): 775–80. http://dx.doi.org/10.1126/science.aav9105.

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The concept of topological phases is a powerful framework for characterizing ground states of quantum many-body systems that goes beyond the paradigm of symmetry breaking. Topological phases can appear in condensed-matter systems naturally, whereas the implementation and study of such quantum many-body ground states in artificial matter require careful engineering. Here, we report the experimental realization of a symmetry-protected topological phase of interacting bosons in a one-dimensional lattice and demonstrate a robust ground state degeneracy attributed to protected zero-energy edge states. The experimental setup is based on atoms trapped in an array of optical tweezers and excited into Rydberg levels, which gives rise to hard-core bosons with an effective hopping generated by dipolar exchange interaction.

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Zhang, Xu, Wenjie Jiang, Jinfeng Deng, Ke Wang, Jiachen Chen, Pengfei Zhang, Wenhui Ren, et al. "Digital quantum simulation of Floquet symmetry-protected topological phases." Nature 607, no. 7919 (July 20, 2022): 468–73. http://dx.doi.org/10.1038/s41586-022-04854-3.

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AbstractQuantum many-body systems away from equilibrium host a rich variety of exotic phenomena that are forbidden by equilibrium thermodynamics. A prominent example is that of discrete time crystals1–8, in which time-translational symmetry is spontaneously broken in periodically driven systems. Pioneering experiments have observed signatures of time crystalline phases with trapped ions9,10, solid-state spin systems11–15, ultracold atoms16,17 and superconducting qubits18–20. Here we report the observation of a distinct type of non-equilibrium state of matter, Floquet symmetry-protected topological phases, which are implemented through digital quantum simulation with an array of programmable superconducting qubits. We observe robust long-lived temporal correlations and subharmonic temporal response for the edge spins over up to 40 driving cycles using a circuit of depth exceeding 240 and acting on 26 qubits. We demonstrate that the subharmonic response is independent of the initial state, and experimentally map out a phase boundary between the Floquet symmetry-protected topological and thermal phases. Our results establish a versatile digital simulation approach to exploring exotic non-equilibrium phases of matter with current noisy intermediate-scale quantum processors21.

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Okamura, Koshi. "Bloch state constrained by spatial and time-reversal symmetries." Journal of Physics A: Mathematical and Theoretical 56, no. 33 (July 28, 2023): 335003. http://dx.doi.org/10.1088/1751-8121/ace4a7.

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Abstract The time-reversal symmetry in a nonmagnetic condensed-matter system is revised to the form dependent on the spatial symmetry of two-fold rotation in addition to the conventional inversion. The Bloch state within the constraints of spatial and time-reversal symmetries is demonstrated for representative systems of Si and GaAs on the basis of first-principles calculations. The nondegenerate gapless state in a topological system is also assessed.

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Van Mechelen, Todd, and Zubin Jacob. "Unidirectional Maxwellian spin waves." Nanophotonics 8, no. 8 (June 19, 2019): 1399–416. http://dx.doi.org/10.1515/nanoph-2019-0092.

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AbstractIn this article, we develop a unified perspective of unidirectional topological edge waves in nonreciprocal media. We focus on the inherent role of photonic spin in nonreciprocal gyroelectric media, i.e. magnetized metals or magnetized insulators. Due to the large body of contradicting literature, we point out at the outset that these Maxwellian spin waves are fundamentally different from well-known topologically trivial surface plasmon polaritons. We first review the concept of a Maxwell Hamiltonian in nonreciprocal media, which immediately reveals that the gyrotropic coefficient behaves as a photon mass in two dimensions. Similar to the Dirac mass, this photonic mass opens bandgaps in the energy dispersion of bulk propagating waves. Within these bulk photonic bandgaps, three distinct classes of Maxwellian edge waves exist – each arising from subtle differences in boundary conditions. On one hand, the edge wave solutions are rigorous photonic analogs of Jackiw-Rebbi electronic edge states. On the other hand, for the exact same system, they can be high frequency photonic counterparts of the integer quantum Hall effect, familiar at zero frequency. Our Hamiltonian approach also predicts the existence of a third distinct class of Maxwellian edge wave exhibiting topological protection. This occurs in an intriguing topological bosonic phase of matter, fundamentally different from any known electronic or photonic medium. The Maxwellian edge state in this unique quantum gyroelectric phase of matter necessarily requires a sign change in gyrotropy arising from nonlocality (spatial dispersion). In a Drude system, this behavior emerges from a spatially dispersive cyclotron frequency that switches sign with momentum. A signature property of these topological electromagnetic edge states is that they are oblivious to the contacting medium, i.e. they occur at the interface of the quantum gyroelectric phase and any medium (even vacuum). This is because the edge state satisfies open boundary conditions – all components of the electromagnetic field vanish at the interface. Furthermore, the Maxwellian spin waves exhibit photonic spin-1 quantization in exact analogy with their supersymmetric spin-1/2 counterparts. The goal of this paper is to discuss these three foundational classes of edge waves in a unified perspective while providing in-depth derivations, taking into account nonlocality and various boundary conditions. Our work sheds light on the important role of photonic spin in condensed matter systems, where this definition of spin is also translatable to topological photonic crystals and metamaterials.

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Ono, Seishiro, Hoi Chun Po, and Haruki Watanabe. "Refined symmetry indicators for topological superconductors in all space groups." Science Advances 6, no. 18 (May 2020): eaaz8367. http://dx.doi.org/10.1126/sciadv.aaz8367.

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Topological superconductors are exotic phases of matter featuring robust surface states that could be leveraged for topological quantum computation. A useful guiding principle for the search of topological superconductors is to relate the topological invariants with the behavior of the pairing order parameter on the normal-state Fermi surfaces. The existing formulas, however, become inadequate for the prediction of the recently proposed classes of topological crystalline superconductors. In this work, we advance the theory of symmetry indicators for topological (crystalline) superconductors to cover all space groups. Our main result is the exhaustive computation of the indicator groups for superconductors under a variety of symmetry settings. We further illustrate the power of this approach by analyzing fourfold symmetric superconductors with or without inversion symmetry and show that the indicators can diagnose topological superconductors with surface states of different dimensionalities or dictate gaplessness in the bulk excitation spectrum.

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Yang, Fan, Shaojie Ma, Kun Ding, Shuang Zhang, and J. B. Pendry. "Continuous topological transition from metal to dielectric." Proceedings of the National Academy of Sciences 117, no. 29 (July 7, 2020): 16739–42. http://dx.doi.org/10.1073/pnas.2003171117.

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Metal and dielectric have long been thought as two different states of matter possessing highly contrasting electric and optical properties. A metal is a material highly reflective to electromagnetic waves for frequencies up to the optical region. In contrast, a dielectric is transparent to electromagnetic waves. These two different classical electrodynamic properties are distinguished by different signs of the real part of permittivity: The metal has a negative sign while the dielectric has a positive one. Here, we propose a different topological understanding of metal and dielectric. By considering metal and dielectric as just two limiting cases of a periodic metal–dielectric layered metamaterial, from which a metal can continuously transform into a dielectric by varying the metal filling ratio from 1 to 0, we further demonstrate the abrupt change of a topological invariant at a certain point during this transition, classifying the metamaterials into metallic state and dielectric state. The topological phase transition from the metallic state to the dielectric state occurs when the filling ratio is one-half. These two states generalize our previous understanding of metal and dielectric: The metamaterial with metal filling ratio larger/smaller than one-half is named as the “generalized metal/dielectric.” Interestingly, the surface plasmon polariton (SPP) at a metal/dielectric interface can be understood as the limiting case of a topological edge state.

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Doria, Mauro M., and Edinardo I. B. Rodrigues. "Properties of the spin-momentum locked state." Journal of Physics: Conference Series 2164, no. 1 (March 1, 2022): 012064. http://dx.doi.org/10.1088/1742-6596/2164/1/012064.

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Abstract Spin-momentum locking is becoming a cornerstone for the understanding and applications of novel condensed matter systems. Here we assume that it holds locally in position space and from it predict the existence of a local magnetic field. Although residual, this local magnetic field is important because it brings the topological stability that transforms particles into quasi-particles. The present approach shows that the Rashba term is already contained in the Schrödinger kinetic energy and a Dirac linear spectrum can be obtained without invoking a Dirac equation for the particles.

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NECHAEV, SERGEI. "OVERVIEW OF POLYMER TOPOLOGY." International Journal of Modern Physics B 04, no. 11n12 (September 1990): 1809–47. http://dx.doi.org/10.1142/s0217979290000899.

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The modern state of the theory of topological constraints in statistical physics of polymers is reviewed. Attention is paid mainly to the most general problems concerning the topological properties of polymers represented as Markov paths. The different approaches and methods used for solving the concrete topological problems are systematized. On the phenomenological level the role of topological constraints in kinetics of polymers is investigated.

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Schmeltzer, D., and A. Saxena. "Surface state photoelectrons in topological insulators: Green’s function approach." Journal of Physics: Condensed Matter 27, no. 48 (November 13, 2015): 485601. http://dx.doi.org/10.1088/0953-8984/27/48/485601.

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HE, CHENG, LIANG LIN, XIAO-CHEN SUN, XIAO-PING LIU, MING-HUI LU, and YAN-FENG CHEN. "TOPOLOGICAL PHOTONIC STATES." International Journal of Modern Physics B 28, no. 02 (December 15, 2013): 1441001. http://dx.doi.org/10.1142/s021797921441001x.

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As exotic phenomena in optics, topological states in photonic crystals have drawn much attention due to their fundamental significance and great potential applications. Because of the broken time-reversal symmetry under the influence of an external magnetic field, the photonic crystals composed of magneto-optical materials will lead to the degeneracy lifting and show particular topological characters of energy bands. The upper and lower bulk bands have nonzero integer topological numbers. The gapless edge states can be realized to connect two bulk states. This topological photonic states originated from the topological property can be analogous to the integer quantum Hall effect in an electronic system. The gapless edge state only possesses a single sign of gradient in the whole Brillouin zone, and thus the group velocity is only in one direction leading to the one-way energy flow, which is robust to disorder and impurity due to the nontrivial topological nature of the corresponding electromagnetic states. Furthermore, this one-way edge state would cross the Brillouin center with nonzero group velocity, where the negative-zero-positive phase velocity can be used to realize some interesting phenomena such as tunneling and backward phase propagation. On the other hand, under the protection of time-reversal symmetry, a pair of gapless edge states can also be constructed by using magnetic–electric coupling meta-materials, exhibiting Fermion-like spin helix topological edge states, which can be regarded as an optical counterpart of topological insulator originating from the spin–orbit coupling. The aim of this article is to have a comprehensive review of recent research literatures published in this emerging field of photonic topological phenomena. Photonic topological states and their related phenomena are presented and analyzed, including the chiral edge states, polarization dependent transportation, unidirectional waveguide and nonreciprocal optical transmission, all of which might lead to novel applications such as one-way splitter, optical isolator and delay line. In addition, the possible prospect and development of related topics are also discussed.

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Lai, Hsin-Hua, and Hsiang-Hsuan Hung. "Short-ranged interaction effects on Z2 topological phase transitions: The perturbative mean-field method." International Journal of Modern Physics B 29, no. 06 (March 2, 2015): 1530005. http://dx.doi.org/10.1142/s0217979215300054.

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Time-reversal symmetric topological insulator (TI) is a novel state of matter that a bulk-insulating state carries dissipationless spin transport along the surfaces, embedded by the Z2 topological invariant. In the noninteracting limit, this exotic state has been intensively studied and explored with realistic systems, such as HgTe/(Hg, Cd)Te quantum wells. On the other hand, electronic correlation plays a significant role in many solid-state systems, which further influences topological properties and triggers topological phase transitions. Yet an interacting TI is still an elusive subject and most related analyses rely on the mean-field approximation and numerical simulations. Among the approaches, the mean-field approximation fails to predict the topological phase transition, in particular at intermediate interaction strength without spontaneously breaking symmetry. In this paper, we develop an analytical approach based on a combined perturbative and self-consistent mean-field treatment of interactions that is capable of capturing topological phase transitions beyond either method when used independently. As an illustration of the method, we study the effects of short-ranged interactions on the Z2 TI phase, also known as the quantum spin Hall (QSH) phase, in three generalized versions of the Kane–Mele (KM) model at half-filling on the honeycomb lattice. The results are in excellent agreement with quantum Monte Carlo (QMC) calculations on the same model and cannot be reproduced by either a perturbative treatment or a self-consistent mean-field treatment of the interactions. Our analytical approach helps to clarify how the symmetries of the one-body terms of the Hamiltonian determine whether interactions tend to stabilize or destabilize a topological phase. Moreover, our method should be applicable to a wide class of models where topological transitions due to interactions are in principle possible, but are not correctly predicted by either perturbative or self-consistent treatments.

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LIN, HAI, and SHING-TUNG YAU. "ON EXOTIC SPHERE FIBRATIONS, TOPOLOGICAL PHASES, AND EDGE STATES IN PHYSICAL SYSTEMS." International Journal of Modern Physics B 27, no. 19 (July 15, 2013): 1350107. http://dx.doi.org/10.1142/s0217979213501075.

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We suggest that exotic sphere fibrations can be mapped to band topologies in condensed matter systems. These fibrations can correspond to geometric phases of two double bands or state vector bases with second Chern numbers m+n and -n, respectively. They can be related to topological insulators, magnetoelectric effects, and photonic crystals with special edge states. We also consider time-reversal symmetry breaking perturbations of topological insulator, and heterostructures of topological insulators with normal insulators and with superconductors. We consider periodic TI/NI/TI/NI′ heterostructures, and periodic TI/SC/TI/SC′ heterostructures. They also give rise to models of Weyl semimetals which have thermal and electrical transports.

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Nguyen, Thi Thuy Nhung, Niels de Vries, Hrag Karakachian, Markus Gruschwitz, Johannes Aprojanz, Alexei A. Zakharov, Craig Polley, et al. "Topological Surface State in Epitaxial Zigzag Graphene Nanoribbons." Nano Letters 21, no. 7 (April 5, 2021): 2876–82. http://dx.doi.org/10.1021/acs.nanolett.0c05013.

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Yan, Yuan, Zhi-Min Liao, Xiaoxing Ke, Gustaaf Van Tendeloo, Qinsheng Wang, Dong Sun, Wei Yao, et al. "Topological Surface State Enhanced Photothermoelectric Effect in Bi2Se3Nanoribbons." Nano Letters 14, no. 8 (July 23, 2014): 4389–94. http://dx.doi.org/10.1021/nl501276e.

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41

Huang, Beibing, Xiaosen Yang, Qinfang Zhang, and Ning Xu. "Chiral Majorana edge modes and vortex Majorana zero modes in superconducting antiferromagnetic topological insulator." Journal of Physics: Condensed Matter 34, no. 11 (January 4, 2022): 115503. http://dx.doi.org/10.1088/1361-648x/ac4531.

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Abstract The antiferromagnetic topological insulator (AFTI) is topologically protected by the combined time-reversal and translational symmetry T c . In this paper we investigate the effects of the s-wave superconducting pairings on the multilayers of AFTI, which breaks T c symmetry and can realize quantum anomalous Hall insulator with unit Chern number. For the weakly coupled pairings, the system corresponds to the topological superconductor (TSC) with the Chern number C = ±2. We answer the following questions whether the local Chern numbers and chiral Majorana edge modes of such a TSC distribute around the surface layers. By the numerical calculations based on a theoretic model of AFTI, we find that when the local Chern numbers are always dominated by the surface layers, the wavefunctions of chiral Majorana edge modes must not localize on the surface layers and show a smooth crossover from spatially occupying all layers to only distributing near the surface layers, similar to the hinge states in a three dimensional second-order topological phases. The latter phase, denoted by the hinged TSC, can be distinguished from the former phase by the measurements of the local density of state. In addition we also study the superconducting vortex phase transition in this system and find that the exchange field in the AFTI not only enlarges the phase space of topological vortex phase but also enhances its topological stability. These conclusions will stimulate the investigations on superconducting effects of AFTI and drive the studies on chiral Majorana edge modes and vortex Majorana zero modes into a new era.

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ZHAO, BO, and ZENG-BING CHEN. "EDGE STATE IN ATOMIC HALL EFFECT." Modern Physics Letters B 18, no. 21n22 (September 30, 2004): 1127–33. http://dx.doi.org/10.1142/s0217984904007645.

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We study the edge state of atomic Hall fluids. It is described by a chiral 1D bosonic field theory and the atomic excitations are a type of bosonic Luttinger liquid. We investigate the dynamical property of edge state and propose an experiment to measure the topological number, which could be verified experimentally in future.

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Teng, Yu Jia. "Heusler Compounds and their Topological Semimetal States." Materials Science Forum 1027 (April 2021): 33–41. http://dx.doi.org/10.4028/www.scientific.net/msf.1027.33.

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Heusler compounds are a family of materials with high tunability due to their structure and lots of states or properties have been discovered in it. Topological semimetals (TSM) are a new phase of quantum matter that many materials have been reported to have this phase, including Heusler compounds. In this review, basic concepts of Heusler compounds and main properties of three TSMs are first reviewed, followed by analysis of topological semimetal states in Heusler compounds. In the end, the most suitable TSM state in Heusler compound is given.

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Lesser, Omri, and Yuval Oreg. "Majorana zero modes induced by superconducting phase bias." Journal of Physics D: Applied Physics 55, no. 16 (January 21, 2022): 164001. http://dx.doi.org/10.1088/1361-6463/ac4a37.

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Abstract Majorana zero modes in condensed matter systems have been the subject of much interest in recent years. Their non-Abelian exchange statistics, making them a unique state of matter, and their potential applications in topological quantum computation, earned them attention from both theorists and experimentalists. It is generally understood that in order to form Majorana zero modes in quasi-one-dimensional topological insulators, time-reversal symmetry must be broken. The straightforward mechanisms for doing so—applying magnetic fields or coupling to ferromagnets—turned out to have many unwanted side effects, such as degradation of superconductivity and the formation of sub-gap states, which is part of the reason Majorana zero modes have been eluding direct experimental detection for a long time. Here we review several proposal that rely on controlling the phase of the superconducting order parameter, either as the sole mechanism for time-reversal-symmetry breaking, or as an additional handy knob used to reduce the applied magnetic field. These proposals hold practical promise to improve Majorana formation, and they shed light on the physics underlying the formation of the topological superconducting state.

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Li, Xiao-Xue, Yun-Tuan Fang, and Li-Xia Yang. "Dual modulation of topological edge states from two-dimensional photonic crystals with lattice shrink." Modern Physics Letters B 35, no. 14 (March 12, 2021): 2150236. http://dx.doi.org/10.1142/s0217984921502365.

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The current topological edge states lack dynamical modulation and the intense field localization effect. To solve these problems, we construct a topological edge state structure based on two-dimensional photonic crystals with lattice shrink. Through the optimization of structure parameters, a nearly flat edge state dispersion curve occurs in a wide bandgap. The topological edge states with intense field localization take on some unique properties such that the transport directions can be controlled by both the source spin and the source position. The transport modes can be dynamically switched between the two opposite unidirectional channels just through moving the source position.

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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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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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Biesenthal, Tobias, Lukas J. Maczewsky, Zhаoju Yang, Mark Kremer, Mordechai Segev, Alexander Szameit, and Matthias Heinrich. "Fractal photonic topological insulators." Science, May 12, 2022. http://dx.doi.org/10.1126/science.abm2842.

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Topological insulators constitute a novel state of matter with scatter-free edge states surrounding an insulating bulk. Conventional wisdom regards the insulating bulk as essential, since the invariants describing the topological properties of the system are defined therein. Here, we study fractal topological insulators based on exact fractals comprised exclusively of edge sites. We present experimental proof that, despite the lack of bulk bands, photonic lattices of helical waveguides support topologically protected chiral edge states. We show that light transport in our topological fractal system features increased velocities compared to the corresponding honeycomb lattice. By going beyond the confines of the bulk-boundary correspondence, our findings pave the way toward an expanded perception of topological insulators and open a new chapter of topological fractals.

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Denner, M. Michael, Anastasiia Skurativska, Frank Schindler, Mark H. Fischer, Ronny Thomale, Tomáš Bzdušek, and Titus Neupert. "Exceptional topological insulators." Nature Communications 12, no. 1 (September 28, 2021). http://dx.doi.org/10.1038/s41467-021-25947-z.

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AbstractWe introduce the exceptional topological insulator (ETI), a non-Hermitian topological state of matter that features exotic non-Hermitian surface states which can only exist within the three-dimensional topological bulk embedding. We show how this phase can evolve from a Weyl semimetal or Hermitian three-dimensional topological insulator close to criticality when quasiparticles acquire a finite lifetime. The ETI does not require any symmetry to be stabilized. It is characterized by a bulk energy point gap, and exhibits robust surface states that cover the bulk gap as a single sheet of complex eigenvalues or with a single exceptional point. The ETI can be induced universally in gapless solid-state systems, thereby setting a paradigm for non-Hermitian topological matter.

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Corbae, Paul, Julia D. Hannukainen, Quentin Marsal, Daniel Muñoz-Segovia, and Adolfo G. Grushin. "Amorphous topological matter: Theory and experiment." Europhysics Letters, March 9, 2023. http://dx.doi.org/10.1209/0295-5075/acc2e2.

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Abstract Topological phases of matter are ubiquitous in crystals, but less is known about their existence in amorphous systems, that lack long-range order. In this perspective, we review the recent progress made on theoretically defining amorphous topological phases and the newphenomenology that they can open. We revisit key experiments suggesting that amorphous topological phases exist in both solid-state and synthetic amorphous systems. We finish by discussing the open questions in the field, that promises to significantly enlarge the set of materials andsynthetic systems benefiting from the robustness of topological matter.

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Journal articles on the topic 'Topological state of matter'

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