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Classification of flat bands according to the band-crossing singularity of Bloch wave functions
摘要： We show that ?at bands can be categorized into two distinct classes, that is, singular and nonsingular ?at bands, by exploiting the singular behavior of their Bloch wave functions in momentum space. In the case of a singular ?at band, its Bloch wave function possesses immovable discontinuities generated by the band-crossing with other bands, and thus the vector bundle associated with the ?at band cannot be de?ned. This singularity precludes the compact localized states from forming a complete set spanning the ?at band. Once the degeneracy at the band crossing point is lifted, the singular ?at band becomes dispersive and can acquire a ?nite Chern number in general, suggesting a new route for obtaining a nearly ?at Chern band. On the other hand, the Bloch wave function of a nonsingular ?at band has no singularity, and thus forms a vector bundle. A nonsingular ?at band can be completely isolated from other bands while preserving the perfect ?atness. All one-dimensional ?at bands belong to the nonsingular class. We show that a singular ?at band displays a novel bulk-boundary correspondence such that the presence of the robust boundary mode is guaranteed by the singularity of the Bloch wave function. Moreover, we develop a general scheme to construct a ?at band model Hamiltonian in which one can freely design its singular or nonsingular nature. Finally, we propose a general formula for the compact localized state spanning the ?at band, which can be easily implemented in numerics and offer a basis set useful in analyzing correlation effects in ?at bands.
关键词： Chern number,singular band touching,flat bands,nonsingular band touching,bulk-boundary correspondence,compact localized states,Bloch wave functions
更新于2025-09-23 15:23:52
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Electromagnetic and gravitational responses of photonic Landau levels
摘要： Topology has recently become a focus in condensed matter physics, arising in the context of the quantum Hall effect and topological insulators. In both of these cases, the topology of the system is defined through bulk properties (‘topological invariants’) but detected through surface properties. Here we measure three topological invariants of a quantum Hall material—photonic Landau levels in curved space—through local electromagnetic and gravitational responses of the bulk material. Viewing the material as a many-port circulator, the Chern number (a topological invariant) manifests as spatial winding of the phase of the circulator. The accumulation of particles near points of high spatial curvature and the moment of inertia of the resultant particle density distribution quantify two additional topological invariants—the mean orbital spin and the chiral central charge. We find that these invariants converge to their global values when probed over increasing length scales (several magnetic lengths), consistent with the intuition that the bulk and edges of a system are distinguishable only for sufficiently large samples (larger than roughly one magnetic length). Our experiments are enabled by applying quantum optics tools to synthetic topological matter (here twisted optical resonators). Combined with advances in Rydberg-mediated photon collisions, our work will enable precision characterization of topological matter in photon fluids.
关键词： photonic Landau levels,quantum Hall effect,chiral central charge,Chern number,mean orbital spin,topological invariants
更新于2025-09-23 15:23:52
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Crystalline topological Dirac semimetal phase in rutile structure
摘要： Based on first-principles calculations and symmetry analysis, we propose that a transition-metal rutile oxide, in particular β-PtO2, can host a three-dimensional topological Dirac semimetal phase. We find that β-PtO2 possesses an inner nodal chain structure when spin-orbit coupling is neglected. Incorporating spin-orbit coupling gaps the nodal chain while preserving a single pair of three-dimensional Dirac points protected by a screw rotation symmetry. These Dirac points are created by a band inversion of two d bands, which is a realization of a Dirac semimetal phase in a correlated electron system. Moreover, a mirror plane in the momentum space carries a nontrivial mirror Chern number nM = -2, which distinguishes β-PtO2 from the Dirac semimetals known so far, such as Na3Bi and Cd3As2. If we apply a perturbation that breaks the rotation symmetry and preserves the mirror symmetry, the Dirac points are gapped, and the system becomes a topological crystalline insulator.
关键词： PtO2,band inversion,symmetry analysis,rutile structure,topological Dirac semimetal,mirror Chern number
更新于2025-09-23 15:22:29
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Topological Quantum Optics Using Atomlike Emitter Arrays Coupled to Photonic Crystals
摘要： We propose an experimentally feasible nanophotonic platform for exploring many-body physics in topological quantum optics. Our system is composed of a two-dimensional lattice of nonlinear quantum emitters with optical transitions embedded in a photonic crystal slab. The emitters interact through the guided modes of the photonic crystal, and a uniform magnetic field gives rise to large topological band gaps, robust edge states, and a nearly flat band with a nonzero Chern number. The presence of a topologically nontrivial nearly flat band paves the way for the realization of fractional quantum Hall states and fractional topological insulators in a topological quantum optical setting.
关键词： Chern number,quantum emitters,fractional quantum Hall states,photonic crystals,topological quantum optics
更新于2025-09-23 15:21:01
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Universal numerical calculation method for the Berry curvature and Chern numbers of typical topological photonic crystals
摘要： Chern number is one of the most important criteria by which the existence of a topological photonic state among various photonic crystals can be judged; however, few reports have presented a universal numerical calculation method to directly calculate the Chern numbers of different topological photonic crystals and have denoted the in?uence of different structural parameters. Herein, we demonstrate a direct and universal method based on the ?nite element method to calculate the Chern number of the topological photonic crystals by dividing the typical Brillouin zone into small zones, establishing new properties to obtain the discrete Chern number, and simultaneously drawing the Berry curvature of the ?rst Brillouin zone. We also explore the manner in which the topological properties are in?uenced by the different structure types, air duty ratios, and rotating operations of the unit cells; meanwhile, we obtain large Chern numbers from – 2 to 4. Furthermore, we can tune the topological phase change via different rotation operations of triangular dielectric pillars. This study provides a highly ef?cient and simple method for calculating the Chern numbers and plays a major role in the prediction of novel topological photonic states.
关键词： Chern number,?nite element method,symmetry,topological photonic crystal
更新于2025-09-16 10:30:52
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Dynamics of weakly interacting bosons in optical lattices with flux
摘要： Realization of strong synthetic magnetic fields in driven optical lattices has enabled implementation of topological bands in cold-atom setups. A milestone has been reached by a recent measurement of a finite Chern number based on the dynamics of incoherent bosonic atoms. The measurements of the quantum Hall effect in semiconductors are related to the Chern-number measurement in a cold-atom setup; however, the design and complexity of the two types of measurements are quite different. Motivated by these recent developments, we investigate the dynamics of weakly interacting incoherent bosons in a two-dimensional driven optical lattice exposed to an external force, which provides a direct probe of the Chern number. We consider a realistic driving protocol in the regime of high driving frequency and focus on the role of weak repulsive interactions. We find that interactions lead to the redistribution of atoms over topological bands both through the conversion of interaction energy into kinetic energy during the expansion of the atomic cloud and due to an additional heating. Remarkably, we observe that the moderate atomic repulsion facilitates the measurement by flattening the distribution of atoms in the quasimomentum space. Our results also show that weak interactions can suppress the contribution of some higher-order nontopological terms in favor of the topological part of the effective model.
关键词： weakly interacting bosons,Chern number,topological bands,synthetic magnetic fields,optical lattices,Floquet theory
更新于2025-09-09 09:28:46
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Topological one-way fiber of second Chern number
摘要： One-way waveguides have been discovered as topological edge states in two-dimensional (2D) photonic crystals. Here, we design one-way fiber modes in a 3D magnetic Weyl photonic crystal realizable at microwave frequencies. We first obtain a 3D Chern crystal with a non-zero first Chern number by annihilating the Weyl points through supercell modulation. When the modulation becomes helixes, one-way modes develop along the winding axis, with the number of modes determined by the spatial frequency of the helix. These single-polarization single-mode and multi-mode one-way fibers, having nearly identical group and phase velocities, are topologically-protected by the second Chern number in the 4D parameter space of the 3D wavevectors plus the winding angle of the helix. This work suggests a unique way to utilize high-dimensional topological physics using topological defects.
关键词： topological defects,Chern number,Weyl photonic crystals,one-way waveguides,topological photonics
更新于2025-09-04 15:30:14