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1. Topological quadratic-node semimetal in a photonic microring lattice

   https://doi.org/10.1038/s41467-023-38861-3  

   Gao, Zihe; Zhao, Haoqi; Wu, Tianwei; Feng, Xilin; Zhang, Zhifeng; Qiao, Xingdu; Chiu, Ching-Kai; Feng, Liang (December 2023, Nature Communications)

   Abstract Graphene, with its two linearly dispersing Dirac points with opposite windings, is the minimal topological nodal configuration in the hexagonal Brillouin zone. Topological semimetals with higher-order nodes beyond the Dirac points have recently attracted considerable interest due to their rich chiral physics and their potential for the design of next-generation integrated devices. Here we report the experimental realization of the topological semimetal with quadratic nodes in a photonic microring lattice. Our structure hosts a robust second-order node at the center of the Brillouin zone and two Dirac points at the Brillouin zone boundary—the second minimal configuration, next to graphene, that satisfies the Nielsen–Ninomiya theorem. The symmetry-protected quadratic nodal point, together with the Dirac points, leads to the coexistence of massive and massless components in a hybrid chiral particle. This gives rise to unique transport properties, which we demonstrate by directly imaging simultaneous Klein and anti-Klein tunnelling in the microring lattice. 

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2. Classification of Classical Spin Liquids: Typology and Resulting Landscape

   Yan, Han; Benton, Owen; Moessner, Roderich; Nevidomskyy, Andriy H. (April 2023, arXivorg)

   Classical spin liquids (CSL) lack long-range magnetic order and are characterized by an extensive ground state degeneracy. We propose a classification scheme of CSLs based on the structure of the flat bands of their Hamiltonians. Depending on absence or presence of the gap from the flat band, the CSL are classified as algebraic or fragile topological, respectively. Each category is further classified: the algebraic case by the nature of the emergent Gauss's law at the gap-closing point(s), and the fragile topological case by the homotopy of the eigenvector winding around the Brillouin zone. Previously identified instances of CSLs fit snugly into our scheme, which finds a landscape where algebraic CSLs are located at transitions between fragile topological ones. It also allows us to present a new, simple family of models illustrating that landscape, which hosts both fragile topological and algebraic CSLs, as well as transitions between them 

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3. First-principles study of the electronic structure, Z 2 invariant, and quantum oscillation in the kagome material CsV3Sb5

   https://doi.org/10.1063/5.0232167  

   Bhandari, Shalika R; Zeeshan, Mohd; Gusain, Vivek; Shrestha, Keshav; Rai, D P (December 2024, APL Quantum)

   NA (Ed.)

   This work presents a detailed study of the electronic structure, phonon dispersion, Z2 invariant calculation, and Fermi surface of the newly discovered kagome superconductor CsV3Sb5, using density functional theory. The phonon dispersion in the pristine state reveals two negative modes at the M and L points of the Brillouin zone, indicating lattice instability. CsV3Sb5 transitions into a structurally stable 2 × 2 × 1 charge density wave (CDW) phase, confirmed by positive phonon modes. The electronic band structure shows several Dirac points near the Fermi level, with a narrow gap opening due to spin–orbit coupling (SOC), although the effect of SOC on other bands is minimal. In the pristine phase, this material exhibits a quasi-2D cylindrical Fermi surface, which undergoes reconstruction in the CDW phase. We calculated quantum oscillation frequencies using Onsager’s relation, finding good agreement with experimental results in the CDW phase. To explore the topological properties of CsV3Sb5, we computed the Z2 invariant in both pristine and CDW phases, resulting in a value of (ν0; ν1ν2ν3) = (1; 000), suggesting the strong topological nature of this material. Our detailed analysis of phonon dispersion, electronic bands, Fermi surface mapping, and Z2 invariant provides insights into the topological properties, CDW order, and unconventional superconductivity in AV3Sb5 (A = K, Rb, and Cs). 

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4. Dirac points for twisted bilayer graphene with in-plane magnetic field

   https://doi.org/10.4171/JST/504  

   Becker, Simon; Zworski, Maciej (June 2024, Journal of Spectral Theory)

   We study Dirac points of the chiral model of twisted bilayer graphene (TBG) with constant in-plane magnetic field. The striking feature of the chiral model is the presence of perfectly flat bands atmagic anglesof twisting. The Dirac points for zero magnetic field and non-magic angles of twisting are fixed at high symmetry pointsKandK'in the Brillouin zone, with\Gammadenoting the remaining high symmetry point. For a fixed small constant in-plane magnetic field, we show that as the angle of twisting varies between magic angles, the Dirac points move betweenK,K'points and the\Gammapoint. In particular, near magic angles, the Dirac points are located near the\Gammapoint. For special directions of the magnetic field, we show that the Dirac points move, as the twisting angle varies, along straight lines and bifurcate orthogonally at distinguished points. At the bifurcation points, the linear dispersion relation of the merging Dirac points disappears and exhibit a quadratic band crossing point (QBCP). The results are illustrated by links to animations suggesting interesting additional structure. 

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5. Quantized topological phases beyond square lattices in Floquet synthetic dimensions [Invited]

   https://doi.org/10.1364/OME.546801  

   Sriram, Samarth; Sridhar, Sashank_Kaushik; Dutt, Avik (January 2025, Optical Materials Express)

   Topological effects manifest in a variety of lattice geometries. While square lattices, due to their simplicity, have been used for models supporting nontrivial topology, several exotic topological phenomena such as Dirac points, Weyl points, and Haldane phases are most commonly supported by non-square lattices. Examples of prototypical non-square lattices include the honeycomb lattice of graphene and 2D materials, and the Kagome lattice, both of which break fundamental symmetries and can exhibit quantized transport, especially when long-range hoppings and gauge fields are incorporated. The challenge of controllably realizing such long-range hoppings and gauge fields has motivated a large body of research focused on harnessing lattices encoded in synthetic dimensions. Photons in particular have many internal degrees of freedom and hence show promise for implementing these synthetic dimensions; however, most photonic synthetic dimensions have hitherto created 1D or 2D square lattices. Here we show that non-square lattice Hamiltonians such as the Haldane model and its variations can be implemented using Floquet synthetic dimensions. Our construction uses dynamically modulated ring resonators and provides the capacity for directk-space engineering of lattice Hamiltonians. Thisk-space construction lifts constraints on the orthogonality of lattice vectors that make square geometries simpler to implement in lattice-space constructions and instead transfers the complexity to the engineering of tailored, complex Floquet drive signals. We simulate topological signatures of the Haldane and the brick-wall Haldane model and observe them to be robust in the presence of external optical drive and photon loss, and discuss unique characteristics of their topological transport when implemented on these Floquet lattices. Our proposal demonstrates the potential of driven-dissipative Floquet synthetic dimensions as a new architecture fork-space Hamiltonian simulation of high-dimensional lattice geometries, supported by scalable photonic integration, that lifts the constraints of several existing platforms for topological photonics and synthetic dimensions. 

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