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1. Emergence of Nontrivial Low‐Energy Dirac Fermions in Antiferromagnetic EuCd 2 As 2

   https://doi.org/10.1002/adma.201907565  

   Ma, Junzhang ; Wang, Han ; Nie, Simin ; Yi, Changjiang ; Xu, Yuanfeng ; Li, Hang ; Jandke, Jasmin ; Wulfhekel, Wulf ; Huang, Yaobo ; West, Damien ; et al ( February 2020 , Advanced Materials)

   Parity‐time symmetry plays an essential role for the formation of Dirac states in Dirac semimetals. So far, all of the experimentally identified topologically nontrivial Dirac semimetals (DSMs) possess both parity and time reversal symmetry. The realization of magnetic topological DSMs remains a major issue in topological material research. Here, combining angle‐resolved photoemission spectroscopy with density functional theory calculations, it is ascertained that band inversion induces a topologically nontrivial ground state in EuCd₂As₂. As a result, ideal magnetic Dirac fermions with simplest double cone structure near the Fermi level emerge in the antiferromagnetic (AFM) phase. The magnetic order breaks time reversal symmetry, but preserves inversion symmetry. The double degeneracy of the Dirac bands is protected by a combination of inversion, time‐reversal, and an additional translation operation. Moreover, the calculations show that a deviation of the magnetic moments from thec‐axis leads to the breaking of C3 rotation symmetry, and thus, a small bandgap opens at the Dirac point in the bulk. In this case, the system hosts a novel state containing three different types of topological insulator: axion insulator, AFM topological crystalline insulator (TCI), and higher order topological insulator. The results provide an enlarged platform for the quest of topological Dirac fermions in a magnetic system.

    

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2. Revealing topological attributes of stiff plates by Dirac factorization of their 2D elastic wave equation

   https://doi.org/10.1063/5.0086559  

   Deymier, P. A. ; Runge, K. ( February 2022 , Applied Physics Letters)

   Dirac factorization of the elastic wave equation of two-dimension stiff plates coupled to a rigid substrate reveals the possible topological properties of elastic waves in this system. These waves may possess spin-like degrees of freedom associated with a gapped band structure reminiscent of the spin Hall effect. In semi-infinite plates or strips with zero displacement edges, the Dirac-factored elastic wave equation shows the possibility of edge modes moving in opposite directions. The finite size of strips leads to overlap between edge modes consequently opening a gap in their spectrum eliminating the spin Hall-like effects. This Dirac factorization tells us what solutions of the elastic wave equation would be if we could break some symmetry. Dirac factorization does not break symmetry but simply exposes what topological properties of elastic waves may result from symmetry breaking structural or external perturbations.

    

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3. Dirac lines and loop at the Fermi level in the time-reversal symmetry breaking superconductor LaNiGa2

   https://doi.org/10.1038/s42005-021-00771-5  

   Badger, Jackson R. ; Quan, Yundi ; Staab, Matthew C. ; Sumita, Shuntaro ; Rossi, Antonio ; Devlin, Kasey P. ; Neubauer, Kelly ; Shulman, Daniel S. ; Fettinger, James C. ; Klavins, Peter ; et al ( December 2022 , Communications Physics)

   Abstract Unconventional superconductors have Cooper pairs with lower symmetries than in conventional superconductors. In most unconventional superconductors, the additional symmetry breaking occurs in relation to typical ingredients such as strongly correlated Fermi liquid phases, magnetic fluctuations, or strong spin-orbit coupling in noncentrosymmetric structures. In this article, we show that the time-reversal symmetry breaking in the superconductor LaNiGa 2 is enabled by its previously unknown topological electronic band structure, with Dirac lines and a Dirac loop at the Fermi level. Two symmetry related Dirac points even remain degenerate under spin-orbit coupling. These unique topological features enable an unconventional superconducting gap in which time-reversal symmetry can be broken in the absence of other typical ingredients. Our findings provide a route to identify a new type of unconventional superconductors based on nonsymmorphic symmetries and will enable future discoveries of topological crystalline superconductors. 

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4. Weighing Dirac fermions by nonlinear Hall effect

   Wang, Yang ; Mambakkam, Sivakumar V. ; Law, Stephanie A. ; Xiao, John. Q. ( March 2022 , ArXivorg)

   Breaking the time-reversal symmetry on the surface of a topological insulator can open a gap for the linear dispersion and make the Dirac fermions massive. This can be achieved by either doping a topological insulator with magnetic elements or proximity-coupling it to magnetic insulators. While the exchange gap can be directly imaged in the former case, measuring it at the buried magnetic insulator/topological insulator interface remains to be challenging. Here, we report the observation of a large nonlinear Hall effect in iron garnet/Bi2Se3 heterostructures. Besides illuminating its magnetic origin, we also show that this nonlinear Hall effect can be utilized to measure the size of the exchange gap and the magnetic-proximity onset temperature. Our results demonstrate the nonlinear Hall effect as a spectroscopic tool to probe the modified band structure at magnetic insulator/topological insulator interfaces. 

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5. Classifying Topology in Photonic Heterostructures with Gapless Environments

   https://doi.org/10.1103/PhysRevLett.131.213801  

   Dixon, Kahlil Y. ; Loring, Terry A. ; Cerjan, Alexander ( November 2023 , Physical Review Letters)

   Photonic topological insulators exhibit bulk-boundary correspondence, which requires that boundary-localized states appear at the interface formed between topologically distinct insulating materials. However, many topological photonic devices share a boundary with free space, which raises a subtle but critical problem as free space is gapless for photons above the light-line. Here, we use a local theory of topological materials to resolve bulk-boundary correspondence in heterostructures containing gapless materials and in radiative environments. In particular, we construct the heterostructure’s spectral localizer, a composite operator based on the system’s real-space description that provides a local marker for the system’s topology and a corresponding local measure of its topological protection; both quantities are independent of the material’s bulk band gap (or lack thereof). Moreover, we show that approximating radiative outcoupling as material absorption overestimates a heterostructure’s topological protection. As the spectral localizer is applicable to systems in any physical dimension and in any discrete symmetry class, our results show how to calculate topological invariants, quantify topological protection, and locate topological boundary-localized resonances in topological materials that interface with gapless media in general. 

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