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Abstract Topological magnons give rise to possibilities for engineering novel spintronics devices with critical applications in quantum information and computation, due to their symmetry-protected robustness and low dissipation. However, to make reliable and systematic predictions about the material realization of topological magnons has been a major challenge, due to the lack of neutron scattering data for most materials and the absence of reliable ab initio calculations for magnons. In this work, we significantly advance the symmetry-based approach for identifying topological magnons through developing a fully automated algorithm, utilizing the theory of symmetry indicators, that enables a highly efficient and large-scale search for candidate materials hosting perturbation-driven topological magnons. This progress not only streamlines the discovery process but also expands the scope of materials exploration beyond previous manual or traditional approaches, offering a powerful tool for uncovering novel topological phases in magnetic systems. Performing a large-scale search over all 1649 magnetic materials in the Bilbao Crystallographic Server (BCS) with a commensurate magnetic order, we discover 387 perturbation-induced topological magnon materials, significantly expanding the pool of topological magnon materials and showing that more than 23% of all commensurate magnetic compounds in the BCS database are topological. We further discuss examples and experimental accessibility of the candidate materials, shedding light on future experimental realizations of topological magnons in magnetic materials. We provide anopen-source programthat checks the symmetry-enforced magnon band topology of any commensurate magnetic structure upon perturbations and allows researchers to reproduce our results. 

The Ginzburg-Landau (GL) theory is very successful in describing the pairing symmetry, a fundamental characterization of the broken symmetries in a paired superfluid or superconductor. However, GL theory does not describe fermionic excitations such as Bogoliubov quasiparticles or Andreev bound states that are directly related to topological properties of the superconductor. In this work, we show that the symmetries of the fermionic excitations are captured by a Projective Symmetry Group (PSG), which is a group extension of the bosonic symmetry group in the superconducting state. We further establish a correspondence between the pairing symmetry and the fermion PSG. When the normal and superconducting states share the same spin rotational symmetry, there is a simpler correspondence between the pairing symmetry and the fermion PSG, which we enumerate for all 32 crystalline point groups. We also discuss the general framework for computing PSGs when the spin rotational symmetry is spontaneously broken in the superconducting state. This PSG formalism leads to experimental consequences, and as an example, we show how a given pairing symmetry dictates the classification of topological superconductivity. 

We study the phase diagram of the Yao-Lee model with Kitaev-type spin-orbital interactions in the presence of Dzyaloshinskii-Moriya interactions and external magnetic fields. Unlike the Kitaev model, the Yao-Lee model can still be solved exactly under these perturbations due to the enlarged local Hilbert space. Through a variational analysis, we obtain a rich ground-state phase diagram that consists of a variety of vison crystals with periodic arrangements of background Z2 flux (i.e., visons). With an out-of-plane magnetic field, these phases have gapped bulk and chiral edge states, characterized by a Chern number ν and an associated chiral central charge c=ν/2 of edge states. We also find helical Majorana edge states that are protected by magnetic mirror symmetry. For the bilayer systems, we find that interlayer coupling can also stabilize new topological phases. Our results spotlight the tunability and the accompanying rich physics in exactly solvable spin-orbital generalizations of the Kitaev model.