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1. Bimorphic Floquet topological insulators

   https://doi.org/10.1038/s41563-022-01238-w  

   Pyrialakos, Georgios G.; Beck, Julius; Heinrich, Matthias; Maczewsky, Lukas J.; Kantartzis, Nikolaos V.; Khajavikhan, Mercedeh; Szameit, Alexander; Christodoulides, Demetrios N. (March 2022, Nature Materials)
2. Simulating higher-order topological insulators in density wave insulators

   https://doi.org/10.1103/PhysRevB.103.245107  

   Lin, Kuan-Sen; Bradlyn, Barry (June 2021, Physical Review B)

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3. Theory of oblique topological insulators

   https://doi.org/10.21468/SciPostPhys.14.2.023  

   Moy, Benjamin; Goldman, Hart; Sohal, Ramanjit; Fradkin, Eduardo (January 2023, SciPost Physics)

   A long-standing problem in the study of topological phases of matter has been to understand the types of fractional topological insulator (FTI) phases possible in 3+1 dimensions. Unlike ordinary topological insulators of free fermions, FTI phases are characterized by fractional 𝜃-angles,long-range entanglement, and fractionalization. Starting from a simple family of ℤ_N lattice gauge theories due to Cardy and Rabinovici, we develop a class of FTI phases based on the physical mechanism of oblique confinement and the modern language of generalized global symmetries. We dub these phases oblique topological insulators. Oblique TIs arise when dyons—bound states of electric charges and monopoles—condense, leading to FTI phases characterized by topological order, emergent one-forms symmetries, and gapped boundary states not realizable in 2+1-D alone.Based on the lattice gauge theory, we present continuum topological quantum field theories (TQFTs) for oblique TI phases involving fluctuating one-form and two-form gauge fields. We show explicitly that these TQFTs capture both the generalized global symmetries and topological orders seen in the lattice gauge theory. We also demonstrate that these theories exhibit a universal “generalized magneto-electric effect” in the presence of two-form background gauge fields. Moreover,we characterize the possible boundary topological orders of oblique TIs,finding a new set of boundary states not studied previously for these kinds of TQFTs. 

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4. Hybrid symmetry class topological insulators

   https://doi.org/10.21468/SciPostPhys.18.6.209  

   Das, Sanjib Kumar; Roy, Bitan (January 2025, SciPost Physics)

   Traditional topological materials belong to different Altland-Zirnbauer symmetry classes (AZSCs) depending on their non-spatial symmetries. Here we introduce the notion of hybrid symmetry class topological insulators (HSCTIs): A fusion of two different AZSC topological insulators (TIs) such that they occupy orthogonal Cartesian hyperplanes and their universal massive Dirac Hamiltonian mutually anticommute, a mathematical procedure we name hybridization. The boundaries of HSCTIs can also harbor TIs, typically affiliated with an AZSC that is different from the ones for the parent two TIs. As such, a fusion or hybridization between planar class AII quantum spin Hall and vertical class BDI Su-Schrieffer-Heeger insulators gives birth to a three-dimensional class A HSCTI, accommodating quantum anomalous Hall insulators (class A) of opposite Chern numbers and quantized Hall conductivity of opposite signs on the top and bottom surfaces. Such a response is shown to be stable against weak disorder. We extend this construction to encompass crystalline HSCTI and topological superconductors (featuring half-quantized thermal Hall conductivity of opposite sings on the top and bottom surfaces), and beyond three spatial dimensions. Non-trivial responses of three-dimensional HSCTIs to crystal defects (namely edge dislocations) in terms of mid-gap bound states at zero energy around its core only on the top and bottom surfaces are presented. Possible (meta)material platforms to harness and engineer HSCTIs are discussed. 

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5. Topological properties of multilayer magnon insulators

   https://doi.org/10.1103/PhysRevB.104.064427  

   Hofer, Stephen; Datta, Trinanjan; Tewari, Sumanta; Mazumdar, Dipanjan (August 2021, Physical Review B)