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1. Electric control of a canted-antiferromagnetic Chern insulator

   https://doi.org/10.1038/s41467-022-29259-8  

   Cai, Jiaqi; Ovchinnikov, Dmitry; Fei, Zaiyao; He, Minhao; Song, Tiancheng; Lin, Zhong; Wang, Chong; Cobden, David; Chu, Jiun-Haw; Cui, Yong-Tao; et al (December 2022, Nature Communications)

   Abstract The interplay between band topology and magnetism can give rise to exotic states of matter. For example, magnetically doped topological insulators can realize a Chern insulator that exhibits quantized Hall resistance at zero magnetic field. While prior works have focused on ferromagnetic systems, little is known about band topology and its manipulation in antiferromagnets. Here, we report that MnBi 2 Te 4 is a rare platform for realizing a canted-antiferromagnetic (cAFM) Chern insulator with electrical control. We show that the Chern insulator state with Chern number C  = 1 appears as the AFM to canted-AFM phase transition happens. The Chern insulator state is further confirmed by observing the unusual transition of the C  = 1 state in the cAFM phase to the C  = 2 orbital quantum Hall states in the magnetic field induced ferromagnetic phase. Near the cAFM-AFM phase boundary, we show that the dissipationless chiral edge transport can be toggled on and off by applying an electric field alone. We attribute this switching effect to the electrical field tuning of the exchange gap alignment between the top and bottom surfaces. Our work paves the way for future studies on topological cAFM spintronics and facilitates the development of proof-of-concept Chern insulator devices. 

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2. Chern Insulators at Integer and Fractional Filling in Moiré Pentalayer Graphene

   https://doi.org/10.1103/PhysRevX.15.011045  

   Waters, Dacen; Okounkova, Anna; Su, Ruiheng; Zhou, Boran; Yao, Jiang; Watanabe, Kenji; Taniguchi, Takashi; Xu, Xiaodong; Zhang, Ya-Hui; Folk, Joshua; et al (February 2025, Physical Review X)

   The advent of moiré platforms for engineered quantum matter has led to discoveries of integer and fractional quantum anomalous Hall effects, with predictions for correlation-driven topological states based on electron crystallization. Here, we report an array of trivial and topological insulators formed in a moiré lattice of rhomobohedral pentalayer graphene (R5G). At a doping of one electron per moiré unit cell ( $\nu =1$), we see a correlated insulator with a Chern number that can be tuned between $C=0$and $+1$by an electric displacement field. This is accompanied by a series of additional Chern insulators with $C=+1$originating from fractional fillings of the moiré lattice— $\nu =1/4$, $1/3$, and $2/3$—associated with the formation of moiré-driven topological electronic crystals. At $\nu =2/3$the system exhibits an integer quantum anomalous Hall effect at zero magnetic field, but further develops hints of an incipient $C=2/3$fractional Chern insulator in a modest field. Our results establish moiré R5G as a fertile platform for studying the competition and potential intertwining of integer and fractional Chern insulators. Published by the American Physical Society2025 

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3. Observation of the topological Anderson insulator in disordered atomic wires

   https://doi.org/10.1126/science.aat3406  

   Meier, Eric J.; An, Fangzhao Alex; Dauphin, Alexandre; Maffei, Maria; Massignan, Pietro; Hughes, Taylor L.; Gadway, Bryce (November 2018, Science)

   Topology and disorder have a rich combined influence on quantum transport. To probe their interplay, we synthesized one-dimensional chiral symmetric wires with controllable disorder via spectroscopic Hamiltonian engineering, based on the laser-driven coupling of discrete momentum states of ultracold atoms. Measuring the bulk evolution of a topological indicator after a sudden quench, we observed the topological Anderson insulator phase, in which added disorder drives the band structure of a wire from topologically trivial to nontrivial. In addition, we observed the robustness of topologically nontrivial wires to weak disorder and measured the transition to a trivial phase in the presence of strong disorder. Atomic interactions in this quantum simulation platform may enable realizations of strongly interacting topological fluids. 

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4. Decoupling the electronic gap from the spin Chern number in spin-resolved topological insulators

   https://doi.org/10.1103/PhysRevB.110.214211  

   Tyner, Alexander C; Grindall, Cormac; Pixley, J H (December 2024, Physical Review B)

   In two-dimensional topological insulators, a disorder-induced topological phase transition is typically identified with an Anderson localization transition at the Fermi energy. However, in ${\mathbb{Z}}_2$trivial, spin-resolved topological insulators it is the spectral gap of the spin spectrum, in addition to the bulk mobility gap, which protects the nontrivial topology of the ground state. In this work, we show that these two gaps, the bulk electronic and spin gap, can evolve distinctly on the introduction of quenched short-ranged disorder and that an odd-quantized spin Chern number topologically protects states below the Fermi energy from localization. This decoupling leads to a unique situation in which an Anderson localization transition occurs below the Fermi energy at the topological transition. Furthermore, the presence of topologically protected extended bulk states nontrivial bulk topology typically implies the existence of protected boundary modes. We demonstrate the absence of protected boundary modes in the Hamiltonian and yet the edge modes in the eigenstates of the projected spin operator survive. Our work thus provides evidence that a nonzero spin-Chern number, in the absence of a nontrivial ${\mathbb{Z}}_2$index, does not demand the existence of protected boundary modes at finite or zero energy. Published by the American Physical Society2024 

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5. 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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