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1. Anomalous Landau quantization in intrinsic magnetic topological insulators

   https://doi.org/10.1038/s41467-023-40383-x  

   Chong, Su Kong; Lei, Chao; Lee, Seng Huat; Jaroszynski, Jan; Mao, Zhiqiang; MacDonald, Allan H.; Wang, Kang L. (August 2023, Nature Communications)

   Abstract The intrinsic magnetic topological insulator, Mn(Bi_1−xSb_x)₂Te₄, has been identified as a Weyl semimetal with a single pair of Weyl nodes in its spin-aligned strong-field configuration. A direct consequence of the Weyl state is the layer dependent Chern number,$$C$$ $C$. Previous reports in MnBi₂Te₄thin films have shown higher$$C$$ $C$states either by increasing the film thickness or controlling the chemical potential. A clear picture of the higher Chern states is still lacking as data interpretation is further complicated by the emergence of surface-band Landau levels under magnetic fields. Here, we report a tunable layer-dependent$$C$$ $C$ = 1 state with Sb substitution by performing a detailed analysis of the quantization states in Mn(Bi_1−xSb_x)₂Te₄dual-gated devices—consistent with calculations of the bulk Weyl point separation in the doped thin films. The observed Hall quantization plateaus for our thicker Mn(Bi_1−xSb_x)₂Te₄films under strong magnetic fields can be interpreted by a theory of surface and bulk spin-polarised Landau level spectra in thin film magnetic topological insulators. 

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2. Higher-group symmetry of (3+1)D fermionic $$\mathbb{Z}_2$$ gauge theory: Logical CCZ, CS, and T gates from higher symmetry

   https://doi.org/10.21468/SciPostPhys.16.5.122  

   Barkeshli, Maissam; Hsin, Po-Shen; Kobayashi, Ryohei (January 2024, SciPost Physics)

   It has recently been understood that the complete global symmetry of finite group topological gauge theories contains the structure of a higher-group. Here we study the higher-group structure in (3+1)D\mathbb{Z}_2 ${\mathbb{Z}}_2$gauge theory with an emergent fermion, and point out that pumping chiralp+ip $p+ip$topological states gives rise to a\mathbb{Z}_{8} ${\mathbb{Z}}_8$0-form symmetry with mixed gravitational anomaly. This ordinary symmetry mixes with the other higher symmetries to form a 3-group structure, which we examine in detail. We then show that in the context of stabilizer quantum codes, one can obtain logical CCZ and CS gates by placing the code on a discretization ofT^3 $T^3$(3-torus) andT^2 \rtimes_{C_2} S^1 $T^2{⋊}_{C_2}{S}^1$(2-torus bundle over the circle) respectively, and pumpingp+ip $p+ip$states. Our considerations also imply the possibility of a logicalT $T$gate by placing the code on\mathbb{RP}^3 ${ℝ\mathbb{P}}^3$and pumping ap+ip $p+ip$topological state. 

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3. Undecidable Translational Tilings with Only Two Tiles, or One Nonabelian Tile

   https://doi.org/10.1007/s00454-022-00426-4  

   Greenfeld, Rachel; Tao, Terence (January 2023, Discrete & Computational Geometry)

   Abstract We construct an example of a group$$G = \mathbb {Z}^2 \times G_0$$ $G=Z^2\times G_0$for a finite abelian group $$G_0$$ $G_0$, a subsetEof $$G_0$$ $G_0$, and two finite subsets$$F_1,F_2$$ $F_1,F_2$of G, such that it is undecidable in ZFC whether$$\mathbb {Z}^2\times E$$ $Z^2\times E$can be tiled by translations of$$F_1,F_2$$ $F_1,F_2$. In particular, this implies that this tiling problem isaperiodic, in the sense that (in the standard universe of ZFC) there exist translational tilings ofEby the tiles$$F_1,F_2$$ $F_1,F_2$, but no periodic tilings. Previously, such aperiodic or undecidable translational tilings were only constructed for sets of eleven or more tiles (mostly in $$\mathbb {Z}^2$$ $Z^2$). A similar construction also applies for$$G=\mathbb {Z}^d$$ $G=Z^d$for sufficiently large d. If one allows the group$$G_0$$ $G_0$to be non-abelian, a variant of the construction produces an undecidable translational tiling with only one tile F. The argument proceeds by first observing that a single tiling equation is able to encode an arbitrary system of tiling equations, which in turn can encode an arbitrary system of certain functional equations once one has two or more tiles. In particular, one can use two tiles to encode tiling problems for an arbitrary number of tiles. 

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4. Kitaev spin-orbital bilayers and their moiré superlattices

   https://doi.org/10.1038/s41535-023-00541-2  

   Nica, Emilian Marius; Akram, Muhammad; Vijayvargia, Aayush; Moessner, Roderich; Erten, Onur (February 2023, npj Quantum Materials)

   Abstract We determine the phase diagram of a bilayer, Yao-Lee spin-orbital model with inter-layer interactions (J), for several stackings and moiré superlattices. For AA stacking, a gapped$${{\mathbb{Z}}}_{2}$$ $Z_2$quantum spin liquid phase emerges at a finiteJ_c. We show that this phase survives in the well-controlled large-Jlimit, where an isotropic honeycomb toric code emerges. For moiré superlattices, a finite-qinter-layer hybridization is stabilized. This connects inequivalent Dirac points, effectively ‘untwisting’ the system. Our study thus provides insight into the spin-liquid phases of bilayer spin-orbital Kitaev materials. 

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5. Local structure elucidation of tungsten-substituted vanadium dioxide (V$$_{1-x}$$W$$_x$$O$$_2$$)

   https://doi.org/10.1038/s41598-022-18575-0  

   Wilson, Catrina E.; Gibson, Amanda E.; Cuillier, Paul M.; Li, Cheng-Han; Crosby, Patrice H. N.; Trigg, Edward B.; Najmr, Stan; Murray, Christopher B.; Jinschek, Joerg R.; Doan-Nguyen, Vicky (August 2022, Scientific Reports)

   Abstract Initially, vanadium dioxide seems to be an ideal first-order phase transition case study due to its deceptively simple structure and composition, but upon closer inspection there are nuances to the driving mechanism of the metal-insulator transition (MIT) that are still unexplained. In this study, a local structure analysis across a bulk powder tungsten-substitution series is utilized to tease out the nuances of this first-order phase transition. A comparison of the average structure to the local structure using synchrotron x-ray diffraction and total scattering pair-distribution function methods, respectively, is discussed as well as comparison to bright field transmission electron microscopy imaging through a similar temperature-series as the local structure characterization. Extended x-ray absorption fine structure fitting of thin film data across the substitution-series is also presented and compared to bulk. Machine learning technique, non-negative matrix factorization, is applied to analyze the total scattering data. The bulk MIT is probed through magnetic susceptibility as well as differential scanning calorimetry. The findings indicate the local transition temperature ($$T_c$$ $T_c$) is less than the average$$T_c$$ $T_c$supporting the Peierls-Mott MIT mechanism, and demonstrate that in bulk powder and thin-films, increasing tungsten-substitution instigates local V-oxidation through the phase pathway VO$$_2\, \rightarrow$$ ${}_2\to$V$$_6$$ ${}_6$O$$_{13} \, \rightarrow$$ ${}_{13}\to$V$$_2$$ ${}_2$O$$_5$$ ${}_5$. 

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