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1. Topological minibands and interaction driven quantum anomalous Hall state in topological insulator based moiré heterostructures

   https://doi.org/10.1038/s41467-024-46717-7  

   Yang, Kaijie ; Xu, Zian ; Feng, Yanjie ; Schindler, Frank ; Xu, Yuanfeng ; Bi, Zhen ; Bernevig, B. Andrei ; Tang, Peizhe ; Liu, Chao-Xing ( March 2024 , Nature Communications)

   The presence of topological flat minibands in moiré materials provides an opportunity to explore the interplay between topology and correlation. In this work, we study moiré minibands in topological insulator films with two hybridized surface states under a moiré superlattice potential created by two-dimensional insulating materials. We show the lowest conduction (highest valence) Kramers’ pair of minibands can be$${{\mathbb{Z}}}_{2}$$$Z_2$non-trivial when the minima (maxima) of moiré potential approximately form a hexagonal lattice with six-fold rotation symmetry. Coulomb interaction can drive the non-trivial Kramers’ minibands into the quantum anomalous Hall state when they are half-filled, which is further stabilized by applying external gate voltages to break inversion. We propose the monolayer Sb₂on top of Sb₂Te₃films as a candidate based on first principles calculations. Our work demonstrates the topological insulator based moiré heterostructure as a potential platform for studying interacting topological phases.

    

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2. High-pressure induced Weyl semimetal phase in 2D Tellurium

   https://doi.org/10.1038/s42005-023-01460-1  

   Niu, Chang ; Zhang, Zhuocheng ; Graf, David ; Lee, Seungjun ; Wang, Mingyi ; Wu, Wenzhuo ; Low, Tony ; Ye, Peide D. ( November 2023 , Communications Physics)

   Relativistic Weyl fermion quasiparticles in Weyl semimetal bring the electron’s chirality degree of freedom into the electrical transport and give rise to exotic phenomena. A topological phase transition from a topological trivial phase to a topological non-trivial phase offers a route to control electronic devices through its topological properties. Here, we report the Weyl semimetal phase in hydrothermally grown two-dimensional Tellurium (2D Te) induced by high hydrostatic pressure (up to 2.47 GPa). The unique chiral crystal structure gives rise to chiral fermions with different topological chiral charges ($${{C}}=-{{1}},+{{1}},{{and}}-{{2}}$$$C=-1,+1,and-2$). The highly tunable chemical potential in 2D Te provides comprehensive information for understanding the pressure-dependent electron band structure. The pressure-induced insulator-to-metal transition, two-carrier transport, and the non-trivial π Berry phase shift in quantum oscillations are observed in the 2D Te Weyl semimetal phase. Our work demonstrates the pressure-induced bandgap closing in the inversion asymmetric narrow bandgap semiconductor 2D Te.

    

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3. Spin structure and dynamics of the topological semimetal Co3Sn2-xInxS2

   https://doi.org/10.1038/s41535-022-00523-w  

   Neubauer, Kelly J. ; Ye, Feng ; Shi, Yue ; Malinowski, Paul ; Gao, Bin ; Taddei, Keith M. ; Bourges, Philippe ; Ivanov, Alexandre ; Chu, Jiun-Haw ; Dai, Pengcheng ( December 2022 , npj Quantum Materials)

   The anomalous Hall effect (AHE), typically observed in ferromagnetic (FM) metals with broken time-reversal symmetry, depends on electronic and magnetic properties. In Co₃Sn_2-xIn_xS₂, a giant AHE has been attributed to Berry curvature associated with the FM Weyl semimetal phase, yet recent studies report complicated magnetism. We use neutron scattering to determine the spin dynamics and structures as a function ofxand provide a microscopic understanding of the AHE and magnetism interplay. Spin gap and stiffness indicate a contribution from Weyl fermions consistent with the AHE. The magnetic structure evolves fromc-axis ferromagnetism at$$x = 0$$$x=0$to a canted antiferromagnetic (AFM) structure with reducedc-axis moment and in-plane AFM order at$$x = 0.12$$$x=0.12$and further reducedc-axis FM moment at$$x = 0.3$$$x=0.3$. Since noncollinear spins can induce non-zero Berry curvature in real space acting as a fictitious magnetic field, our results revealed another AHE contribution, establishing the impact of magnetism on transport.

    

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4. Partons as unique ground states of quantum Hall parent Hamiltonians: The case of Fibonacci anyons

   https://doi.org/10.21468/SciPostPhys.15.2.043  

   Tanhayi Ahari, Mostafa ; Bandyopadhyay, Sumanta ; Nussinov, Zohar ; Seidel, Alexander ; Ortiz, Gerardo ( January 2023 , SciPost Physics)

   We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate S-duality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing parton-like states, specifically at filling factor\nu=2/3$\nu =2/3$. The emergent Entangled Pauli Principle (EPP), introduced in [Phys. Rev. B 98, 161118(R) (2018)] and which defines the “DNA” of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closed-shell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zero-energy mode is a unique parton state. We conjecture that parton-like states generally span the subspace of many-body wave functions with the two-bodyM$M$-clustering property within any given number of Landau levels, that is, wave functions withM$M$th-order coincidence plane zeroes and both holomorphic and anti-holomorphic dependence on variables. General arguments are supplemented by rigorous considerations for theM=3$M=3$case of fermions in four Landau levels. For this case, we establish that the zero mode counting can be done by enumerating certain patterns consistent with an underlying EPP. We apply the coherent state approach of [Phys. Rev. X 1, 021015 (2011)] to show that the elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates that the DNA associated with fractional quantum Hall states encodes all universal properties. Specifically, for parton-like states, we establish a link with tensor network structures of finite bond dimension that emerge via root level entanglement.

    

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5. Realization of unpinned two-dimensional dirac states in antimony atomic layers

   https://doi.org/10.1038/s41467-022-32327-8  

   Lu, Qiangsheng ; Cook, Jacob ; Zhang, Xiaoqian ; Chen, Kyle Y. ; Snyder, Matthew ; Nguyen, Duy Tung ; Reddy, P. V. Sreenivasa ; Qin, Bingchao ; Zhan, Shaoping ; Zhao, Li-Dong ; et al ( August 2022 , Nature Communications)

   Two-dimensional (2D) Dirac states with linear dispersion have been observed in graphene and on the surface of topological insulators. 2D Dirac states discovered so far are exclusively pinned at high-symmetry points of the Brillouin zone, for example, surface Dirac states at$$\overline{{{\Gamma }}}$$$\overline{\Gamma }$in topological insulators Bi₂Se(Te)₃and Dirac cones atKand$$K^{\prime}$$$K^{\prime }$points in graphene. The low-energy dispersion of those Dirac states are isotropic due to the constraints of crystal symmetries. In this work, we report the observation of novel 2D Dirac states in antimony atomic layers with phosphorene structure. The Dirac states in the antimony films are located at generic momentum points. This unpinned nature enables versatile ways such as lattice strains to control the locations of the Dirac points in momentum space. In addition, dispersions around the unpinned Dirac points are highly anisotropic due to the reduced symmetry of generic momentum points. The exotic properties of unpinned Dirac states make antimony atomic layers a new type of 2D Dirac semimetals that are distinct from graphene.

    

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