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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)

   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. Strong and fragile topological Dirac semimetals with higher-order Fermi arcs

   https://doi.org/10.1038/s41467-020-14443-5  

   Wieder, Benjamin J. ; Wang, Zhijun ; Cano, Jennifer ; Dai, Xi ; Schoop, Leslie M. ; Bradlyn, Barry ; Bernevig, B. Andrei ( January 2020 , Nature Communications)

   Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of ans–d-hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw–Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- (α) and intermediate-temperature (α″) phases of Cd₃As₂, KMgBi, and rutile-structure ($$ \beta ^{\prime} $$${\beta }^{\prime }$-) PtO₂.

    

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3. Electrically and magnetically switchable nonlinear photocurrent in РТ-symmetric magnetic topological quantum materials

   https://doi.org/10.1038/s41524-020-00462-9  

   Wang, Hua ; Qian, Xiaofeng ( December 2020 , npj Computational Materials)

   Nonlinear photocurrent in time-reversal invariant noncentrosymmetric systems such as ferroelectric semimetals sparked tremendous interest of utilizing nonlinear optics to characterize condensed matter with exotic phases. Here we provide a microscopic theory of two types of second-order nonlinear direct photocurrents, magnetic shift photocurrent (MSC) and magnetic injection photocurrent (MIC), as the counterparts of normal shift current (NSC) and normal injection current (NIC) in time-reversal symmetry and inversion symmetry broken systems. We show that MSC is mainly governed by shift vector and interband Berry curvature, and MIC is dominated by absorption strength and asymmetry of the group velocity difference at time-reversed ±kpoints. Taking$${\cal{P}}{\cal{T}}$$$PT$-symmetric magnetic topological quantum material bilayer antiferromagnetic (AFM) MnBi₂Te₄as an example, we predict the presence of large MIC in the terahertz (THz) frequency regime which can be switched between two AFM states with time-reversed spin orderings upon magnetic transition. In addition, external electric field breaks$${\cal{P}}{\cal{T}}$$$PT$symmetry and enables large NSC response in bilayer AFM MnBi₂Te₄, which can be switched by external electric field. Remarkably, both MIC and NSC are highly tunable under varying electric field due to the field-induced large Rashba and Zeeman splitting, resulting in large nonlinear photocurrent response down to a few THz regime, suggesting bilayer AFM-zMnBi₂Te₄as a tunable platform with rich THz and magneto-optoelectronic applications. Our results reveal that nonlinear photocurrent responses governed by NSC, NIC, MSC, and MIC provide a powerful tool for deciphering magnetic structures and interactions which could be particularly fruitful for probing and understanding magnetic topological quantum materials.

    

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4. 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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5. Lower Bounds Against Sparse Symmetric Functions of ACC Circuits: Expanding the Reach of #SAT Algorithms

   https://doi.org/10.1007/s00224-022-10106-8  

   Vyas, Nikhil ; Williams, R. Ryan ( November 2022 , Theory of Computing Systems)

   We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in$\mathsf {Quasi}\text {-}\mathsf {NP} = \mathsf {NTIME}[n^{(\log n)^{O(1)}}]$$\mathrm{Quasi}-\mathrm{NP}=\mathrm{NTIME}\left[n^{{\left(\log n\right)}^{O\left(1\right)}}\right]$and other complexity classes do not have small circuits (in the worst case and/or on average) from various circuit classes$\mathcal { C}$$C$, by showing that$\mathcal { C}$$C$admits non-trivial satisfiability and/or#SAT algorithms which beat exhaustive search by a minor amount. In this paper, we present a new strong lower bound consequence of having a non-trivial#SAT algorithm for a circuit class${\mathcal C}$$C$. Say that a symmetric Boolean functionf(x₁,…,x_n) issparseif it outputs 1 onO(1) values of${\sum }_{i} x_{i}$${\sum }_i{x}_i$. We show that for every sparsef, and for all “typical”$\mathcal { C}$$C$, faster#SAT algorithms for$\mathcal { C}$$C$circuits imply lower bounds against the circuit class$f \circ \mathcal { C}$$f\circ C$, which may bestrongerthan$\mathcal { C}$$C$itself. In particular:

   #SAT algorithms forn^k-size$\mathcal { C}$$C$-circuits running in 2ⁿ/n^ktime (for allk) implyNEXPdoes not have$(f \circ \mathcal { C})$$(f\circ C)$-circuits of polynomial size.

   #SAT algorithms for$2^{n^{{\varepsilon }}}$$2^{n^{\epsilon }}$-size$\mathcal { C}$$C$-circuits running in$2^{n-n^{{\varepsilon }}}$$2^{n-n^{\epsilon }}$time (for someε> 0) implyQuasi-NPdoes not have$(f \circ \mathcal { C})$$(f\circ C)$-circuits of polynomial size.

   Applying#SAT algorithms from the literature, one immediate corollary of our results is thatQuasi-NPdoes not haveEMAJ∘ACC⁰∘THRcircuits of polynomial size, whereEMAJis the “exact majority” function, improving previous lower bounds againstACC⁰[Williams JACM’14] andACC⁰∘THR[Williams STOC’14], [Murray-Williams STOC’18]. This is the first nontrivial lower bound against such a circuit class.

    

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