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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. 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)

   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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3. 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)

   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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4. 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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5. Weyl Fermions and broken symmetry phases of laterally confined 3 He films

   https://doi.org/10.1088/1361-648X/acf42b  

   Wu, Hao ; Sauls, J. A. ( September 2023 , Journal of Physics: Condensed Matter)

   Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D)³He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum,$L_z=(N/2)\hslash$, for$N/2$Cooper pairs. The power law suppression of the angular momentum,$L_z(T)\simeq (N/2)\hslash [1-\frac{2}{3}(\pi T/\mathrm{\Delta }{)}^2]$for$0⩽T\ll T_c$, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing edge boundaries on the edge currents, ground-state angular momentum and ground-state order parameter of superfluid³He thin films. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry at$D_{c2}\sim 16{\xi }_0$. The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement length$D\to D_{c_2}$. The PDW phase breaks time-reversal symmetry, translation invariance, but is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and originates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral ‘polar phase’ at$D_{c1}\sim 9{\xi }_0$, in which a single p-wave orbital state of Cooper pairs is aligned along the channel.

    

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