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1. Nature of charge density wave in kagome metal ScV6Sn6

   https://doi.org/10.1038/s41535-024-00620-y  

   Lee, Seongyong ; Won, Choongjae ; Kim, Jimin ; Yoo, Jonggyu ; Park, Sudong ; Denlinger, Jonathan ; Jozwiak, Chris ; Bostwick, Aaron ; Rotenberg, Eli ; Comin, Riccardo ; et al ( January 2024 , npj Quantum Materials)

   Recently, kagome lattice materials have emerged as a new model material platform for discovering and engineering novel quantum phases of matter. In this work, we elucidate the driving mechanism of the$$\sqrt{{{3}}}$$$\sqrt{3}$×$$\sqrt{{{3}}}$$$\sqrt{3}$charge order in a newly discovered kagome metal ScV₆Sn₆. Through multimodal investigations combining angle-resolved photoemission spectroscopy, phonon dispersion calculations, and phase diagram study, we identify the central role of unstable planar Sn and Sc phonon modes, while the electronic instability and van Hove singularities originating from the V kagome lattice have a marginal influence. Our results highlight that the$$\sqrt{{{3}}}$$$\sqrt{3}$×$$\sqrt{{{3}}}$$$\sqrt{3}$charge order in ScV₆Sn₆is fundamentally distinguished from the electronically driven 2 × 2 charge order in the canonical kagome system AV₃Sb₅, uncovering a new mechanism to induce symmetry-breaking phase transition in kagome lattice materials.

    

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2. Enumeration of Rooted Binary Unlabeled Galled Trees

   https://doi.org/10.1007/s11538-024-01270-8  

   Agranat-Tamir, Lily ; Mathur, Shaili ; Rosenberg, Noah A. ( March 2024 , Bulletin of Mathematical Biology)

   Rooted binarygalledtrees generalize rooted binary trees to allow a restricted class of cycles, known asgalls. We build upon the Wedderburn-Etherington enumeration of rooted binary unlabeled trees withnleaves to enumerate rooted binary unlabeled galled trees withnleaves, also enumerating rooted binary unlabeled galled trees withnleaves andggalls,$$0 \leqslant g \leqslant \lfloor \frac{n-1}{2} \rfloor $$$0⩽g⩽\lfloor \frac{n-1}{2}\rfloor$. The enumerations rely on a recursive decomposition that considers subtrees descended from the nodes of a gall, adopting a restriction on galls that amounts to considering only the rooted binarynormalunlabeled galled trees in our enumeration. We write an implicit expression for the generating function encoding the numbers of trees for alln. We show that the number of rooted binary unlabeled galled trees grows with$$0.0779(4.8230^n)n^{-\frac{3}{2}}$$$0.0779(4.{8230}^n)n^{-\frac{3}{2}}$, exceeding the growth$$0.3188(2.4833^n)n^{-\frac{3}{2}}$$$0.3188(2.{4833}^n)n^{-\frac{3}{2}}$of the number of rooted binary unlabeled trees without galls. However, the growth of the number of galled trees with only one gall has the same exponential order 2.4833 as the number with no galls, exceeding it only in the subexponential term,$$0.3910n^{\frac{1}{2}}$$$0.3910n^{\frac{1}{2}}$compared to$$0.3188n^{-\frac{3}{2}}$$$0.3188n^{-\frac{3}{2}}$. For a fixed number of leavesn, the number of gallsgthat produces the largest number of rooted binary unlabeled galled trees lies intermediate between the minimum of$$g=0$$$g=0$and the maximum of$$g=\lfloor \frac{n-1}{2} \rfloor $$$g=\lfloor \frac{n-1}{2}\rfloor$. We discuss implications in mathematical phylogenetics.

    

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3. Modified supersymmetric indices in AdS3/CFT2

   https://doi.org/10.1007/JHEP01(2024)099  

   Ardehali, Arash Arabi ; Krishna, Hare ( January 2024 , Journal of High Energy Physics)

   We consider the 𝒩 = (2, 2) AdS₃/CFT₂dualities proposed by Eberhardt, where the bulk geometry is AdS₃× (S³×T⁴)/ℤ_k, and the CFT is a deformation of the symmetric orbifold of the supersymmetric sigma modelT⁴/ℤ_k(withk= 2, 3, 4, 6). The elliptic genera of the two sides vanish due to fermionic zero modes, so for microstate counting applications one must consider modified supersymmetric indices. In an analysis similar to that of Maldacena, Moore, and Strominger for the standard 𝒩 = (4, 4) case ofT⁴, we study the appropriate helicity-trace index of the boundary CFTs. We encounter a strange phenomenon where a saddle-point analysis of our indices reproduces only a fraction (respectively$$ \frac{1}{2} $$$\frac{1}{2}$,$$ \frac{2}{3} $$$\frac{2}{3}$,$$ \frac{3}{4} $$$\frac{3}{4}$,$$ \frac{5}{6} $$$\frac{5}{6}$) of the Bekenstein-Hawking entropy of the associated macroscopic black branes.

    

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4. Negative moments of the Riemann zeta-function

   https://doi.org/10.1515/crelle-2023-0091  

   Bui, Hung M ; Florea, Alexandra ( January 2024 , Journal für die reine und angewandte Mathematik (Crelles Journal))

   Assuming the Riemann Hypothesis, we study negative moments of the Riemann zeta-function and obtain asymptotic formulas in certain ranges of the shift in$\zeta (s)${\zeta(s)}. For example, integrating${|\zeta (\frac{1}{2}+\alpha +it)|}^{-2k}${|\zeta(\frac{1}{2}+\alpha+it)|^{-2k}}with respect totfromTto$2T${2T}, we obtain an asymptotic formula when the shift α is roughly bigger than$\frac{1}{\log T}${\frac{1}{\log T}}and$k<\frac{1}{2}${k<\frac{1}{2}}. We also obtain non-trivial upper bounds for much smaller shifts, as long as$\log \frac{1}{\alpha }\ll \log \log T${\log\frac{1}{\alpha}\ll\log\log T}. This provides partial progress towards a conjecture of Gonek on negative moments of the Riemann zeta-function, and settles the conjecture in certain ranges. As an application, we also obtain an upper bound for the average of the generalized Möbius function.

    

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5. High resolution X-ray spectra of the time evolution of emission from metastable electronic states of highly charged Ni-like ions

   https://doi.org/10.1140/epjd/s10053-024-00872-0  

   Burke, Timothy ; Takacs, Endre ; Dipti ; Hosier, Adam ; O’Neil, Galen ; Tan, Joseph ; Staiger, Hunter ; Naing, Aung ; Marler, Joan ; Ralchenko, Yuri ( June 2024 , The European Physical Journal D)

   Metastable levels of highly charged ions that can only decay via highly forbidden transitions can have a significant effect on the properties of high temperature plasmas. For example, the highly forbidden 3d$$^{10}$$$_{}^{10}$$$_{J=0}$$$_{J=0}^{}$- 3d$$^9$$$_{}^9$4 s$$(\frac{5}{2},\frac{1}{2})_{J=3}$$${(\frac{5}{2},\frac{1}{2})}_{J=3}$magnetic octupole (M3) transition in nickel-like ions can result in a large metastable population of its upper level which can then be ionized by electrons of energies below the ground state ionization potential. We present a method to study metastable electronic states in highly charged ions that decay by x-ray emission in electron beam ion traps (EBIT). The time evolution of the emission intensity can be used to study the parameters of ionization balance dynamics and the lifetime of metastable states. The temporal and energy resolution of a new transition-edge sensor microcalorimeter array enables these studies at the National Institute of Standards and Technology EBIT.

   NOMAD calculated time evolution of the ratio of the Ni-like and Co-like lines in Nd at varying electron densities compared with measured ratios

    

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