 Award ID(s):
 2045826
 NSFPAR ID:
 10382300
 Date Published:
 Journal Name:
 Scientific Reports
 Volume:
 12
 Issue:
 1
 ISSN:
 20452322
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract We study several modeltheoretic aspects of W $$^*$$ ∗ probability spaces, that is, $$\sigma $$ σ finite von Neumann algebras equipped with a faithful normal state. We first study the existentially closed W $$^*$$ ∗ spaces and prove several structural results about such spaces, including that they are type III $$_1$$ 1 factors that tensorially absorb the Araki–Woods factor $$R_\infty $$ R ∞ . We also study the existentially closed objects in the restricted class of W $$^*$$ ∗ probability spaces with Kirchberg’s QWEP property, proving that $$R_\infty $$ R ∞ itself is such an existentially closed space in this class. Our results about existentially closed probability spaces imply that the class of type III $$_1$$ 1 factors forms a $$\forall _2$$ ∀ 2 axiomatizable class. We show that for $$\lambda \in (0,1)$$ λ ∈ ( 0 , 1 ) , the class of III $$_\lambda $$ λ factors is not $$\forall _2$$ ∀ 2 axiomatizable but is $$\forall _3$$ ∀ 3 axiomatizable; this latter result uses a version of Keisler’s Sandwich theorem adapted to continuous logic. Finally, we discuss some results around elementary equivalence of III $$_\lambda $$ λ factors. Using a result of Boutonnet, Chifan, and Ioana, we show that, for any $$\lambda \in (0,1)$$ λ ∈ ( 0 , 1 ) , there is a family of pairwise nonelementarily equivalent III $$_\lambda $$ λ factors of size continuum. While we cannot prove the same result for III $$_1$$ 1 factors, we show that there are at least three pairwise nonelementarily equivalent III $$_1$$ 1 factors by showing that the class of full factors is preserved under elementary equivalence.more » « less

Abstract The status of nickelate superconductors in relation to cuprate high temperature superconductors is one of the concepts being discussed in high temperature superconductivity in correlated transition metal oxides. New additions to the class of infinite layer nickelates can provide essential input relating to connections or distinctions. A recently synthesized compound Ba_{2}NiO_{2}(AgSe)_{2}, which contains isolated ‘infinite layer’ NiO_{2}planes, may lead to new insights. Our investigations have discovered that, at density functional theory mean field level, the ground state consists of an unusual
singlet on the Ni^{2+}ion arising from large but separate Mott insulating gaps in both ${e}_{\mathrm{g}}$ orbitals, but with different, antiHund’s, spin directions of their moments. This textured singlet incorporates at the least new physics, and potentially a new platform for nickelate superconductivity, which might be of an unconventional form for transition metal oxides due to the unconventional undoped state. We include in this paper a comparison of electronic structure parameters of Ba_{2}NiO_{2}(AgSe)_{2}with a better characterized infinite layer nickelate LaNiO_{2}. We provide more analysis of the ${e}_{\mathrm{g}}$d ^{8}antiHund’s singlet that emerges in this compound, and consider a minimally correlated wavefunction for this singlet in an itinerant background, and begin discussion of excitations—real or virtual—that may figure into new electronic phases. 
Allsolidstate batteries (ASSBs) have garnered increasing attention due to the enhanced safety, featuring nonflammable solid electrolytes as well as the potential to achieve high energy density. 1 The advancement of the ASSBs is expected to provide, arguably, the most straightforward path towards practical, highenergy, and rechargeable batteries based on metallic anodes. 1 However, the sluggish ion transmission at the cathodeelectrolyte (solid/solid) interface would result in the high resistant at the contact and limit the practical implementation of these all solidstate materials in real world batteries. 2 Several methods were suggested to enhance the kinetic condition of the ion migration between the cathode and the solid electrolyte (SE). 3 A composite strategy that mixes active materials and SEs for the cathode is a general way to decrease the ion transmission barrier at the cathodeelectrolyte interface. 3 The active material concentration in the cathode is reduced as much as the SE portion increases by which the energy density of the ASSB is restricted. In addition, the mixing approach generally accompanies lattice mismatches between the cathode active materials and the SE, thus providing only limited improvements, which is imputed by random contacts between the cathode active materials and the SE during the mixing process. Implementing highpressure for the electrode and electrolyte of ASSB in the assembling process has been verified is a but effective way to boost the ion transmission ability between the cathode active materials and the SE by decreasing the grain boundary impedance. Whereas the shortcircuit of the battery would be induced by the mechanical deformation of the electrolyte under high pressure. 4 Herein, we demonstrate a novel way to address the ion transmission problem at the cathodeelectrolyte interface in ASSBs. Starting from the cathode configuration, the finite element method (FEM) was employed to evaluate the current concentration and the distribution of the space charge layer at the cathodeelectrolyte interface. Hierarchical threedimensional (HTD) structures are found to have a higher Li + transfer number (t Li+ ), fewer free anions, and the weaker spacecharge layer at the cathodeelectrolyte interface in the resulting FEM simulation. To take advantage of the HTD structure, stereolithography is adopted as a manufacturing technique and singlecrystalline Nirich (SCN) materials are selected as the active materials. Next, the manufactured HTD cathode is sintered at 600 °C in an N 2 atmosphere for the carbonization of the resin, which induces sufficient electronic conductivity for the cathode. Then, the gellike Li 1.4 Al 0.4 Ti 1.6 (PO 4 ) 3 (LATP) precursor is synthesized and filled into the voids of the HTD structure cathode sufficiently. And the filled HTD structure cathodes are sintered at 900 °C to achieve the crystallization of the LATP gel. Scanning transmission electron microscopy (STEM) is used to unveil the morphology of the cathodeelectrolyte interface between the sintered HTD cathode and the insitu generated electrolyte (LATP). A transient phase has been found generated at the interface and matched with both lattices of the SCN and the SE, accelerating the transmission of the Liions, which is further verified by density functional theory calculations. In addition, Electron Energy Loss Spectroscopy demonstrates the preserved interface between HTD cathode and SEs. Atomic force microscopy is employed to measure the potential image of the crosssectional interface by the peak force tapping mode. The average potential of modified samples is lower than the sample that mix SCN and SEs simply in the 2D planar structure, which confirms a weakened space charge layer by the enhanced contact capability as well as the ion transmission ability. To see if the demonstrated method is universally applicable, LiNi 0.8 Co 0.1 Mn 0.1 O 2 (NCM811) is selected as the cathode active material and manufactured in the same way as the SCN. The HTD cathode based on NCM811 exhibits higher electrochemical performance compared with the reference sample based on the 2D planar mixingtype cathode. We believe such a demonstrated universal strategy provides a new guideline to engineer the cathode/electrolyte interface by revolutionizing electrode structures that can be applicable to allsolidstate batteries. Figure 1. Schematic of comparing of traditional 2D planar cathode and HTD cathode in ASSB Tikekar, M. D. , et al. , Nature Energy (2016) 1 (9), 16114 Banerjee, A. , et al. , Chem Rev (2020) 120 (14), 6878 Chen, R. , et al. , Chem Rev (2020) 120 (14), 6820 Cheng, X. , et al. , Advanced Energy Materials (2018) 8 (7) Figure 1more » « less

Abstract We prove three results concerning the existence of Bohr sets in threefold sumsets. More precisely, letting
G be a countable discrete abelian group and be commuting endomorphisms whose images have finite indices, we show that$\phi _1, \phi _2, \phi _3: G \to G$ If
has positive upper Banach density and$A \subset G$ , then$\phi _1 + \phi _2 + \phi _3 = 0$ contains a Bohr set. This generalizes a theorem of Bergelson and Ruzsa in$\phi _1(A) + \phi _2(A) + \phi _3(A)$ and a recent result of the first author.$\mathbb {Z}$ For any partition
, there exists an$G = \bigcup _{i=1}^r A_i$ such that$i \in \{1, \ldots , r\}$ contains a Bohr set. This generalizes a result of the second and third authors from$\phi _1(A_i) + \phi _2(A_i)  \phi _2(A_i)$ to countable abelian groups.$\mathbb {Z}$ If
have positive upper Banach density and$B, C \subset G$ is a partition,$G = \bigcup _{i=1}^r A_i$ contains a Bohr set for some$B + C + A_i$ . This is a strengthening of a theorem of Bergelson, Furstenberg and Weiss.$i \in \{1, \ldots , r\}$ All results are quantitative in the sense that the radius and rank of the Bohr set obtained depends only on the indices
, the upper Banach density of$[G:\phi _j(G)]$ A (in (1)), or the number of sets in the given partition (in (2) and (3)). 
null (Ed.)The recent observation of superconductivity in N d 0.8 S r 0.2 N i O 2 has raised fundamental questions about the hierarchy of the underlying electronic structure. Calculations suggest that this system falls in the Mott–Hubbard regime, rather than the chargetransfer configuration of other nickel oxides and the superconducting cuprates. Here, we use stateoftheart, locally resolved electron energyloss spectroscopy to directly probe the Mott–Hubbard character of N d 1 − x S r x N i O 2 . Upon doping, we observe emergent hybridization reminiscent of the Zhang–Rice singlet via the oxygenprojected states, modification of the Nd 5d states, and the systematic evolution of Ni 3d hybridization and filling. These experimental data provide direct evidence for the multiband electronic structure of the superconducting infinitelayer nickelates, particularly via the effects of hole doping on not only the oxygen but also nickel and rareearth bands.more » « less