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Spatial, momentum and energy separation of electronic spins in condensed matter systems guides the development of novel devices where spin-polarized current is generated and manipulated. Recent attention on a set of previously overlooked symmetry operations in magnetic materials leads to the emergence of a new type of spin splitting besides the well-studied Zeeman, Rashba and Dresselhaus effects, enabling giant and momentum dependent spin polarization of energy bands on selected antiferromagnets independent of relativistic spin-orbit interaction. Despite the ever-growing theoretical predictions, the direct spectroscopic proof of such spin splitting is still lacking. Here, we provide solid spectroscopic and computational evidence for the existence of such materials. In the noncoplanar antiferromagnet MnTe$_2$, the in-plane components of spin are found to be antisymmetric about the high-symmetry planes of the Brillouin zone, comprising a plaid-like spin texture in the antiferromagnetic ground state. Such an unconventional spin pattern, further found to diminish at the high-temperature paramagnetic state, stems from the intrinsic antiferromagnetic order instead of the relativistic spin-orbit coupling. Our finding demonstrates a new type of spin-momentum locking with a nonrelativistic origin, placing antiferromagnetic spintronics on a firm basis and paving the way for studying exotic quantum phenomena in related materials., Comment: Version 2, 30 pages, 4 main figures and 8 supporting figures

The magnitude for algebras is a generalization of the Euler characteristic. We investigate the magnitude for Nakayama algebras. Using Ringel's resolution quiver, the existence and the value of rational magnitude is given. As a result, we show that the finite global dimension criteria for Nakayama algebras of Madsen and the first author are equivalent.

This is a follow-up of \cite{KS:Kerr1} on the general covariant modulated (GCM) procedure in perturbations of Kerr. In this paper, we construct GCM hypersurfaces, which play a central role in extending GCM admissible spacetimes in \cite{KS:main} where decay estimates are derived in the context of nonlinear stability of Kerr family for $|a|\ll m$. As in \cite{KS}, the central idea of the construction of GCM hypersurfaces is to concatenate a $1$--parameter family of GCM spheres of \cite{KS:Kerr1} by solving an ODE system. The goal of this paper is to get rid of the symmetry restrictions in the GCM procedure introduced in \cite{KS} and thus remove an essential obstruction in extending the results to a full stability proof of the Kerr family., Comment: 113 pages, 2 figures, minor improvements, accepted in Annals of PDE. arXiv admin note: substantial text overlap with arXiv:1911.00697 by other authors

Fundamental understanding and control of the electronic structure evolution in rare-earth nickelates is a fascinating and meaningful issue, as well as being helpful to understand the mechanism of recently discovered superconductivity. Here we systematically study the dimensionality effect on the ground electronic state in high-quality (NdNiO3)m/(SrTiO3)1 superlattices through transport and soft x-ray absorption spectroscopy. The metal-to-insulator transition temperature decreases with the thickness of the NdNiO3 slab decreasing from bulk to 7 unit cells, then increases gradually as m further reduces to 1 unit cell. Spectral evidence demonstrates that the stabilization of insulating phase can be attributed to the increase of the charge-transfer energy between O 2p and Ni 3d bands. The prominent multiplet feature on the Ni L3 edge develops with the decrease of NdNiO3 slab thickness, suggesting the strengthening of the charge disproportionate state under the dimensional confinement. Our work provides convincing evidence that dimensionality is an effective knob to modulate the charge-transfer energy and thus the collective ground state in nickelates., Comment: 17 pages,4 figures

Layered kagome-lattice materials with 3$d$ transition metals provide a fertile playground for studies on geometry frustration, band topology and other novel ordered states. A representative class of materials AV$_3$Sb$_5$ (A=K, Rb, Cs) have been proved to possess various unconventional phases such as superconductivity, non-trivial $\mathbb{Z}_2$ band topology, and electronic nematicity, which are intertwined with multiple interlaced charge density waves (CDW). However, the interplay among these novel states and their mechanisms are still elusive. Recently, the discovery of isostructural titanium-based single-crystals ATi$_3$Bi$_5$ (A=K, Rb, Cs), which demonstrate similar multiple exotic states but in the absence of the concomitant intertwined CDW, has been offering an ideal opportunity to disentangle these complex novel states in kagome-lattice. Here, we combine the high-resolution angle-resolved photoemission spectroscopy and first-principles calculations to systematically investigate the low-lying electronic structure of RbTi$_3$Bi$_5$. For the first time, we experimentally demonstrate the coexistence of flat bands and multiple non-trivial topological states, including type-II Dirac nodal lines and non-trivial $\mathbb{Z}_2$ topological surface states therein. Furthermore, our findings as well provide the hint of rotation symmetry breaking in RbTi$_3$Bi$_5$, suggesting the directionality of the electronic structure and possibility of emerging pure electronic nematicity in this new family of kagome compounds, which may provide important insights into the electronic nematic phase in correlated kagome metals., Comment: 6 pages, 5 figures

In 1993, the global stability of Minkowski spacetime has been proven in the celebrated work of Christodoulou and Klainerman \cite{Ch-Kl} in a maximal foliation. In 2003, Klainerman and Nic\`olo \cite{Kl-Ni} gave a second proof of the stability of Minkowski in the case of the exterior of an outgoing null cone. In this paper, we give a new proof of \cite{Kl-Ni}. Compared to \cite{Kl-Ni}, we reduce the number of derivatives needed in the proof, simplify the treatment of the last slice, and provide a unified treatment of the decay of initial data. Also, concerning the treatment of curvature estimates, we replace the vectorfield method used in \cite{Kl-Ni} by the $r^p$--weighted estimates of Dafermos and Rodnianski \cite{Da-Ro}., Comment: 80 pages, 3 figures

We have used angle-dependent soft x-ray absorption spectroscopy (XAS) at the O K edge and first-principles calculations to investigate the electronic structures of iridate-based superlattices (SrIrO3)m/(SrTiO3) (m=1, 2, 3, and ∞). We focus on the pre-edge Ir 5d t2g-O 2p orbital hybridization feature in the XAS spectra. By varying the measurement geometry relative to the incident photon polarization, we are able to extract the dichroic contrast and observe the systematic increase in the anisotropy of Ir 5d orbitals as m decreases. First-principles calculations elucidate the orbital anisotropy coming mainly from the enhanced out-of-plane compression of IrO6 octahedra in the SrIrO3 layers that are adjacent to the inserted SrTiO3 layers. As m decreases, the increased volume fraction of these interfacial SrIrO3 layers and their contact with the SrTiO3 layers within the (SrIrO3)m/(SrTiO3) supercell lead to enhanced orbital anisotropy. Furthermore, the tilt and rotation of IrO6 octahedra are shown to be essential to understand the subtle orbital anisotropy in these superlattices, and constraining these degrees of freedom will give an incorrect trend. Our results demonstrate that the structural constraint from the inserted SrTiO3 layers, in addition to other electronic means such as polar interface and charge transfer, can serve as a knob to control the orbital degree of freedom in these iridate-based superlattices.

Intrinsic ferromagnetism is a crucial ingredient to realize quantum anomalous Hall effect in quasi two dimensional materials, thus the search of intrinsic ferromagnetic topological materials is one of the most concerned issues in the field of topological phases of matter. In this work, combining magnetotransport measurements, first principles calculations, and angle-resolved photoemission spectroscopy studies, we find that in MnSb6Te10, the n = 2 member of the MnSb2Te4/(Sb2Te3)n family, the strong magnetic competition realizes a fragile ferromagnetic ground state, which whereas easily enters into ferrimagnetic and the Z_2 antiferromagnetic topological insulator phase with warming to higher temperature. Interestingly, the system stays in an inversion-symmetry-protected axion insulator phase in the ferromagnetic ground state as well as in the external magnetic field driven spin-polarized FM phase and can be converted into a Weyl semimetal with multiple Weyl nodes in the valence bands with hole doping, which are manifested by the measured notable intrinsic anomalous Hall effect. Our work thus provides an intrinsic magnetic topological material which is highly tunable into versatile topological phases by temperature, magnetic field, as well as carrier doping., Comment: main text+SI, 27 pages, 10 figues and 1 table. arXiv admin note: text overlap with arXiv:2101.10149

The augmented Bergman complex of a matroid is a simplicial complex introduced recently in work of Braden, Huh, Matherne, Proudfoot and Wang. It may be viewed as a hybrid of two well-studied pure shellable simplicial complexes associated to matroids: the independent set complex and Bergman complex. It is shown here that the augmented Bergman complex is also shellable, via two different families of shelling orders. Furthermore, comparing the description of its homotopy type induced from the two shellings re-interprets a known convolution formula counting bases of the matroid. The representation of the automorphism group of the matroid on the homology of the augmented Bergman complex turns out to have a surprisingly simple description. This last fact is generalized to closures beyond those coming from a matroid., Comment: Very minor edits

Quantum confinement is a restriction on the motion of electrons in a material to specific region, resulting in discrete energy levels rather than continuous energy bands. In certain materials quantum confinement could dramatically reshape the electronic structure and properties of the surface with respect to the bulk. Here, in the recently discovered kagome superconductor CsV$_3$Sb$_5$ (A=K, Rb, Cs) family of materials, we unveil the dominant role of quantum confinement in determining their surface electronic structure. Combining angle-resolved photoemission spectroscopy (ARPES) measurement and density-functional theory simulation, we report the observations of two-dimensional quantum well states due to the confinement of bulk electron pocket and Dirac cone to the nearly isolated surface layer. The theoretical calculations on the slab model also suggest that the ARPES observed spectra are almost entirely contributed by the top two layers. Our results not only explain the disagreement of band structures between the recent experiments and calculations, but also suggest an equally important role played by quantum confinement, together with strong correlation and band topology, in shaping the electronic properties of this family of materials.

In finite group theory, studying the prime graph of a group has been an important topic for almost the past half-century. Recently, prime graphs of solvable groups have been characterized in graph theoretical terms only. This now allows the study of these graphs without any knowledge of the group theoretical background. In this paper we study prime graphs from a linear algebra angle and focus on the class of minimally connected prime graphs introduced in earlier work on the subject. As our main results, we determine the determinants of the adjacency matrices and the spectra of some important families of these graphs., Comment: 23 pages, 4 figures

Using angle-resolved photoemission spectroscopy (ARPES) and low-energy electron diffraction (LEED), together with density-functional theory (DFT) calculation, we report the formation of charge density wave (CDW) and its interplay with the Kondo effect and topological states in CeSbTe. The observed Fermi surface (FS) exhibits parallel segments that can be well connected by the observed CDW ordering vector, indicating that the CDW order is driven by the electron-phonon coupling (EPC) as a result of the nested FS. The CDW gap is large (~0.3 eV) and momentum-dependent, which naturally explains the robust CDW order up to high temperatures. The gap opening leads to a reduced density of states (DOS) near the Fermi level (EF), which correspondingly suppresses the many-body Kondo effect, leading to very localized 4f electrons at 20 K and above. The topological Dirac cone at the X point is found to remain gapless inside the CDW phase. Our results provide evidence for the competition between CDW and the Kondo effect in a Kondo lattice system. The robust CDW order in CeSbTe and related compounds provide an opportunity to search for the long-sought-after axionic insulator.