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The discovery of superconductivity in thin films ($\sim$10 nm) of infinite-layer hole-doped NdNiO$_2$ has invigorated the field of high-temperature superconductivity research, reviving the debate over contrasting views that nickelates that are isostructural with cuprates are either (1) sisters of the high-temperature superconductors, or (2) that differences between nickel and copper at equal band filling should be the focus of attention. Each viewpoint has its merits, and each has its limitations, suggesting that such a simple picture must be superseded by a more holistic comparison of the two classes. Several recent studies have begun this generalization, raising a number of questions without suggesting any consensus. In this paper, we organize the findings of the electronic structures of $n$-layered NiO$_2$ materials ($n$= 1 to $\infty$) to outline (ir)regularities and to make comparisons with cuprates, with the hope that important directions of future research will emerge.

The discovery of the first high critical temperature (Tc) transition metal diboride superconductor, MgB2 structure alpha-MoB2 under pressure with Tc up to 32 K at 100 GPa, provides new input into some unexplained aspects of electron-phonon coupling in intermetallic compounds. We establish that MoB2 is a phonon-mediated superconductor but has little in common with MgB2 (Tc=40 K at zero pressure). MoB2 is a strongly metallic, three dimensional, multi-Fermi surface material, becoming of additional interest because it displays a frequency separation of Mo and B vibrations that mirrors that of metal superhydrides with Tc approaching room temperature. This separation, which is unusual in intermetallic compounds, allows an analysis separately for Mo and B providing, amongst the other parameters essential for understanding phonon coupling, the matrix elements for scattering by the individual atoms. Strong coupling (lambda(Mo)=1.48) is provided by Mo (total lambda=1.67). A factor of 15 weaker coupling to each B atom is compensated by that coupling being to mean high frequency modes around 85-90 meV (maximum of 140 meV), versus 18-20 meV for Mo. As a result, B enhances Tc by 43% over the Mo-only value, to 33 K, corresponding to the experimental value. These results provide a guideline for designing higher Tc materials from a cooperation of strong coupling from heavy atoms with weakly coupled light atoms. The new high Tc paradigm discovered here highlights the need for studying and engineering larger ionic scattering matrix elements., Comment: 13 pages, 9 figures, 56 references

The application of an external magnetic field of sufficient strength to a spin system composed of a localized singlet can overcome the energy gap and trigger bosonic condensation and so provide an alternative method to realize exotic phases of matter in real materials. Previous research has indicated that a spin Hamiltonian with on-site Kondo coupling may be the effective many-body Hamiltonian for $\text{Ba}_2\text{NiO}_2\text{(AgSe)}_2$ (BNOAS) and here we study such a Hamiltonian using a tensor network ansatz in two dimensions. Our results unveil a phase diagram which indicates the underlying phases of BNOAS. We propose, in response to the possible doping-induced superconductivity of BNOAS, a fermionic model for further investigation. We hope that our discovery can bring up further interest in both theoretical and experimental researches for related nickelate compounds., Comment: 11 pages, 6 figures, 2 tables

We present a computational study of antiferromagnetic transition in RuO$_2$. The rutile structure with the magnetic sublattices coupled by $\pi/2$-rotation leads to a spin-polarized band structure in the antiferromagnetic state, which gives rise to a $d$-wave modulation of the Fermi surface in the spin-triplet channel. We argue a finite spin conductivity that changes sign in the $ab$ plane is expected RuO$_2$ because of this band structure. We analyze the origin of the antiferromagnetic instability and link it to presence of a nodal line close to the Fermi level., Comment: 5 pages, 5 figures

Using Wannier functions to represent the density functional results we calculate the hybridization corrections to the orbital momentum operator in the Os 5d shell of Mott insulators Ba2NaOsO6 and Ba2YOsO6. The g-factors are obtained by evaluating the spin and orbital momentum operators in the atomic ground states of the Os ion. While the hybridization corrections play minor role in d3 ion of Ba2YOsO6 with dominant spin moment, they are instrumental for observation of non- zero g-factor of the d1 ions of Ba2NaOsO6. In addition we analyze the exchange interactions in Ba2YOsO6 and find them consistent with the reported magnetic structure., Comment: published version (estimate of Van Vleck susceptibility added)

Based on the refined crystal structure comprised of columns of 3*4 planar blocks of NbO6 octahedra and first principles electronic structure methods, we find that orthorhombic (o)-Nb$_{12}$O$_{29}$ introduces a new class of transition metal oxide. The electronic system consists of a large Nb dimer-based localized orbital comparable in size to those in organometallic compounds, yet is tightly bound and weakly interacting with itinerant electronic bands. These local moments, a rare occurrence for Nb, form one-dimensional spin chains that criss-cross perpendicularly oriented conducting nanowires. The local moment bandwidth is comparable to what is seen in rare earth compounds with extremely localized orbitals. The microscopic origin is traced to the local structure of the NbO6 octahedra and associated orbital+spin ordering. The resulting 1D$_s$*1D$_c$ anisotropic two dimensional Heisenberg-Kondo lattice model (s=spin, c=charge) provides a strongly anisotropic spin-fermion lattice system for further study., Comment: 6+ pages, 6 embedded figures

We investigate the electronic structure of (Sr$_{1-x}$La$_x$)$_2$RhO$_4$ using a combination of the density functional and dynamical mean-field theories. Unlike the earlier local density approximation plus Hubbard $U$ (LDA+U) studies, we find no sizable enhancement of the spin-orbit splitting due to electronic correlations and show that such an enhancement is a spurious effect of the static mean-field approximation of the LDA+U method. The electron doping suppresses the importance of electronic correlations, which is reflected in quasi-particle bandwidth increasing with $x$. (Sr$_{1-x}$La$_x$)$_2$RhO$_4$ can be classified as weakly correlated metal, which becomes an itinerant in-plane ferromagnet (but possibly A-type antiferromagnet) due to Stoner instability around $x=0.2$., Comment: Corrected a factor of 2 error in our definition of doping x

SrPt3P has recently been reported to exhibit superconductivity with Tc = 8.4 K. To explore its superconducting mechanism, we have performed electron and phonon band calculations based on the density functional theory, and found that the superconductivity in SrPt3P is well described by the strong coupling phonon-mediated mechanism. We have demonstrated that superconducting charge carriers come from pd\pi-hybridized bands between Pt and P ions, which couple to low energy (~ 5 meV) phonon modes confined on the ab in-plane. These in-plane phonon modes, which do not break antipolar nature of SrPt3P, enhance both the electron-phonon coupling constant \lambda and the critical temperature Tc. There is no hint of a specific phonon softening feature in the phonon dispersion, and the effect of the spin-orbit coupling on the superconductivity is found to be negligible., Comment: 5 pages, 5 figures, 1 table

Calculations of the zone center optical mode frequencies (including LO-TO splitting), Born effective charges Z$^*_{\alpha\alpha}$ for each atom, dielectric constants $\epsilon_{0}$ and $\epsilon_{\infty}$, and the dielectric response in the infrared, using density functional linear response theory, are reported. Calculated Raman modes are in excellent agreement with experimental values (170 cm$^{-1}$ and 1170 cm$^{-1}$), while it will require better experimental data to clarify the infrared active mode frequencies. The Born effective charges Z$^*_{\alpha \alpha}$ (i) have surprisingly different values for B and C, and (ii) show considerable anisotropy. Relationships between the effective charges and LO-TO splitting are discussed, and the predicted reflectivity in the range 0 -- 1400 cm$^{-1}$ is presented. These results hold possible implications for Li removal in LiBC, and C substition for B in MgB$_2$., Comment: 6 pages, 3 figures