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An textit{ab initio} electronic structure calculation based on the generalized gradient approximation in the density functional theory is carried out to study the basic electronic states of hollandite vanadate K$_2$V$_8$O$_{16}$. We find that the states near the Fermi energy consist predominantly of the three $t_{2g}$-orbital components and the hybridization with oxygen $2p$ orbitals is small. The $d_{yz}$ and $d_{zx}$ orbitals are exactly degenerate and are lifted from the $d_{xy}$ orbital. The calculated band dispersion and Fermi surface indicate that the system is not purely one-dimensional but the coupling between the VO double chains is important. Comparison with available experimental data suggests the importance of electron correlations in this system.
We consider electronic properties of hollandite vanadate K$_2$V$_8$O$_{16}$, a one-dimensional zigzag-chain system of $t_{2g}$ orbitals in a mixed valent state. We first calculate the Madelung energy and obtain the relative stability of several charg
Based on the first-principles electronic structure calculations, we predict that a chromium oxide K$_2$Cr$_8$O$_{16}$ of hollandite type should be a half-metallic ferromagnet where the Fermi level crosses only the majority-spin band, whereas the mino
We report $^{51}$V nuclear magnetic resonance (NMR) and inelastic neutron scattering (INS) measurements on a quasi-1D antiferromagnet BaCo$_2$V$_2$O$_8$ under transverse field along the [010] direction. The scaling behavior of the spin-lattice relaxa
We present an ab initio $GW$ self-energy calculation of the electronic structure of LaNiO$_2$. With respect to density-functional theory we find that in $GW$ the La 4$f$ states undergo an important $+$2 eV upward shift from the Fermi level, while the
The first part of this article centers on the fact that key features of the dynamical response of weakly-correlated materials (the alkalis, Al), have been found experimentally to differ qualitatively from simple-model behavior. In the absence of ab i