This is the third paper of a series of three papers presenting a combined study by band theory and angle-resolved photoemission spectroscopy (ARPES) of lithium purple bronze. The first paper laid the foundation for the theory, and the second paper discussed a general comparison between theory and experiment, including deriving an ARPES selection rule. The present paper III focuses in detail on the two metallic, quasi-one-dimensional (quasi-1D) $xy$-like bands left in the 0.4 eV dimerization gap between the $xz$ and $yz$ valence and conduction (V) bands. The hybridizations with the latter change the perpendicular dispersions of --- and splitting between --- the resulting $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{xy}$ bands. The edges of the V (C) bands, in particular, push resonance peaks up (down) in the $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{xy}$ bands which are now described by a two-band Hamiltonian whose two first terms consist of the pure $xy$ block of the six-band tight-binding (TB) Hamiltonian and whose four following terms describe the resonant coupling to (i.e., indirect hopping via) the V bands. The two-band Hamiltonian extends the selection rule derived in the previous paper to the hybridized $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{xy}$ bands, which enables extracting the split quasi-1D Fermi surface (FS) from the raw ARPES data. The complex shape of the FS, verified in detail by our ARPES, depends strongly on the Fermi-energy position in the gap, implying a great sensitivity to Li stoichiometry of properties dependent on the FS, such as FS nesting or superconductivity. The strong resonances prevent either a two-band TB model or a related real-space ladder picture from giving a valid description of the low-energy electronic structure. Down to a temperature of $6\phantom{\rule{4pt}{0ex}}\mathrm{K}$, we find no evidence for a theoretically expected downward renormalization of perpendicular single-particle hopping due to LL fluctuations in the quasi-1D chains.

In this and the two following papers, we present the results of a combined study by density-functional band theory and angle-resolved photoemission spectroscopy (ARPES) of lithium purple bronze, ${\mathrm{Li}}_{1x}{\mathrm{Mo}}_{6}{\mathrm{O}}_{17}$. This material is particularly notable for its unusually robust quasi-one-dimensional (quasi-1D) behavior. The band structure, in a large energy window around the Fermi energy, is basically two-dimensional and formed by three Mo ${t}_{2g}$-like extended Wannier orbitals (WOs), each one giving rise to a 1D band running at a ${120}^{\ensuremath{\circ}}$ angle to the two others. A structural ``dimerization'' from $\mathbf{c}/2$ to $\mathbf{c}$ gaps the $xz$ and $yz$ bands while leaving the $xy$ bands metallic in the gap but resonantly coupled to the gap edges and, hence, to the two other directions. The resulting complex shape of the quasi-1D Fermi surface (FS), verified by our ARPES, thus depends strongly on the Fermi energy position in the gap, implying a great sensitivity to Li stoichiometry of properties dependent on the FS, such as FS nesting or superconductivity. The theory is verified in detail by the recognition and application of an ARPES selection rule that enables the separation in ARPES spectra of the two barely split $xy$ bands and the observation of their complex split FS. The strong resonances prevent either a two-band tight-binding model or a related real-space ladder picture from giving a valid description of the low-energy electronic structure. Down to a temperature of 6 K we find no evidence for a theoretically expected downward renormalization of perpendicular single-particle hopping due to LL fluctuations in the quasi-1D chains. This paper I introduces the material, motivates our study, summarizes the $N\mathrm{th}$-order muffin-tin orbital (NMTO) method that we use, analyzes the crystal structure and the basic electronic structure, and presents our NMTO calculation of the ${t}_{2g}$ low-energy WOs and the resulting tight-binding Hamiltonian for the six lowest energy bands, only the four lowest being occupied. Thus this paper sets the theoretical framework and nomenclature for the following two papers.

In this set of three papers, we present the results of a combined study by density-functional (LDA) band theory (NMTO) and angle-resolved photoemission spectroscopy (ARPES) of lithium purple bronze, 2(Li$_{1x}$Mo$_{6}$O$_{17}$). This material is particularly notable for its unusually robust quasi-one-dimensional (quasi-1D) behavior. The band structure, in a large energy window around the Fermi energy, is basically 2D and formed by three Mo $t_{2g}$-like extended Wannier orbitals (WOs) per cell, each one giving rise to a 1D band running at a 120$^{\circ }$ angle to the two others. A structural "dimerization" from $\mathbf{c}/2$ to $\mathbf{c}$ gaps the $xz$ and $yz$ bands while leaving the $xy$ bands metallic in the gap but resonantly coupled to the gap edges and, hence, to the two other directions. The resulting complex shape of the quasi-1D Fermi surface (FS), verified by our ARPES, thus depends strongly on the Fermi energy position in the gap, implying a great sensitivity to Li stoichiometry of properties dependent on the FS, such as FS nesting or superconductivity. The band structure, expressed as a six-band, analytical tight-binding (TB) Hamiltonian, is verified in detail by the recognition and application of an ARPES selection rule that enables, for the first time, the separation in ARPES spectra of the two barely split $xy$ bands and the observation of their complex split FS. The strong resonances prevent either a two-band TB model or a related real-space ladder picture from giving a valid description of the low-energy electronic structure. Down to a temperature of 6$\,$K we find no evidence for a theoretically expected downward renormalization of perpendicular single particle hopping due to LL fluctuations in the quasi-1D chains.

A method for 3D interpolation between hard spheres is described. The function to be interpolated could be the charge density between atoms in condensed matter. Its electrostatic potential is found analytically, and so are various integrals. Periodicity is not required. The interpolation functions are localized structure-adapted linear combinations of spherical waves, the so-called unitary spherical waves (USWs), ${\ensuremath{\psi}}_{RL}\left(\ensuremath{\varepsilon},\mathbf{r}\right),$ centered at the spheres $R,$ where they have cubic-harmonic character $L.$ Input to the interpolation are the coefficients in the cubic-harmonic expansions of the target function at and slightly outside the spheres; specifically, the values and the three first radial derivatives labeled by $d=0$ (value) and 1--3 (derivatives). To fit this, we use USWs with four negative energies, $\ensuremath{\varepsilon}={\ensuremath{\epsilon}}_{1},{\ensuremath{\epsilon}}_{2},{\ensuremath{\epsilon}}_{3}$, and ${\ensuremath{\epsilon}}_{4}.$ Each interpolation function, ${\ensuremath{\varrho}}_{dRL}\left(\mathbf{r}\right),$ is actually a linear combination of these four sets of USWs with the following properties. (1) It is centered at a specific sphere where it has a specific cubic-harmonic character and radial derivative. (2) Its value and the first three radial derivatives vanish at all other spheres and for all other cubic-harmonic characters, and is therefore highly localized, essentially inside its Voronoi cell. Value-and-derivative (v) functions were originally introduced and used by Methfessel [Phys. Rev. B 38, 1537 (1988)], but only for the first radial derivative. Explicit expressions are given for the v functions and their Coulomb potentials in terms of the USWs at the four energies, plus ${\ensuremath{\epsilon}}_{0}\ensuremath{\equiv}0$ for the potentials. The coefficients, as well as integrals over the interstitial such as the electrostatic energy, are given entirely in terms of the structure matrix, ${S}_{RL,{R}^{\ensuremath{'}}{L}^{\ensuremath{'}}}\left({\ensuremath{\epsilon}}_{n}\right)$, describing the slopes of the USWs at the five energies and their expansions in Hankel functions. For open structures, additional constraints are installed to pinpoint the interpolated function deep in the interstitial. The strong localization of the v functions makes the method uniquely suited for complicated structures. Use of point- and space-group symmetries can significantly reduce matrix sizes and the number of v functions. As simple examples, we consider a constant density and the valence-electron densities in zinc-blende structured Si, ZnSe, and CuBr.

The short coherence lengths characteristic of low-dimensional superconductors are associated with usefully high critical fields or temperatures. Unfortunately, such materials are often sensitive to disorder and suffer from phase fluctuations in the superconducting order parameter which diverge with temperature T, magnetic field H, or current I. We propose an approach to overcome synthesis and fluctuation problems: building superconductors from inhomogeneous composites of nanofilaments. Macroscopic crystals of quasi-one-dimensional Na2-δMo6Se6 featuring Na vacancy disorder (δ ≈ 0.2) are shown to behave as percolative networks of superconducting nanowires. Long-range order is established via transverse coupling between individual one-dimensional filaments, yet phase coherence remains unstable to fluctuations and localization in the zero (T,H,I) limit. However, a region of reentrant phase coherence develops upon raising (T,H,I). We attribute this phenomenon to an enhancement of the transverse coupling due to electron delocalization. Our observations of reentrant phase coherence coincide with a peak in the Josephson energy EJ at nonzero (T,H,I), which we estimate using a simple analytical model for a disordered anisotropic superconductor. Na2-δMo6Se6 is therefore a blueprint for a future generation of nanofilamentary superconductors with inbuilt resilience to phase fluctuations at elevated (T,H,I).

We investigate the superconducting pairing instabilities of eight-band models for the iron arsenides. Using a functional renormalization group treatment, we determine how the critical energy scale for superconductivity depends on the electronic band structure. Most importantly, if we vary the parameters from values corresponding to LaFeAsO to SmFeAsO, the pairing scale is strongly enhanced, in accordance with the experimental observation. We analyze the reasons for this trend and compare the results of the eight-band approach to those found using five-band models.

We use the Gutzwiller variational theory to calculate the ground-state phase diagram and quasiparticle bands of LaOFeAs. The Fe3d-As4p Wannier-orbital basis obtained from density-functional theory defines the band part of our eight-band Hubbard model. The full atomic interaction between the electrons in the iron orbitals is parametrized by the Hubbard interaction U and an average Hund's-rule interaction J. We reproduce the experimentally observed small ordered magnetic moment over a large region of (U,J) parameter space. The magnetically ordered phase is a stripe spin-density wave of quasiparticles.

4 NMTOs 16 4.1 Smoothness and products of NMTOs . . . . . . . . . . . . . . . . . . . . . . . 20 4.2 Hamiltonian and overlap matrices . . . . . . . . . . . . . . . . . . . . . . . . 21 4.3 Orthonormal NMTOs (Wannier orbitals) . . . . . . . . . . . . . . . . . . . . . 22 4.4 LMTOs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.5 Example: NiO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Nature Communications 1, Article number: 105 (2010); published: 02 November 2010; updated: 17 January 2012. In Figure 2 of this Article, panel labels c and d were inadvertently switched. A typographical error was also introduced in the last sentence of the legend, which should have read 'The scale bar in panel c represents 10 μm'.

We demonstrate how ab initio cluster calculations including the full Coulomb vertex can be done in the basis of the localized, generalized Wannier orbitals which describe the low-energy density functional (LDA) band structure of the infinite crystal, e.g. the transition metal 3d and oxygen 2p orbitals. The spatial extend of our 3d Wannier orbitals (orthonormalized Nth order muffin-tin orbitals) is close to that found for atomic Hartree-Fock orbitals. We define Ligand orbitals as those linear combinations of the O 2p Wannier orbitals which couple to the 3d orbitals for the chosen cluster. The use of ligand orbitals allows for a minimal Hilbert space in multiplet ligand-field theory calculations, thus reducing the computational costs substantially. The result is a fast and simple ab initio theory, which can provide useful information about local properties of correlated insulators. We compare results for NiO, MnO and SrTiO3 with x-ray absorption, inelastic x-ray scattering, and photoemission experiments. The multiplet ligand field theory parameters found by our ab initio method agree within ~10% to known experimental values.

The crystal structure and magnetic ordering pattern of PdAs2O6 were investigated by neutron powder diffraction. While the magnetic structure of PdAs2O6 is identical to that of its isostructural 3d homologue NiAs2O6, its Neel temperature (140 K) is much higher than that of NiAs2O6 (30 K). This is surprising in view of the long distance and indirect exchange path between the magnetic Pd2+ ions. Density-functional calculations yield insight into the electronic structure and the geometry of the exchange-bond network of both PdAs2O6 and NiAs2O6, and provide a semiquantitative explanation of the large amplitude difference between their primary exchange interaction parameters.

BiOCuS is a band insulator that becomes metallic upon hole doping. Superconductivity was recently reported in doped BiOCu$_{1-x}$S and attributed to spin fluctuations as a pairing mechanism. Based on first principles calculations of the electron-phonon coupling, we argue that the latter is very strong in this material, and probably drives superconductivity, which is however strongly depressed by the proximity to magnetism. We find however that BiOCu$_{1-x}$S is a quite unique compound where both a conventional phonon-driven and an unconventional triplet superconductivity are possible, and compete with each other. We argue that, in this material, it should be possible to switch from conventional to unconventional superconductivity by varying such parameters as doping or pressure.

A hundred years after the discovery of superconductivity, no new superconductor has yet been found by design, but merely by chance, or by following empirical rules which the next discovery then proved to be of limited validity. The discoveries of the A15 compounds in the seventies, the cuprates in the eighties, MgB2 in 2001, and the iron pnictides in 2008 all testify to this. Despite 25 years’ intensive research, hightemperature superconductivity in the cuprates has not been understood and no superconductor with Tc higher than 150 K has been found since 1993. This record-holding material is triple layer, pressurized HgBa2Ca2Cu3O8. Even in cases like MgB2 where the superconductivity mechanism has been understood, this has not helped to design a better superconductor.

We have investigated charge dynamics and electronic structures for single crystals of metallic layered nickelates, R(2-x)Sr(x)NiO4 (R = Nd, Eu), isostructural to La(2-x)Sr(x)CuO4. Angle-resolved photoemission spectroscopy on the barely metallic Eu(0.9)Sr(1.1)NiO4 (R = Eu, x = 1.1) has revealed a large hole surface of x2-y2 character with a high-energy pseudogap of the same symmetry and comparable magnitude with those of underdoped (x<0.1) cuprates, although the antiferromagnetic interactions are 1 order of magnitude smaller. This finding strongly indicates that the momentum-dependent pseudogap feature in the layered nickelate arises from the real-space charge correlation.

This paper explains the multi-orbital band structures and itinerant magnetism of the iron-pnictide and chalcogenide superconductors. We first describe the generic band structure of a single, isolated FeAs layer. Use of its Abelian glide-mirror group allows us to reduce the primitive cell to one FeAs unit. For the lines and points of high symmetry in the corresponding large, square Brillouin zone, we specify how the one-electron Hamiltonian factorizes. From density-functional theory, and for the observed structure of LaOFeAs, we generate the set of eight Fe d and As p localized Wannier functions and their tight-binding (TB) Hamiltonian, h(k). For comparison, we generate the set of five Fe d Wannier orbitals. The topology of the bands, i.e. allowed and avoided crossings, specifically the origin of the d(6) pseudogap, is discussed, and the role of the As p orbitals and the elongation of the FeAs4 tetrahedron emphasized. We then couple the layers, mainly via interlayer hopping between As p(z) orbitals, and give the formalism for simple tetragonal and body-centered tetragonal (bct) stackings. This allows us to explain the material-specific 3D band structures, in particular the complicated ones of bct BaFe2As2 and CaFe2As2 whose interlayer hoppings are large. Due to the high symmetry, several level inversions take place as functions of k(z) or pressure, and linear band dispersions (Dirac cones) are found at many places. The underlying symmetry elements are, however, easily broken by phonons or impurities, for instance, so that the Dirac points are not protected. Nor are they pinned to the Fermi level because the Fermi surface has several sheets. From the paramagnetic TB Hamiltonian, we form the band structures for spin spirals with wavevector q by coupling h(k) and h(k + q). The band structure for stripe order is studied in detail as a function of the exchange potential, Delta, or moment, m, using Stoner theory. Gapping of the Fermi surface (FS) for small Delta requires matching of FS dimensions (nesting) and d-orbital characters. The interplay between pd hybridization and magnetism is discussed using simple 4 x 4 Hamiltonians. The origin of the propeller-shaped Fermi surface is explained in detail. Finally, we express the magnetic energy as the sum over band-structure energies and this enables us to understand to what extent the magnetic energies might be described by a Heisenberg Hamiltonian, and to address the much discussed interplay between the magnetic moment and the elongation of the FeAs4 tetrahedron. c (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

The three-dimensional Fermi-surface structure of hole-doped metallic layered nickelate Eu2-xSrxNiO4 (x = 1.1), an important counterpart to the isostructural superconducting cuprate La2-xSrxCuO4, is investigated by energy-dependent soft-x-ray angle-resolved photoemission spectroscopy. In addition to a large cylindrical hole Fermi surface analogous to the cuprates, we observe a Gamma-centered 3z(2) - r(2)-derived small electron pocket. This finding demonstrates that in the layered nickelate the 3z(2) - r(2) band resides close to the x(2) - y(2) one in energy. The resultant multiband feature with varying orbital character as revealed may strongly work against the emergence of the high-temperature superconductivity.