By calculation and analysis of the bare conduction bands in a large number of hole-doped high-temperature superconductors, we have identified the energy of the so-called axial-orbital as the essential, material-dependent parameter. It is uniquely related to the range of the intra-layer hopping. It controls the Cu 4s-character, influences the perpendicular hopping, and correlates with the observed Tc at optimal doping. We explain its dependence on chemical composition and structure, and present a generic tight-binding model. PACS numbers: 74.25.Jb, 74.62.Bf, 74.62.Fj, The mechanism of high-temperature superconductivity (HTSC) in the hole-doped cuprates remains a puzzle [1]. Many families with CuO 2 -layers have been synthesized and all exhibit a phase diagram with T c going through a maximum as a function of doping. The prevailing explanation is that at low doping, superconductivity is destroyed with rising temperature by the loss of phase coherence, and at high doping by pair-breaking [2]. For the materials-dependence of T c at optimal doping, T c max , the only known, but not understood, systematics is that for materials with multiple CuO 2 -layers, such as HgBa 2 Ca n−1 Cu n O 2n+2 , T c max increases with the number of layers, n, until n ∼3. There is little clue as to why for n fixed, T c max depends strongly on the family, e.g. why for n=1, T c max is 40 K for La 2 CuO 4 and 85 K for Tl 2 Ba 2 CuO 6 , although the Neel temperatures are fairly similar. A wealth of structural data has been obtained, and correlations between structure and T c have often been looked for as functions of doping, pressure, uniaxial strain, and family. However, the large number of structural and compositional parameters makes it difficult to find what besides doping controls the superconductivity. Insight was recently provided by Seo et al. [3] who grew ultrathin epitaxial La 1.9 Sr 0.1 CuO 4 films with varying degrees of strain and measured all relevant structural parameters and physical properties. For this single-layer material it was concluded that the distance between the charge reservoir and the CuO 2 -plane is the key structural parameter determining the normal state and superconducting properties.Most theories of HTSC are based on a Hubbard model with one Cu d x 2 −y 2 -like orbital per CuO 2 unit. The oneelectron part of this model is, in the k-representation:with t, t ′ , t ′′ , ... denoting the hopping integrals (≥ 0) on the square lattice (Fig. 1) Relation between the one-orbital model (t, t ′ , t ′′ , ...) and the nearest-neighbor four-orbital model [4] (ε d − εp ∼ 1 eV, t pd ∼ 1.5 eV, εs − εp ∼ 16 − 4 eV, tsp ∼ 2 eV) .The LDA band structure of the best known, and only stoichiometric optimally doped HTSC, YBa 2 Cu 3 O 7 , is more complicated than what can be described with the t-t ′ model. Nevertheless, careful analysis has shown [4] that the low-energy, layer-related features, which are the only generic ones, can be described by a nearest-neighbor, tight-binding model with four orbitals per layer (Fig. 1), Cu d x 2 −...

Using t2g Wannier-functions, a low-energy Hamiltonian is derived for orthorhombic 3d 1 transitionmetal oxides. Electronic correlations are treated with a new implementation of dynamical mean-field theory for non-cubic systems. Good agreement with photoemission data is obtained. The interplay of correlation effects and cation covalency (GdFeO3-type distortions) is found to suppress orbital fluctuations in LaTiO3, and even more in YTiO3, and to favor the transition to the insulating state.

In the series of 3d (t 2g ) 1 perovskites, SrVO 3 -CaVO 3 -LaTiO 3 -YTiO 3 ,

We study the origin of the temperature-induced Mott transition in Ca2RuO4. As a method we use the local-density approximation+dynamical mean-field theory. We show the following. (i) The Mott transition is driven by the change in structure from long to short c-axis layered perovskite (L-Pbca → S-Pbca); it occurs together with orbital order, which follows, rather than produces, the structural transition. (ii) In the metallic L-Pbca phase the orbital polarization is ∼ 0. (iii) In the insulating S-Pbca phase the lower energy orbital, ∼ xy, is full. (iv) The spin-flip and pair-hopping Coulomb terms reduce the effective masses in the metallic phase. Our results indicate that a similar scenario applies to Ca2−xSrxRuO4 (x ≤ 0.2). In the metallic x ≤ 0.5 structures electrons are progressively transferred to the xz/yz bands with increasing x, however we find no orbital-selective Mott transition down to ∼ 300 K. ) undergoes a paramagnetic metal-paramagnetic insulator transition (MIT) at T MIT ∼ 360 K [1]. A similar insulator-to-metal transition happens also by application of a modest (∼ 0.5 GPa) pressure [2] and finally when Ca is partially substituted by Sr (Ca 2−x Sr x RuO 4 , x ≤ 0.2) [3,4]. The nature of these transitions, in particular across x = 0.2, has been debated for a decade [5][6][7][8][9][10][11][12][13]. While it is clear that a Mott-type mechanism makes the 2/3-filled t 2g bands insulating, two opposite scenarios, with different orbital occupations n = (n xy , n xz + n yz ) and polarizations p ≡ n xy − (n xz + n yz )/2, have been suggested. In the first, only the xy band becomes metallic, i.e. the transition is orbital-selective (OSMT) [5]; n and p jump from (2, 2) and 1 in the insulator to (1, 3) and −1/2 in the metal. In the second, there is a single Mott transition, assisted by the crystal-field splitting ∆ = ǫ xz/yz −ǫ xy > 0 [13], similar to the case of 3d 1 perovskites [14]; p > 0 in all phases. To date the issue remains open. Recently, for x = 0.2 a novel (xy insulating, n xy = 1.5 and p = 1/4) OSMT was inferred from angle-resolved photoemission (ARPES) experiments [7], but other ARPES data show three metallic bands and no OSMT [8].Ca 2 RuO 4 is made of RuO 2 layers built up of cornersharing RuO 6 octhahedra (space group Pbca [3,15]). This structure (Fig. 1) combines a rotation of the octahedra around the c axis with a tilt around the b axis. It is similar to that of the tetragonal unconventional superconductor Sr 2 RuO 4 ; the corresponding pseudo-tetragonal axes x, y and z are shown in Fig. 1. The structure of Ca 2 RuO 4 is characterized by a long c axis (L-Pbca) above T S ∼ 356 K and by a short one (S-Pbca) below T S . The L-and S-Pbca phases are also observed in Ca 2−x Sr x RuO 4 for all x ≤ 0.2, but T S decreases with increasing x; for x > 0.2 the system becomes tetragonal (for x < 1.5: I4 1 /acd, c-axis rotations only).Because of the layered structure, the ∼ xz, yz band- width, W xz/yz , is about one half of the ∼ xy bandwidth, W xy . Due to the structural distortions, the t 2g manifold splits i...

We investigate the importance of quantum orbital fluctuations in the orthorhombic and monoclinic phases of the Mott insulators LaVO3 and YVO3. First, we construct ab-initio material-specific t2g Hubbard models. Then, by using dynamical mean-field theory, we calculate the spectral matrix as a function of temperature. Our Hubbard bands and Mott gaps are in very good agreement with spectroscopy. We show that in orthorhombic LaVO3, quantum orbital fluctuations are strong and that they are suppressed only in the monoclinic 140 K phase. In YVO3 the suppression happens already at 300 K. We show that Jahn-Teller and GdFeO3-type distortions are both crucial in determining the type of orbital and magnetic order in the low temperature phases. The Mott insulating t 2 2g perovskites LaVO 3 and YVO 3 exhibit an unusual series of structural and magnetic phase transitions ( Fig. 1) with temperature-induced magnetization reversal phenomena [1] and other exotic properties [2,3]. While it is now recognized that the V-t 2g orbital degrees of freedom and the strong Coulomb repulsion are the key ingredients, it is still controversial whether classical (orbital order) [1,4,5,6,7,8] or quantum (orbital fluctuations) [2, 9] effects are responsible for the rich physics of these vanadates.At 300 K, LaVO 3 and YVO 3 are orthorhombic paramagnetic Mott insulators. Their structure (Fig. 2) can be derived from the cubic perovskite ABO 3 , with A=La,Y and B=V, by tilting the VO 6 octahedra in alternating directions around the b-axis and rotating them around the c-axis. This GdFeO 3 -type distortion is driven by AO covalency which pulls a given O atom closer to one of its four nearest A-neighbors [10,11]. Since the Y 4d level is closer to the O 2p level than the La 5d level, the AO covalency increases when going from LaVO 3 to YVO 3 and, hence, the shortest AO distance decreases from being 14 to being 20 % shorter than the average, while the angle of tilt increases from 12 to 18 0 , and that of rotation from 7 to 13 0 [12,13]. Finally, the A-cube is deformed such that one or two of the ABA body-diagonals is smaller than the average by, respectively, 4 and 10 % in LaVO 3 and YVO 3 . These 300 K structures are determined mainly by the strong covalent interactions between O 2p and the empty B e g and A d orbitals, hardly by the weak interactions involving B t 2g orbitals, and are thus very similar to the structures of the t 1 2g La and Y titanates [10,11].

The topology of the Fermi surface of Sr2RuO4 is well described by local-density approximation calculations with spin-orbit interaction, but the relative size of its different sheets is not. By accounting for many-body effects via dynamical mean-field theory, we show that the standard isotropic Coulomb interaction alone worsens or does not correct this discrepancy. In order to reproduce experiments, it is essential to account for the Coulomb anisotropy. The latter is small but has strong effects; it competes with the Coulomb-enhanced spin-orbit coupling and the isotropic Coulomb term in determining the Fermi surface shape. Its effects are likely sizable in other correlated multi-orbital systems. In addition, we find that the low-energy self-energy matrix -responsible for the reshaping of the Fermi surface -sizably differ from the static Hartree-Fock limit. Finally, we find a strong spin-orbital entanglement; this supports the view that the conventional description of Cooper pairs via factorized spin and orbital part might not apply to Sr2RuO4. ) electronic configuration and Ru atoms at sites with D 4h symmetry; due to the layered structure the Ru t 2g xz and yz bands are almost one-dimensional and very narrow, with a band width W xz = W yz about half as large as that of the two-dimensional Ru xy band, W xy . Experimentally, the Fermi surface of Sr 2 RuO 4 has been studied via both the de Haas-van Alphen technique [14-16] and angle-resolved photoemission spectroscopy (ARPES) [17][18][19][20]. It is made (Fig. 1) by three sheets, the electron-like γ (xy band) and β (xz, yz bands) sheets and the hole-like α sheet (xz, yz bands). Theoretically, ab-initio calculations based on the local-density approximation (LDA) qualitatively reproduce the FS topology, provided that the spin-orbit (SO) interaction is taken into account [22,23]. Indeed, several experiments point to a sizable SO coupling [1,25,26]. These calculations fail, however, in describing the relative size of the sheets, suggesting that perhaps many-body effects play a key role. The relevance of the Coulomb interaction for the electronic properties of Sr 2 RuO 4 , as well as its interplay with bands of different width, was shown early on via model many-body studies [21]. More recently, LDA+DMFT (local-density approximation + dy- namical mean-field theory) calculations have emphasized the interplay of Coulomb interaction and t 2g crystal field (CF) [9,27], and the role of the Hund's rule coupling [10]. LDA+slave-boson calculations point to SO effects on the correlated bands [28]. It remains however unclear to what extent many-body effects actually modify the Fermi surface, and how they compete with other effects. In this Letter, by using the LDA+DMFT method with SO interaction, we investigate, for the first time, the interplay between Coulomb repulsion, spin-orbit and sym-

The origin of the cooperative Jahn-Teller distortion and orbital order in LaMnO3 is central to the physics of the manganites. The question is complicated by the simultaneous presence of tetragonal and GdFeO3-type distortions and the strong Hund's rule coupling between e{g} and t{2g} electrons. To clarify the situation we calculate the transition temperature for the Kugel-Khomskii superexchange mechanism by using the local density approximation+dynamical mean-field method, and disentangle the effects of superexchange from those of lattice distortions. We find that superexchange alone would yield T{KK} approximately 650 K. The tetragonal and GdFeO3-type distortions, however, reduce T{KK} to approximately 550 K. Thus electron-phonon coupling is essential to explain the persistence of local Jahn-Teller distortions to greater than or approximately 1150 K and to reproduce the occupied orbital deduced from neutron scattering.

The Mott insulating perovskite KCuF3 is considered the archetype of an orbitally ordered system. By using the local-density approximation+dynamical mean-field theory method, we investigate the mechanism for orbital ordering in this material. We show that the purely electronic Kugel-Khomskii super-exchange mechanism alone leads to a remarkably large transition temperature of T(KK) to approximately 350 K. However, orbital order is experimentally believed to persist to at least 800 K. Thus, Jahn-Teller distortions are essential for stabilizing orbital order at such high temperatures.