Stripes and Pairing in High Temperature Superconductors

We review briefly several approaches used to investigate the stability of stripe phases in high temperature superconductors, where charge inhomogeneities arise from competing kinetic and magnetic energies. The mechanism of stripe formation, their consequences for the normal state and enhancement of pairing interaction triggered by charge inhomogeneities are briefly summarized. Finally, we demonstrate that orbital degeneracy ($i$) leads to a more subtle mechanism of stripe formation, and ($ii$) plays an important role and determines the symmetry of the superconducting state in pnictides.Comment: 7 pages, no figure

One-dimensional frustrated plaquette compass model: Nematic phase and spontaneous multimerization

We introduce a one-dimensional (1D) pseudospin model on a ladder where the Ising interactions along the legs and along the rungs alternate between $X_{i}X_{i+1}$ and $Z_{i}Z_{i+1}$ for even/odd bond (rung). We include also the next nearest neighbor Ising interactions on plaquettes' diagonals that alternate in such a way that a model where only leg interactions are switched on is equivalent to the one when only the diagonal ones are present. Thus in the absence of rung interactions the model can interpolate between two 1D compass models. The model posses local symmetries which are the parities within each $2\times 2$ cell (plaquette) of the ladder. We find that for different values of the interaction it can realize ground states that differ by the patterns formed by these local parities. By exact diagonalization we derive detailed phase diagrams for small systems of $L=4$, 6 and 8 plaquettes, and use next $L=12$ to identify generic phases that appear in larger systems as well. Among them we find a nematic phase with macroscopic degeneracy when the leg and diagonal interactions are equal and the rung interactions are larger than a critical value. The nematic phase is similar to the one found in the two-dimensional compass model. For particular parameters the low-energy sector of the present plaquette model reduces to a 1D compass model with spins $S=1$ which suggests that it realizes peculiar crossovers within the class of compass models. Finally, we show that the model can realize phases with broken translation invariance which can be either dimerized, trimerized, \textit{etcetera}, or completely disordered and highly entangled in a~well identified window of the phase diagram.Comment: 18 pages, 14 figures, accepted by Physical Review

Exact spectral function for hole-magnon coupling in the ferromagnetic CuO3_3-like chain

We present the exact spectral function for a single oxygen hole with spin opposite to ferromagnetic order within a one-dimensional CuO$_{3}$-like spin chain. We find that local Kondo-like exchange interaction generates five different states in the strong coupling regime. It stabilizes a spin polaron which is a bound state of a moving charge dressed by magnon excitations, with essentially the same dispersion as predicted by mean field theory. We then examine in detail the evolution of the spectral function for increasing strength of the hole-magnon interaction. We also demonstrate that the $s$ and $p$ symmetry of orbital states in the conduction band are essentially equivalent to each other and find that the simplified models do not suffice to reproduce subtle aspects of hole-magnon coupling in the charge-transfer model.Comment: 9 pages, 5 figure

A possibility of high spin hole states in doped CoO2_2 layered systems

We introduce and investigate an effective five-band model for $t_{2g}$ and $e_g$ electrons to describe doped cobalt oxides with Co$^{3+}$ and Co$^{4+}$ ions in two-dimensional CoO$_2$ triangular lattice layers, as in Na$_{1-x}$CoO$_2$. The effective Hamiltonian includes anisotropic kinetic energy (due to both direct Co-Co and indirect Co-O-Co hoppings), on-site Coulomb interactions parameterized by intraorbital Hubbard repulsion $U$ and full Hund's exchange tensor, crystal-field terms and Jahn-Teller static distortions. We study it using correlated wave functions on $6\times 6$ clusters with periodic boundary conditions. The computations indicate low S=0 spin to high S=2 spin abrupt transition in the undoped systems when increasing strength of the crystal field, while intermediate S=1 spins are not found. Surprisingly, for the investigated realistic Hamiltonian parameters describing low spin states in CoO$_2$ planes, doping generates high $S=\frac{5}{2}$ spins at Co$^{4+}$ ions that are pairwise bound into singlets, seen here as pairs of up and down spins. It is found that such singlet pairs self-organize at higher doping into lines of spins with coexisting antiferromagnetic and ferromagnetic bonds, forming stripe-like structures. The ground states are insulating within the investigated range of doping because computed HOMO-LUMO gaps are never small enough.Comment: 20 pages, 5 figure

d−pd-p model and spin-orbital order in the vanadium perovskites

Using the multi-band $d-p$ model and unrestricted Hartree-Fock approximation we investigate the electronic structure and spin-orbital order in three-dimensional VO$_3$ lattice. The main aim of this investigation is testing if simple $d-p$ model, with partly filled $3d$ orbitals (at vanadium ions) and $2p$ orbitals (at oxygen ions), is capable of reproducing correctly nontrivial coexisting spin-orbital order observed in the vanadium perovskites. We point out that the multi-band $d-p$ model has to include partly filled $e_g$ orbitals at vanadium ions. The results suggest weak self-doping as an important correction beyond the ionic model and reproduce the possible ground states with broken spin-orbital symmetry on vanadium ions: either $C$-type alternating orbital order accompanied by $G$-type antiferromagnetic spin order, or $G$-type alternating orbital order accompanied by $C$-type antiferromagnetic spin order. Both states are experimentally observed and compete with each other in YVO$_3$ while only the latter was observed in LaVO$_3$. Orbital order is induced and stabilized by particular patterns of oxygen distortions arising from the Jahn-Teller effect. In contrast to time-consuming \textit{ab-initio} calculations, the computations using $d-p$ model are very quick and should be regarded as very useful in solid state physics, provided the parameters are selected carefully.Comment: 10 pages, 3 figures, accepted by Physical Review

Symmetry properties and spectra of the two-dimensional quantum compass model

We use exact symmetry properties of the two-dimensional quantum compass model to derive nonequivalent invariant subspaces in the energy spectra of $L\times L$ clusters up to L=6. The symmetry allows one to reduce the original $L\times L$ compass cluster to the $(L-1)\times (L-1)$ one with modified interactions. This step is crucial and enables: (i) exact diagonalization of the $6\times 6$ quantum compass cluster, and (ii) finding the specific heat for clusters up to L=6, with two characteristic energy scales. We investigate the properties of the ground state and the first excited states and present extrapolation of the excitation energy with increasing system size. Our analysis provides physical insights into the nature of nematic order realized in the quantum compass model at finite temperature. We suggest that the quantum phase transition at the isotropic interaction point is second order with some admixture of the discontinuous transition, as indicated by the entropy, the overlap between two types of nematic order (on horizontal and vertical bonds) and the existence of the critical exponent. Extrapolation of the specific heat to the $L\to\infty$ limit suggests the classical nature of the quantum compass model and high degeneracy of the ground state with nematic order.Comment: 15 pages, 12 figures; accepted for publication in Physical Review

Multiband d−pd-p model and self-doping in the electronic structure of Ba2_2IrO4_4

We introduce and investigate the multiband $d-p$ model describing a IrO$_4$ layer (such as realized in Ba$_2$IrO$_4$) where all $34$ orbitals per unit cell are partly occupied, i.e., $t_{2g}$ and $e_g$ orbitals at iridium and $2p$ orbitals at oxygen ions. The model takes into account anisotropic iridium-oxygen $d-p$ and oxygen-oxygen $p-p$ hopping processes, crystal-field splittings, spin-orbit coupling, and the on-site Coulomb interactions, both at iridium and at oxygen ions. We show that the predictions based on assumed idealized ionic configuration (with $n_0=5+4\times 6=29$ electrons per IrO$_4$ unit) do not explain well the independent \textit{ab initio} data and the experimental data for Ba$_2$IrO$_4$. Instead we find that the total electron density in the $d-p$ states is smaller, $n=29-x0$). When we fix $x=1$, the predictions for the $d-p$ model become more realistic and weakly insulating antiferromagnetic ground state with the moments lying within IrO$_2$ planes along (110) direction is found, in agreement with experiment and \textit{ab initio} data. We also show that: (i) holes delocalize over the oxygen orbitals and the electron density at iridium ions is enhanced, hence (ii) their $e_g$ orbitals are occupied by more than one electron and have to be included in the multiband $d-p$ model describing iridates.Comment: 12 pages, 4 figure

Charge transfer model for the electronic structure of layered ruthenates

Motivated by the earlier experimental results and \textit{ab initio} studies on the electronic structure of layered ruthenates (Sr$_2$RuO$_4$ and Ca$_2$RuO$_4$) we introduce and investigate the multiband $d-p$ charge transfer model describing a single RuO$_4$ layer, similar to the charge transfer model for a single CuO$_2$ plane including apical oxygen orbitals in high $T_c$ cuprates. The present model takes into account nearest-neighbor anisotropic ruthenium-oxygen $d-p$ and oxygen-oxygen $p-p$ hopping elements, crystal-field splittings and spin-orbit coupling. The intraorbital Coulomb repulsion and Hund's exchange are defined not only at ruthenium but also at oxygen ions. Our results demonstrate that the RuO$_4$ layer cannot be regarded to be a pure ruthenium $t_{2g}$ system. We examine a different scenario in which ruthenium $e_g$ orbitals are partly occupied and highlight the significance of oxygen orbitals. We point out that the predictions of an idealized model based on ionic configuration (with $n_0=4+4\times 6=28$ electrons per RuO$_4$ unit) do not agree with the experimental facts for Sr$_2$RuO$_4$ which support our finding that the electron number in the $d-p$ states is significantly smaller. In fact, we find the electron occupation of $d$ and $p$ orbitals for a single RuO$_4$ unit $n=28-x$, being smaller by at least 1--1.5 electrons from that in the ionic model and corresponding to self-doping with $x\simeq 1.5$.Comment: 12 pages, 3 figure