Carriers binding to excitons: Crystal-field excitations in doped Mott-Hubbard insulators

Orbital Symmetry and Orbital Excitations in High-Tc Superconductors

We discuss a few possibilities of high- T c superconductivity with more than one orbital symmetry contributing to the pairing. First, we show that the high energies of orbital excitations in various cuprates suggest a simplified model with a single orbital of x 2 − y 2 symmetry doped by holes. Next, several routes towards involving both e g orbital symmetries for doped holes are discussed: (i) some give superconductivity in a CuO 2 monolayer on Bi2212 superconductors, Sr 2 CuO 4 − δ , Ba 2 CuO 4 − δ , while (ii) others as nickelate heterostructures or Eu 2 − x Sr x NiO 4 , could in principle realize it as well. At low electron filling of Ru ions, spin-orbital entangled states of t 2 g symmetry contribute in Sr 2 RuO 4 . Finally, electrons with both t 2 g and e g orbital symmetries contribute to the superconducting properties and nematicity of Fe-based superconductors, pnictides or FeSe. Some of them provide examples of orbital-selective Cooper pairing.

Nodeless High-T_{c} Superconductivity in the Highly Overdoped CuO_{2} Monolayer

We study the electronic structure and superconductivity in a CuO_{2} monolayer grown recently on the d-wave cuprate superconductor Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}. Density functional theory calculations indicate a significant charge transfer across the interface such that the CuO_{2} monolayer is heavily overdoped into the hole-rich regime yet inaccessible in bulk cuprates. We show that both the Cu d_{x^{2}-y^{2}} and d_{3z^{2}-r^{2}} orbitals become important and the Fermi surface contains one electron and one hole pocket associated with the two orbitals, respectively. Constructing a minimal correlated two-orbital model for the e_{g} complex, we show that the spin-orbital exchange interactions produce a nodeless superconductor with extended s-wave pairing symmetry and a pairing energy gap comparable to the bulk d-wave gap, in agreement with recent experiments. The findings point to a direction of realizing new high-T_{c} superconductors in ozone grown transition-metal-oxide monolayer heterostructures.

A possibility of high spin hole states in doped CoO2 layered systems

We introduce and investigate an effective five-band model for t2g and eg electrons to describe doped cobalt oxides with Co(3+) and Co(4+) ions in two-dimensional CoO2 triangular lattice layers, as in Na1-xCoO2. 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 × 6 clusters with periodic boundary conditions. The computations indicate a 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 CoO2 planes, doping generates high S = 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 magnetic ions with coexisting antiferromagnetic and ferromagnetic bonds between them, forming stripe-like structures. The ground states are insulating within the investigated range of doping because computed HOMO-LUMO gaps are never small enough.

Fingerprints of spin-orbital entanglement in transition metal oxides

The concept of spin-orbital entanglement on superexchange bonds in transition metal oxides is introduced and explained on several examples. It is shown that spin-orbital entanglement in superexchange models destabilizes the long-range (spin and orbital) order and may lead either to a disordered spin-liquid state or to novel phases at low temperature which arise from strongly frustrated interactions. Such novel ground states cannot be described within the conventionally used mean field theory which separates spin and orbital degrees of freedom. Even in cases where the ground states are disentangled, spin-orbital entanglement occurs in excited states and may become crucial for a correct description of physical properties at finite temperature. As an important example of this behaviour we present spin-orbital entanglement in the RV O(3) perovskites, with R = La,Pr,…,Y b,Lu, where the finite temperature properties of these compounds can be understood only using entangled states: (i) the thermal evolution of the optical spectral weights, (ii) the dependence of the transition temperatures for the onset of orbital and magnetic order on the ionic radius in the phase diagram of the RV O(3) perovskites, and (iii) the dimerization observed in the magnon spectra for the C-type antiferromagnetic phase of Y V O(3). Finally, it is shown that joint spin-orbital excitations in an ordered phase with coexisting antiferromagnetic and alternating orbital order introduce topological constraints for the hole propagation and will thus radically modify the transport properties in doped Mott insulators where hole motion implies simultaneous spin and orbital excitations.

Absence of hole confinement in transition-metal oxides with orbital degeneracy

We investigate the spectral properties of a hole moving in a two-dimensional Hubbard model for strongly correlated t(2g) electrons. Although superexchange interactions are Ising-like, a quasi-one-dimensional coherent hole motion arises due to effective three-site terms. This mechanism is fundamentally different from the hole motion via quantum fluctuations in the conventional spin model with SU(2) symmetry. The orbital model describes also propagation of a hole in some e(g) compounds, and we argue that orbital degeneracy alone does not lead to hole self-localization.

Interplay between the orbital and magnetic order in monolayer La(1-x)Sr(1+x)MnO(4) manganites

A two-dimensional model which describes e(g) electrons in a monolayer of an undoped and half doped manganite La(1-x)Sr(1+x)MnO(4) is studied using correlated wavefunctions. The effective Hamiltonian takes into account the kinetic energy, the crystal field splitting between x(2)-y(2) and 3z(2)-r(2) orbitals, and on-site Coulomb interactions for e(g) electrons. They interact with S = 3/2 spins due to t(2g) electrons, which are treated as frozen core spins. Furthermore, the model includes antiferromagnetic superexchange interaction between core spins, and the coupling between e(g) electrons and Jahn-Teller modes. The model reproduces the antiferromagnetic order in the undoped LaSrMnO(4) compound, with occupied 3z(2)-r(2) orbitals and elongated MnO(6) octahedra along the direction perpendicular to the Mn-O plane. In half doped La(0.5)Sr(1.5)MnO(4) manganite one finds robust chequerboard-like charge order using realistic parameters. However, the experimentally observed CE phase is more difficult to stabilize, and we discuss the necessary conditions to obtain it within the present model. Altogether, we conclude that the Jahn-Teller effect plays a crucial role in the entire regime of doping.