Complete phase diagram for three-band Hubbard model with orbital degeneracy lifted by crystal field splitting

Abstract

Motivated by the unexplored complexity of the phase diagrams for multi-orbital Hubbard models, a three-band Hubbard model at integer fillings (N = 4) with orbital degeneracy lifted partially by crystal field splitting is analyzed systematically in this work. By using single site dynamical meanfield theory and rotationally invariant Gutzwiller approximation, we have computed the full phase diagram with Coulomb interaction strength U and crystal field splitting ∆. We find a large region in the phase diagram, where an orbital selective Mott phase will be stabilized by the positive crystal field lifting the orbital degeneracy. Further analysis indicates that the Hund's rule coupling is essential for the orbital selective Mott phase and the transition toward this phase is accompanied by a high-spin to low-spin transition. Such a model may be relevant for the recently discovered pnictides and ruthenates correlated materials.

Numerical optimization algorithm for rotationally invariant multi-orbital slave-boson method

“…All above results demonstrate that the OSMP region of two-orbital model strongly depends on the spin-flip Hund's rule coupling term, since it enhances the itinerancy of the electrons in wide orbital. However, the situation of three-orbital model is very different, where the Ising-type Hund's rule coupling term and crystal field splitting become the key factors for OSMP at integer filling [27,28,30,31]. Away from half filling, the critical value U c of the Mott transition of the narrow orbital is not seriously affected by the spin-flip and pair-hopping terms.…”

“…It has been known that the Hund's rule coupling can be divided into longitudinal (the Isingtype z-component) and transverse (the spin-flip and orbital pairhopping) terms, and most of previous literatures only considered the contribution of Ising-type term. The magnetic phase diagram and metal-insulating transition of multi-orbital systems strongly depend on the Hund's rule coupling [27][28][29]. To explore the effects of spin-flip and pair-hopping terms on the Mott transition and antiferromagnetic ground state, we discuss the dependence of the QP weight and magnetic moments on different Hund's coupling terms.…”

Interface exchange processes inLaAlO3/SrTiO3induced by oxygen vacancies

“…The interacting multi-orbital problem is solved by a real-space formulation of the rotational-invariant slaveboson (RISB) mean-field method [50,[52][53][54][55]. It corresponds to single-site DMFT close to zero temperature with a simpler impurity solver than the CT-QMC, allowing for local self-energies Σ with a linear frequency dependence and static terms.…”

Orbital differentiation in Hund metals

“…The nature of the different phases can be easily understood by looking at the occupations in the atomic limit ( Fig. 1) [19,21]: For large ∆ > 0, the 1-orbital has highest energy; both electrons reside in the half-filled 23-doublet and are likely to form a Mott insulator [49]. For the symmetric model at ∆ = 0, the two electrons are equally distributed among the three degenerate orbitals with occupation n m = 2/3 each, giving rise to metallic behavior (for not too strong interaction).…”