Orbital-selective Mott Research Articles

Electron Correlation and Spin Dynamics in Iron Pnictides and Chalcogenides

Superconductivity in the iron pnictides and chalcogenides is closely connected to a bad-metal normal state and a nearby antiferromagnetic order. Therefore, considerable attention has been focused on the role of electron correlations and spin dynamics. In this article, we summarize some key experiments that quite directly imply strong electron correlations in these materials, and discuss aspects of the recent theoretical studies on these issues. In particular, we outline a w-expansion, which treats the correlation effects using the Mott transition as the reference point. For the parent systems, it gives rise to an effective J1-J2 model that is coupled to the itinerant electrons in the vicinity of the Fermi energy; this model yields an isoelectronically-tuned quantum critical point, and allows a study of the distribution of the spin spectral weight in the energy and momentum space in the paramagnetic phase. Within the same framework, we demonstrate the Mott insulating phase in the iron oxychalcogenides as well as the alkaline iron selenides; for the latter system, we also consider the role of an orbital-selective Mott phase. Finally, we discuss the singlet superconducting pairing driven by the short-range J1-J2 interactions. Our considerations highlight the iron pnictides and chalcogenides as exemplifying strongly-correlated electron systems at the boundary of electronic localization and itinerancy.

Evidence of Strong Correlations and Coherence-Incoherence Crossover in the Iron Pnictide SuperconductorKFe2As2

Using resistivity, heat-capacity, thermal-expansion, and susceptibility measurements we study the normal-state behavior of KFe2As2. Both the Sommerfeld coefficient (γ≈103 mJ mol(-1) K(-2)) and the Pauli susceptibility (χ≈4×10(-4)) are strongly enhanced, which confirm the existence of heavy quasiparticles inferred from previous de Haas-van Alphen and angle-resolved photoemission spectroscopy experiments. We discuss this large enhancement using a Gutzwiller slave-boson mean-field calculation, which shows the proximity of KFe2As2 to an orbital-selective Mott transition. The temperature dependence of the magnetic susceptibility and the thermal expansion provide strong experimental evidence for the existence of a coherence-incoherence crossover, similar to what is found in heavy fermion and ruthenate compounds, due to Hund's coupling between orbitals.

Orbital-selective Mott transitions in a doped two-band Hubbard model with crystal field splitting

We investigate the effects of crystal field splitting in a doped two-band Hubbard model with different bandwidths within dynamical mean-field theory (DMFT), using a quantum Monte Carlo impurity solver. In addition to an orbital-selective Mott phase (OSMP) of the narrow band, which is adiabatically connected with the well-studied OSMP in the half-filled case without crystal field splitting, we find, for sufficiently strong interaction and a suitable crystal field, also an OSMP of the wide band. We establish the phase diagram (in the absence of magnetic or orbital order) at moderate doping as a function of interaction strength and crystal field splitting and show that also the wide-band OSMP is associated with non-Fermi-liquid behavior in the case of Ising type Hund rule couplings. Our numerical results are supplemented by analytical strong-coupling studies of spin order and spectral functions at integer filling.

Orbital-Selective Mott Phase in Multiorbital Models for Alkaline Iron SelenidesK1−xFe2−ySe2

We study a multiorbital model for the alkaline iron selenides K(1-x)Fe(2-y)Se(2) using a slave-spin method. With or without ordered vacancies, we identify a metal-to-Mott-insulator transition at the commensurate filling of six 3d electrons per iron ion. For Hund's couplings beyond a threshold value, this occurs via an intermediate orbital-selective Mott phase, in which the 3d xy orbital is Mott localized while the other 3d orbitals remain itinerant. This phase is still stabilized over a range of carrier dopings. Our results lead to an overall phase diagram for the alkaline iron selenides, which provides a unified framework to understand the interplay between the strength of the vacancy order and carrier doping. In this phase diagram, the orbital-selective Mott phase provides a natural link between the superconducting K(1-x)Fe(2-y)Se(2) and its Mott-insulating parent compound.

Band filling and correlation controlling electronic properties and magnetism in KxFe2−ySe2: a slave boson study

We investigate the electronic and magnetic properties of KxFe2−ySe2 materials at different band fillings utilizing the multi-orbital Kotliar–Ruckenstein slave boson mean-field approach. We find that the ground state of KFe2Se2 is a paramagnetic (PM) bad metal with intermediate correlation, in contrast with the previous antiferromagnetic (AFM) results obtained by the local density approximation. Our PM metallic ground state suggests that KFe2Se2 is the parent phase of superconducting KxFe2−ySe2, supporting a recent scanning tunneling spectroscopy experiment. For pure Fe2+-based systems, the ground state is a striped AFM (SAFM) metal with a spin density wave gap partially opened near the Fermi level. In comparison, for Fe3+-based compounds, besides SAFM, a Néel AFM metal without orbital ordering is observed, and an orbital selective Mott phase (OSMP) accompanied by an intermediate-spin to high-spin transition is also found, giving a possible scenario of an OSMP in KxFe2−ySe2. These results demonstrate that the band filling and correlation control the Fermi surface topology, electronic state and magnetism in KxFe2−ySe2.

Observation of Temperature-Induced Crossover to an Orbital-Selective Mott Phase inAxFe2−ySe2(A=K, Rb) Superconductors

Using angle-resolved photoemission spectroscopy, we observe the low-temperature state of the A(x)Fe(2-y)Se(2) (A=K, Rb) superconductors to exhibit an orbital-dependent renormalization of the bands near the Fermi level-the d(xy) bands heavily renormalized compared to the d(xz)/d(yz) bands. Upon raising the temperature to above 150 K, the system evolves into a state in which the d(xy) bands have depleted spectral weight while the d(xz)/d(yz) bands remain metallic. Combined with theoretical calculations, our observations can be consistently understood as a temperature-induced crossover from a metallic state at low temperatures to an orbital-selective Mott phase at high temperatures. Moreover, the fact that the superconducting state of A(x)Fe(2-y)Se(2) is near the boundary of such an orbital-selective Mott phase constrains the system to have sufficiently strong on-site Coulomb interactions and Hund's coupling, highlighting the nontrivial role of electron correlation in this family of iron-based superconductors.

Emergence of a common energy scale close to the orbital-selective Mott transition.

We calculate the spectra and spin susceptibilities of a Hubbard model with two bands having different bandwidths but the same on-site interaction, with parameters close to the orbital-selective Mott transition, using dynamical mean-field theory. If the Hund's rule coupling is sufficiently strong, one common energy scale emerges which characterizes both the location of kinks in the self-energy and extrema of the diagonal spin susceptibilities. A physical explanation of this energy scale is derived from a Kondo-type model. We infer that for multiband systems local spin dynamics rather than spectral functions determine the location of kinks in the effective band structure.

Orbital selectivity in Hund's metals: The iron chalcogenides

We show that electron correlations lead to a bad metallic state in chalcogenides FeSe and FeTe despite the intermediate value of the Hubbard repulsion $U$ and Hund's rule coupling $J$. The evolution of the quasiparticle weight $Z$ as a function of the interaction terms reveals a clear crossover at $U\ensuremath{\simeq}2.5$ eV. In the weak coupling limit $Z$ decreases for all correlated $d$ orbitals as a function of $U$ and beyond the crossover coupling they become weakly dependent on $U$ while strongly dependent on $J$. A marked orbital dependence of the $Z$'s emerges even if in general the orbital-selective Mott transition only occurs for relatively large values of $U$. This two-stage reduction of the quasiparticle coherence due to the combined effect of Hubbard $U$ and the Hund's $J$ suggests that the iron-based superconductors can be referred to as Hund's correlated metals.

Hall-effect characterization of the metamagnetic transition in FeRh

The antiferromagnetic ground state and the metamagnetic transition to the ferromagnetic state of CsCl-ordered FeRh epilayers have been characterized using Hall and magnetoresistance measurements. On cooling into the ground state, the metamagnetic transition is found to coincide with a suppression in carrier density of at least an order of magnitude below the typical metallic level that is shown by the ferromagnetic state. The carrier density in the antiferromagnetic state is limited by intrinsic doping from Fe/Rh substitution defects, with approximately two electrons per pair of atoms swapped, showing that the decrease in carrier density could be even larger in more perfect specimens. The surprisingly large change in carrier density is a clear quantitative indication of the extent of change at the Fermi surface at the metamagnetic transition, confirming that entropy release at the transition is of electronic origin, and hence that an electronic transition underlies the metamagnetic transition. Regarding the nature of this electronic transition, it is suggested that an orbital selective Mott transition, selective to strongly-correlated Fe 3d electrons, could cause the reduction in the Fermi surface and change in sign of the magnetic exchange from FM to AF on cooling.

Mott Transitions in Three-Orbital Hubbard Model at Fractional Band Filling

We investigate the Mott transitions in the three-orbital Hubbard model by means of the dynamical mean field theory with continuous-time quantum Monte Carlo simulations. We obtain the phase diagram determined in the orbital level splitting versus Hubbard interaction plane in the case of two electrons per site. It is also found that the introduction of holes into the orbital selective Mott insulating phase induces the metallic state with heavy quasiparticles.

Importance of exchange anisotropy and superexchange for the spin-state transitions inRCoO3(R=rare earth) cobaltates

Spin-state transitions are the hallmark of rare-earth cobaltates. In order to understand them, it is essential to identify all relevant parameters which shift the energy balance between spin states and determine their trends. We find that $\ensuremath{\Delta}$, the ${e}_{g}$-${t}_{2g}$ crystal-field splitting, increases by $\ensuremath{\sim}$250 meV when increasing pressure to 8 GPa and by about 150 meV when cooling from 1000 K to 5 K. It changes, however, by less than 100 meV when La is substituted with another rare earth. Moreover, the Hund's rule coupling ${\mathcal{J}}_{\mathrm{avg}}$ is about the same in systems with very different spin-state transition temperature, like LaCoO${}_{3}$ and EuCoO${}_{3}$. Consequently, in addition to $\ensuremath{\Delta}$ and ${\mathcal{J}}_{\mathrm{avg}}$, the Coulomb-exchange anisotropy $\ensuremath{\delta}{\mathcal{J}}_{\mathrm{avg}}$ and the superexchange energy gain $\ensuremath{\delta}{E}_{\mathrm{SE}}$ play a crucial role and are comparable with spin-state-dependent relaxation effects due to covalency. We show that in the LnCoO${}_{3}$ series, with $\mathrm{Ln}=\mathrm{Y}$ or another rare earth ($RE$), superexchange progressively stabilizes a low-spin ground state as the Ln${}^{3+}$ ionic radius decreases. We give a simple model to describe spin-state transitions and show that, at low temperature, the formation of isolated high-spin/low-spin pairs is favored, while in the high-temperature phase, the most likely homogeneous state is high spin rather than intermediate spin. An orbital-selective Mott state could be a fingerprint of such a state.

Effects of non-local spin fluctuations in the orbital-selective Mott transition

Employing the extended dynamical mean field theory (EDMFT) and the quantum Monte Carlo (QMC) method, we investigate the effect of the spatial fluctuations in the two-band Hubbard model with anisotropic bandwidth in the vicinity of the Mott metal-insulator transition. At half filling, we demonstrate that while the inclusion of the non-local spin-spin interaction amounts to enhancing the correlation and suppressing the metallic character, the orbitally selective Mott transition (OSMT) remains stable for various strengths of the non-local correlation. The same is true when the system is doped away from half filling. The OSMT phase is evidenced at low dopant concentration and the simultaneous metallic phase emerges at overdoped regime. From the analysis of the self energy, it follows that the nature of the metallic phase upon doping violates the Fermi liquid character and persists at considerably large doping. Our theory also offers a new perspective for the investigation of the non-local fluctuation in the multi-orbital system within the single-site scheme.

U(1)slave-spin theory and its application to Mott transition in a multiorbital model for iron pnictides

A $U(1)$ slave-spin representation is introduced for multiorbital Hubbard models. As with the ${Z}_{2}$ form of de'Medici et al. [Phys. Rev. B 72, 205124 (2005)], this approach represents a physical electron operator as the product of a slave spin and an auxiliary fermion operator. For nondegenerate multiorbital models, our $U(1)$ approach is advantageous in that it captures the noninteracting limit at the mean-field level. For systems with either a single orbital or degenerate multiple orbitals, the $U(1)$ and ${Z}_{2}$ slave-spin approaches yield the same results in the slave-spin-condensed phase. In general, the $U(1)$ slave-spin approach contains a $U(1)$ gauge redundancy, and properly describes a Mott insulating phase. We apply the $U(1)$ slave-spin approach to study the metal-to-insulator transition in a five-orbital model for parent iron pnictides. We demonstrate a Mott transition as a function of the interactions in this model. The nature of the Mott insulating state is influenced by the interplay between the Hund's rule coupling and crystal-field splittings. In the metallic phase, when the Hund's rule coupling is beyond a threshold, there is a crossover from a weakly correlated metal to a strongly correlated one, through which the quasiparticle spectral weight rapidly drops. The existence of such a strongly correlated metallic phase supports the incipient Mott picture of the parent iron pnictides. In the parameter regime for this phase and in the vicinity of the Mott transition, we find that an orbital selective Mott state has nearly as competitive a ground-state energy.

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

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 mean-field theory and rotationally invariant Gutzwiller approximation, we have computed the full phase diagram with Coulomb interaction strength $U$ and crystal field splitting $\Delta$. 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.

Investigation of on-site interorbital single-electron hoppings in general multiorbital systems

A general multi-orbital Hubbard model, which includes on-site inter-orbital electron hoppings, is introduced and studied. It is shown that the on-site inter-orbital single electron hopping is one of the most basic interactions. Two electron spin-flip and pair-hoppings are shown to be correlation effects of higher order than the on-site inter-orbital single hopping. It is shown how the double and higher hopping interactions can be well-defined for arbitrary systems. The two-orbital Hubbard model is studied numerically to demonstrate the influence of the single electron hopping effect, leading to a change of the shape of the bands and a shrinking of the difference between the two bands. Inclusion of the on-site inter-orbital hopping suppresses the so-called orbital-selective Mott transition.

Pressure-driven orbital selective insulator-to-metal transition and spin-state crossover in cubic CoO

The metal-insulator and spin state transitions of CoO under high pressure are studied by using density functional theory combined with dynamical mean-field theory. Our calculations predict that the metal-insulator transition in CoO is a typical orbital selective Mott transition, where the $t_{2g}$ orbitals of Co 3d shell become metallic firstly around 60 GPa while the $e_g$ orbitals still remain insulating until 170 GPa. Further studies of the spin states of Co 3d shell reveal that the orbital selective Mott phase in the intermediate pressure regime is mainly stabilized by the high-spin state of the Co 3d shell and the transition from this phase to the full metallic state is driven by the high-spin to low-spin transition of the Co$^{2+}$ ions. Our results are in good agreement with the most recent transport and x-ray emission experiments under high pressure.

Quantum critical phase and Lifshitz transition in an extended periodic Anderson model

We study the quantum phase transition in f-electron systems as a quantum Lifshitz transition driven by selective-Mott localization in a realistic extended Anderson lattice model. Using dynamical mean-field theory (DMFT), we find that a quantum critical phase with anomalous ω/T scaling separates a heavy Landau–Fermi liquid from ordered phase(s). This non-Fermi liquid state arises from a lattice orthogonality catastrophe originating from orbital-selective Mott localization. Fermi surface reconstruction occurs via the interplay between and penetration of the Green function zeros to the poles, leading to violation of Luttinger’s theorem in the strange metal. We show how this naturally leads to scale-invariant responses in transport. Thus, our work represents a specific DMFT realization of the hidden-FL and FL* theories, and holds promise for the study of ‘strange’ metal phases in quantum matter.

Orbital-selective crossover and Mott transitions in an asymmetric Hubbard model of cold atoms in optical lattices

We study the asymmetric Hubbard model at half filling as a generic model to describe the physics of two species of repulsively interacting fermionic cold atoms in optical lattices. We use dynamical mean-field theory to obtain the paramagnetic phase diagram of the model as a function of temperature, interaction strength, and hopping asymmetry. A Mott transition with a region of two coexistent solutions is found for all nonzero values of the hopping asymmetry. At low temperatures the metallic phase is a heavy Fermi liquid, qualitatively analogous to the Fermi-liquid state of the symmetric Hubbard model. Above a coherence temperature, an orbital-selective crossover takes place, wherein one fermionic species effectively localizes, and the resulting bad metallic state resembles the non-Fermi-liquid state of the Falicov-Kimball model. We compute observables relevant to cold atom systems such as the double occupation, the specific heat, and entropy, and characterize their behavior in the different phases.

Mott transition in three-orbital Hubbard model with orbital splitting

We study the Mott transition in the three-orbital Hubbard model. To investigate how the orbital level splitting and the Ising-type Hund's coupling affect the Mott transition in the case of two electrons per site, we use the dynamical mean-field theory combined with continuous-time quantum Monte Carlo simulations. The calculation of the double occupancy reveals that the critical interaction strength separating a metallic phase and two kinds of insulating phases shows a nonmonotonic behavior as a function of the level splitting. We find that this behavior is characteristic for $1/3$ filling, in comparison with the preceding results for different fillings and for two-orbital models. Strong competition between the two insulators results in an intriguing first-order transition to an insulating phase having intermediate characters between Mott and band insulators. It is also found that the two insulators show different behaviors in the phase boundary with the metallic phase in the interaction-temperature plane, which is reflected in a difference in the quasiparticle behavior around the transition. We also discuss the orbital selective Mott transition for larger Hund's coupling, which is compared with previous study at zero temperature.

Hund’s coupling and its key role in tuning multiorbital correlations

It is shown how, in multiband materials, the Hund's coupling plays a crucial role in tuning the degree of electronic correlation. While in half-filled systems it enhances the correlations, in all other cases it pushes the boundary for the Mott transition at very high critical couplings. Moreover in weakly hybridized nondegenerate systems the Hund's coupling plays the role of band decoupler, causing a change from a collective to an individual band behavior, due to the freezing of orbital fluctuations. In this situation the physics is strongly dependent on individual filling and electronic structure of each band, and orbital-selective Mott transitions (or even a cascade of such transitions) are to be expected. More generally a heavy differentiation in the actual degree of correlation of different bands arises and the system can show both weakly and strongly correlated electrons.