Mott-Hubbard Insulator Research Articles

Theory for photoinduced phase transition from a charge-density-wave state to a Mott-Hubbard insulator in a quasi-one-dimensional Br-bridged Pd compound

Photoinduced phase transition from a charge-density-wave (CDW) state to a Mott-Hubbard (MH) insulator is studied theoretically. According to the very recent experiment [H. Matsuzaki et al., Phys Rev B 70, 035204 (2004)], a quasi-one-dimensional Br-bridged Pd compound, $[\mathrm{Pd}{(\mathrm{chxn})}_{2}][\mathrm{Pd}{(\mathrm{chxn})}_{2}{\mathrm{Br}}_{2}]{\mathrm{Br}}_{4}$, can become a MH insulator in its metastable phase that is usually hidden by the stable CDW phase. Since this finding strongly suggests the possibility of a light-driven macroscopic phase change from the latter to the former, we investigate possible relaxation paths realizing such phase changes. It is found that both of two initial photoexcited states, namely, the lowest exciton and a separate electron-hole pair yielded by a high-energy excitation, induce the phase change with no energy barrier. This demonstrates a very ``soft'' nature of this material, being consistent with recent experimental results.

Orbital physics in the perovskite Ti oxides

Titanate compounds have been recognized as key materials for understanding the coupling of magnetism and orbitals in strongly correlated electron systems. In the perovskite Ti oxide RTiO3 (where R represents the trivalent rare-earth ions), which is a typical Mott–Hubbard insulator, the Ti t2g orbitals and spins in the 3d1 state couple each other through the strong electron correlations, resulting in a rich variety of orbital–spin phases. One way of controlling the coupling is to change the tiltings of the TiO6 octahedra (namely the GdFeO3-type distortion) by varying the R ions, through which the relative ratio of the electron bandwidth to the Coulomb interaction is controlled. With this control, these Mott insulators exhibit an antiferromagnetic-to-ferromagnetic (AFM–FM) phase transition, which has turned out to be a consequence of rich orbital physics in these materials. The origin and nature of orbital–spin structures of these Mott insulators have been intensively studied both experimentally and theoretically. When the Mott insulators are doped with carriers, the titanates show touchstone properties of the filling controlled Mott transition. In this paper, we first review the state of the art on the studies for understanding physics contained in the properties of the perovskite titanates. On the properties of the insulators, we focus on the following three topics: (1) the origin and nature of the ferromagnetism as well as the orbital ordering in the compounds with relatively small R ions such as GdTiO3 and YTiO3, (2) the origin of the G-type antiferromagnetism and the orbital state in LaTiO3 and (3) the orbital–spin structures in other AFM(G) compounds with relatively large R ions (R = Ce, Pr, Nd and Sm). On the basis of these discussions, we discuss the whole phase diagram together with mechanisms of the magnetic phase transition. On the basis of the microscopic understanding of the orbital–spin states, we show that the Ti t2g degeneracy is inherently lifted in the titanates, which allows the single-band descriptions of the ground-state and the low-energy electronic structures as a good starting point. Our analyses indicate that these compounds offer good touchstone materials described by the single-band Hubbard model on the cubic lattice. From this insight, we also re-analyse the hole-doped titanates TiO3 (where A represents the divalent alkaline-earth ions). Experimentally revealed filling- and bandwidth-dependent properties and the critical behaviour of the metal–insulator transitions are discussed in the light of theories based on the single-band Hubbard models.

Phase diagram for the exciton Mott transition in infinite-dimensional electron–hole systems

To understand the essence of the exciton Mott transition in three-dimensional electron–hole systems, the metal–insulator transition is studied for a two-band Hubbard model in infinite dimensions with interactions of electron–electron (hole–hole) repulsion U and electron–hole attraction - U ′ . By using the dynamical mean-field theory, the phase diagram in the U– U ′ plane is obtained (which is exact in infinite dimensions) assuming that electron–hole pairs do not condense. When both electron and hole bands are half-filled, two types of insulating states appear: the Mott–Hubbard insulator for U > U ′ and the biexciton-like insulator for U < U ′ . Even when away from half-filling, we find the phase transition between the exciton- or biexciton-like insulator and a metallic state. This transition can be assigned to the exciton Mott transition, whereas the Mott–Hubbard transition is absent.

Spin-Controlled Mott-Hubbard Bands inLaMnO3Probed by Optical Ellipsometry

Spectral ellipsometry is used to determine the dielectric function of an untwinned crystal of LaMnO3 in the range 0.5-5.6 eV at temperatures 50<or=T<or=300 K. A pronounced redistribution of spectral weight is found at the Ne el temperature T(N)=140 K. The anisotropy of the spectral weight transfer matches the magnetic ordering pattern. A superexchange model quantitatively describes spectral weight transfer induced by spin correlations. This analysis implies that the lowest-energy transitions around 2 eV are intersite d-d transitions, and that LaMnO3 is a Mott-Hubbard insulator.

Dynamical mean-field theory of the Hubbard-Holstein model at half filling: Zero temperature metal-insulator and insulator-insulator transitions

We study the Hubbard-Holstein model, which includes both the electron-electron and electron-phonon interactions characterized by $U$ and $g$, respectively, employing the dynamical mean-field theory combined with Wilson's numerical renormalization group technique. A zero temperature phase diagram of metal-insulator and insulator-insulator transitions at half-filling is mapped out which exhibits the interplay between $U$ and $g$. As $U$ ($g$) is increased, a metal to Mott-Hubbard insulator (bipolaron insulator) transition occurs, and the two insulating states are distinct and can not be adiabatically connected. The nature of and transitions between the three states are discussed.

Dynamical density-matrix renormalization group for the Mott–Hubbard insulator in high dimensions

We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number in the paramagnetic insulating phase at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity Anderson model with a bath whose properties have to be determined self-consistently. For a controlled and systematic implementation of the self-consistency scheme we use the fixed-energy approach to the DMFT (FE-DMFT). In FE-DMFT, the onset and the width of the Hubbard bands are adjusted self-consistently but the energies of the bath levels are kept fixed relatively to both band edges during the calculation of self-consistent hybridization strengths between impurity and bath sites. Using the dynamical density-matrix renormalization group method (DDMRG) we calculate the density of states with a resolution ranging from 3% of the bare bandwidth W = 4t at high energies to 0.5% in the vicinity of the gap. The DDMRG resolution and accuracy for the density of states and the gap is superior to those obtained with other numerical methods in previous DMFT investigations. We find that the Mott gap closes at a critical coupling Uc/t = 4.45 ± 0.05. At U = 4.5t, we observe prominent shoulders near the onset of the Hubbard bands. They are the remainders of the quasi-particle resonance in the metallic phase which appears to split when the gap opens at Uc.

Inhomogeneous metallic phase in a disordered Mott insulator in two dimensions.

We show that, with increasing randomness, the spectral gap in a 2D Mott-Hubbard insulator is destroyed first at a disorder V(c1), while antiferromagnetism persists up to a higher V(c2). Most unexpectedly, between V(c1) and V(c2) the system is metallic and is sandwiched between the Mott insulator below V(c1) and the Anderson insulator above V(c2). The metal is formed when the spectral gap gets destroyed locally in regions where the disorder potential is high enough to overcome the interelectron repulsion. This generates puddles with enhanced charge fluctuations that percolate with increasing disorder, resulting in a spatially inhomogeneous metallic phase.

Filling of the mott-hubbard gap in the high temperature photoemission spectrum of (V0.972Cr0.028)2O3.

Photoemission spectra of the paramagnetic insulating phase of (V0.972Cr0.028)2O3, taken in ultrahigh vacuum up to the unusually high temperature (T) of 800 K, reveal a property unique to the Mott-Hubbard (MH) insulator that has not been observed previously. With increasing T the MH gap is filled by spectral weight transfer, in qualitative agreement with high-T theoretical calculations combining dynamical mean field theory and band theory in the local density approximation.

Tuning the electronic structure from charge-transfer insulator to Mott-Hubbard and Peierls insulators in one-dimensional halogen-bridged mixed-metal compounds

The electronic structures of one-dimensional (1D) halogen-bridged mixed-metal compounds, $[{\mathrm{Ni}}_{1\ensuremath{-}x}{\mathrm{Pd}}_{x}{(\mathrm{chxn})}_{2}X]{X}_{2}$ ($\mathrm{chxn}$= cyclohexanediamine; $X=\mathrm{Cl}$,$\mathrm{Br}$; $0\ensuremath{\leqslant}x\ensuremath{\leqslant}1$), are investigated through optical and magnetic measurements. The results reveal that the system changes from charge-transfer (CT) insulator to Mott-Hubbard (MH) insulator at around $x\ensuremath{\sim}0.3$, and from MH insulator to Peierls insulator at $x\ensuremath{\sim}0.9$ with increasing $x$. From the analysis of optical conductivity spectra using the 1D two-band extended Peierls-Hubbard model, electronic parameters such as Coulomb repulsion energy, $pd$ hybridization, CT energy, and electron-lattice interaction are determined.

Ambipolar field-effect carrier injections in organic Mott insulators

We report ambipolar field-effect characteristics observed in metal-insulator-semiconductor field-effect transistor (MISFET) device structures based on organic single crystals of the quasi-one-dimensional (Q1D) Mott-Hubbard insulator (BEDT-TTF)$({\mathrm{F}}_{2}\text{TCNQ})$. The main aspects of the measured field-effect properties are well described by the symmetric-gate FET model, which considers the device symmetry of triode FET structures. The temperature-dependent nonlinear nature in the gated-current-voltage characteristics indicates that the ambipolar field-effect carrier injections are present down to $2\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, where the interface barrier potential between the electrode and the Mott insulator appears to be very similar for hole and electron injections, in sharp contrast to the situation involving band insulators.

Electronic Structure and Excited-state Properties of Perovskite-like Oxides

The role of structural distortion, magnetic ordering, and Coulomb-correlation effect on the electronic structure of perovskite-like oxides is analyzed. The density-functional theory (DFT) is originally devised to describe the ground-state properties of materials. However, during recent years it has been seen that the DFT can also be used to study excited state properties succesfully. We have recently calculated the electronic structure and linear optical properties for the series LaXO 3 (X=Sc–Cu) and found that the gradient-corrected DFT describes correctly the insulating behavior of the ionic insulator LaScO 3 and the charge-transfer insulators LaCrO 3, LaFeO 3, and LaMnO 3 although the band gaps are systematically underestimated. For example, the good agreement between experimental and theoretical reflectivity spectra for LaCrO 3 clearly demonstrates that accurate full-potential DFT calculations not only describe the occupied and unoccupied states of the bands well, but also reproduce their characters. We have also calculated XPS, XANES, and magneto-optical spectra for perovskite-like oxides. For Mott–Hubbard insulators such as LaTiO 3 and LaVO 3 the DFT failed to predict insulating behavior and here the LDA+ U method is applied to describe the electronic structure correctly.

Anisotropic metal-insulator transition in epitaxial thin films.

By comparing the properties of In and Pb quantum wells in a scanning tunneling microscopy subsurface imaging experiment, we found the existence of lateral bound states, a 2D Mott-Hubbard correlation gap, induced by transverse confinement. Its formation is attributed to spin or charge overscreening of quasi-2D excitations. The signature of the 2D confinement-deconfinement transition is also experimentally observed, with the correlation gap being pinned in the middle of the conduction band. A self-organized 2D Anderson lattice is suggested as a new ground state.

Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: Slater vs. Mott?Heisenberg

We study antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model at low temperature. Collective spin fluctuations are governed by a non-linear sigma model that we derive from the Hubbard model for any value of the Coulomb repulsion. As the Coulomb repulsion increases, the ground state progressively evolves from a Slater to a Mott–Heisenberg antiferromagnet. At finite temperature, we find a metal–insulator transition between a pseudogap phase at weak coupling and a Mott–Hubbard insulator at strong coupling.

Orbital ordering in charge transfer insulators.

We discuss a new mechanism of orbital ordering, which in charge transfer insulators is more important than the usual exchange interactions and which can make the very type of the ground state of a charge transfer insulator, i.e., its orbital and magnetic ordering, different from that of a Mott-Hubbard insulator. This purely electronic mechanism allows us to explain why orbitals in Jahn-Teller materials typically order at higher temperatures than spins, and to understand the type of orbital ordering in a number of materials, e.g., K2CuF4, without invoking the electron-lattice interaction.

Hybrid density functional theory study of vanadium monoxide

First-principles calculations of nondefective VO in the $\mathrm{Fm}3\ifmmode\bar\else\textasciimacron\fi{}m$ structure based on a range of single-particle Hamiltonians containing varying amounts of exact exchange indicate that the ground electronic state is that of a ${d}^{3}$ high spin, antiferromagnetic (AF), Mott-Hubbard insulator with an ${\mathrm{AF}}_{1}$ spin alignment of the local cation moments. This description remains essentially unchanged down to 10% exact exchange, and only for the pure density functional theory (DFT) potential is the ${\mathrm{AF}}_{1}$ phase found to be metallic. Strong spin-lattice interaction is predicted with differences in lattice constant of up to 1.6% between ${\mathrm{AF}}_{1}$ and FM (ferromagnetic) order. The ${\mathrm{AF}}_{1}$ lattice constant is predicted to be $\ensuremath{\sim}4.37\AA{},$ which is roughly 7% greater than the reported lattice constants for the defective material. The bulk modulus is comparable to those of CaO, MnO, and NiO. A mapping of total energies onto an Ising spin Hamiltonian containing both direct and superexchange interactions reveals the dominant magnetic interaction to be the direct coupling of antiferromagnetically aligned nearest-neighbor cation spins, which leads to the stability of the ${\mathrm{AF}}_{1}$ phase. Direct coupling energies are found in the range $\ensuremath{-}11.1$ to $\ensuremath{-}44.3\mathrm{meV}$ as the proportion of exact exchange is reduced, leading to an estimated critical disorder temperature in the range 300--450 K. However, the limitations of such mapping are exposed by a consideration of the relative stabilities of the ${\mathrm{AF}}_{1}$ and ${\mathrm{AF}}_{3}$ alignments. Orbital projected densities of states reveal filled to unfilled gaps which depend strongly on the proportion of exact exchange and for the B3LYP potential (20% exact exchange) are $\ensuremath{\sim}2.5\mathrm{eV}$ for the spin-forbidden $xy(\ensuremath{\uparrow})\ensuremath{\rightarrow}xy(\ensuremath{\downarrow})$ excitation, $\ensuremath{\sim}3.0\mathrm{eV}$ for $xy(\ensuremath{\uparrow})\ensuremath{\rightarrow}{z}^{2}(\ensuremath{\uparrow}),$ and $\ensuremath{\sim}3.5\mathrm{eV}$ for $\stackrel{\ensuremath{\rightarrow}}{V}\mathrm{O}$ charge transfer. Variationally stable, highly local crystal-field excited states ranging in energy from $\ensuremath{\sim}0.6$ to $\ensuremath{\sim}2.7\mathrm{eV}$ are predicted for exchange-correlation potentials down to 30% exact exchange and from comparisons with the corresponding band excitation estimates of $\ensuremath{\sim}1$ to $\ensuremath{\sim}2\mathrm{eV}$ are obtained for the localization energy of Frenkel excitons. From a mapping of the excited crystal-field energies onto a Kanamori Hamiltonian, values are obtained for the lattice Racah B and C parameters and the $d$-orbital averaged exchange and crystal-field energies. A comparison of mapped and directly calculated energies of the two-electron excitation $(xz,yz)\ensuremath{\rightarrow}{(z}^{2}{,x}^{2}\ensuremath{-}{y}^{2})$ confirms the validity of Kanamori mapping, notably in the limit of exact exchange.

Magnetotransport properties ofLaMnO3

The magnetotransport properties of ${\mathrm{LaMnO}}_{3}$ have been studied using the crystal-field theory and the correlated effective-field theory. The crystal-field theory is used to treat the many-body problem of an atom or ion in the crystal and the correlated effective-field theory is used to treat the many-body effect of the magnetic part of the Hamiltonian. The crystal-field theory exploits the symmetry of the electrostatic field generated by the ligands around the magnetic ion in the transition-metal compounds. The parent compound of colossal magnets, e.g., ${\mathrm{LaMnO}}_{3}$ is a Mott-Hubbard and charge-transfer antiferromagnetic insulator. The magnetotransport properties of this compound have been studied using a theory which goes beyond the mean-field theory. This theory includes fluctuations and explains the experimental results better than the mean-field theory.

Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: A nonlinear sigma model approach

We describe a low-temperature approach to the two-dimensional half-filled Hubbard model which allows us to study both antiferromagnetism and single-particle properties. This approach ignores amplitude fluctuations of the antiferromagnetic (AF) order parameter and is valid below a crossover temperature ${T}_{X}$ which marks the onset of AF short-range order. Directional fluctuations (spin waves) are described by a nonlinear sigma model $(\mathrm{NL}\ensuremath{\sigma}\mathrm{M})$ that we derive from the Hubbard model. The parameters of the $\mathrm{NL}\ensuremath{\sigma}\mathrm{M}$---the spin stiffness and spin-wave velocity---are calculated as a function of the Coulomb repulsion U. The $\mathrm{NL}\ensuremath{\sigma}\mathrm{M}$ is solved by a saddle-point approximation within the ${\mathrm{CP}}^{1}$ representation where the N\'eel field is parametrized by two Schwinger bosons. At zero temperature, there is always Bose condensation of the Schwinger bosons, which signals AF long-range order for any value of the Coulomb repulsion. At finite temperature, the AF long-range order is suppressed (in agreement with the Mermin-Wagner theorem), but the AF correlation length remains exponentially large. In the ${\mathrm{CP}}^{1}$ representation, the fermion field is naturally expressed as the product of a Schwinger boson and a pseudofermion whose spin is quantized along the (fluctuating) N\'eel field. This allows us to write the fermion Green's function as the product (in direct space) of the Schwinger boson propagator (which is derived from the $\mathrm{NL}\ensuremath{\sigma}\mathrm{M})$ and the pseudofermion propagator. At zero temperature and weak coupling, our results are typical of a Slater antiferromagnet. The AF gap is exponentially small; there are well-defined Bogoliubov quasiparticles (QP's) (carrying most of the spectral weight) coexisting with a high-energy incoherent excitation background. As U increases, the Slater antiferromagnet progressively becomes a Mott-Heisenberg antiferromagnet. The Bogoliubov bands evolve into Mott-Hubbard bands separated by a large AF gap. A significant fraction of spectral weight is transferred from the Bogoliubov QP's to incoherent excitations. At finite temperature, there is a metal-insulator transition between a pseudogap phase at weak coupling and a Mott-Hubbard insulator at strong coupling. Finally, we point out that our results straightforwardly translate to the half-filled attractive Hubbard model, where the $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$ charge and $\mathbf{q}=0$ pairing fluctuations combine to form an order parameter with SO(3) symmetry.

Structural, electronic, and magneto-optical properties ofYVO3

Optical and magneto-optical properties of YVO$_3$ single crystal were studied in FIR, visible, and UV regions. Two structural phase transitions at 75 K and 200 K were observed and established to be of the first and second order, respectively. The lattice has an orthorhombic $Pbnm$ symmetry both above 200 K as well as below 75 K, and is found to be dimerized monoclinic $Pb11$ in between. We identify YVO$_3$ as a Mott-Hubbard insulator with the optical gap of 1.6 eV. The electronic excitations in the visible spectrum are determined by three $d$-bands at 1.8, 2.4, and 3.3 eV, followed by the charge-transfer transitions at about 4 eV. The observed structure is in good agreement with LSDA+$U$ band structure calculations. By using ligand field considerations, we assigned these bands to the transitions to the $^4A_{2g}$, $^2E_{g} + ^2T_{1g}$, and $^2T_{2g}$ states. The strong temperature dependence of these bands is in agreement with the formation of orbital order. Despite the small net magnetic moment of 0.01 $\mu_B$ per vanadium, the Kerr effect of the order of $0.01^\circ$ was observed for all three $d$-bands in the magnetically ordered phase $T_{\text{N\'eel}}<116 K$. A surprisingly strong enhancement of the Kerr effect was found below 75 K, reaching a maximum of $0.1^\circ$. The effect is ascribed to the non-vanishing net orbital magnetic moment.

Orbital ordering in YTiO 3:Ti NMR in a single crystal

47,49 Ti NMR measurements on a single crystal of a ferromagnetic Mott–Hubbard insulator, YTiO 3, have been made to study orbital ordering. In particular we have measured frequency-swept NMR spectra in the ferromagnetic state under an external field of 3 T . We analyze the NMR spectra and show that an orbital ordering model in Hartree–Fock and band calculations might be not suitable.

Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: Slater vs. Mott–Heisenberg

Abstract We study antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model at low temperature. Collective spin fluctuations are governed by a non-linear sigma model that we derive from the Hubbard model for any value of the Coulomb repulsion. As the Coulomb repulsion increases, the ground state progressively evolves from a Slater to a Mott–Heisenberg antiferromagnet. At finite temperature, we find a metal–insulator transition between a pseudogap phase at weak coupling and a Mott–Hubbard insulator at strong coupling.