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arXiv:cond-mat/9906412 · Physical review. B, Condensed matter

Metallic surface of a Mott insulator–Mott insulating surface of a metal

Michael Potthoff, Wolfgang Nolting

Published Sep 15, 1999• 101 citations
arXivHTMLPDF

Abstract

The dynamical mean-field theory (DMFT) is employed to study the correlation-driven metal-insulator transition in the semi-infinite Hubbard model at half-filling and zero temperature. We consider the low-index surfaces of the three-dimensional simple-cubic lattice, and systematically vary the model parameters at the very surface, the intralayer and interlayer surface hopping, and the surface Coulomb interaction. Within the DMFT the self-energy functional is assumed to be local. Therewith, the problem is self-consistently mapped onto a set of coupled effective impurity models corresponding to the inequivalent layers parallel to the surface. Assuming that the influence of the high-energy Hubbard bands on the low-energy quasiparticle resonance can be neglected at the critical point, a simplified ``linearized DMFT'' becomes possible. The linearized theory, however, is formally equivalent to the Weiss molecular-field theory for the semi-infinite Ising model. This implies that qualitatively the rich phenomenology of the Landau description of second-order phase transitions at surfaces has a direct analog for the surface Mott transition. Motivated by this formal analogy, we work out the predictions of the linearized DMFT in detail. It is found that under certain circumstances the surface of a Mott insulator can be metallic, while a Mott-insulating surface of a normal metal is not possible. We derive the corresponding phase diagrams, the (mean-field) critical exponents and the critical profiles of the quasiparticle weight. The results are confirmed by a fully numerical evaluation of the DMFT equations using the exact-diagonalization (ED) method. By means of the ED approach, we especially investigate the noncritical parts of the phase diagrams and discuss the U and layer dependence of the quasi-particle weight. For strong modifications of the surface model parameters, the surface low-energy electronic structure dynamically decouples from the bulk.

DOI
10.1103/physrevb.60.7834

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The dynamical mean-field theory (DMFT) is employed to study the correlation-driven metal-insulator transition in the semi-infinite Hubbard model at half-filling and zero temperature. We consider the low-index surfaces of the three-dimensional simple-cubic lattice, and systematically vary the model parameters at the very surface, the intralayer and interlayer surface hopping, and the surface Coulomb interaction. Within the DMFT the self-energy functional is assumed to be local. Therewith, the problem is self-consistently mapped onto a set of coupled effective impurity models corresponding to the inequivalent layers parallel to the surface. Assuming that the influence of the high-energy Hubbard bands on the low-energy quasiparticle resonance can be neglected at the critical point, a simplified ``linearized DMFT'' becomes possible. The linearized theory, however, is formally equivalent to the Weiss molecular-field theory for the semi-infinite Ising model. This implies that qualitatively the rich phenomenology of the Landau description of second-order phase transitions at surfaces has a direct analog for the surface Mott transition. Motivated by this formal analogy, we work out the predictions of the linearized DMFT in detail. It is found that under certain circumstances the surface of a Mott insulator can be metallic, while a Mott-insulating surface of a normal metal is not possible. We derive the corresponding phase diagrams, the (mean-field) critical exponents and the critical profiles of the quasiparticle weight. The results are confirmed by a fully numerical evaluation of the DMFT equations using the exact-diagonalization (ED) method. By means of the ED approach, we especially investigate the noncritical parts of the phase diagrams and discuss the U and layer dependence of the quasi-particle weight. For strong modifications of the surface model parameters, the surface low-energy electronic structure dynamically decouples from the bulk.
The correlation-driven transition from a paramagnetic metal to a paramagnetic Mott-Hubbard insulator is studied within the half-filled Hubbard model for a thin-film geometry. We consider simple-cubic films with different low-index surfaces and film thickness d ranging from d = 1 (twodimensional) up to d = 8. Using the dynamical mean-field theory, the lattice (film) problem is selfconsistently mapped onto a set of d single-impurity Anderson models which are indirectly coupled via the respective baths of conduction electrons. The impurity models are solved at zero temperature using the exact-diagonalization algorithm. We investigate the layer and thickness dependence of the electronic structure in the low-energy regime. Effects due to the finite film thickness are found to be the more pronounced the lower is the film-surface coordination number. For the comparatively open sc(111) geometry we find a strong layer dependence of the quasi-particle weight while it is much less pronounced for the sc(110) and the sc(100) film geometries. For a given geometry and thickness d there is a unique critical interaction strength Uc2(d) at which all effective masses diverge and there is a unique strength Uc1(d) where the insulating solution disappears. Uc2(d) and Uc1(d) gradually increase with increasing thickness eventually approaching their bulk values. A simple analytical argument explains the complete geometry and thickness dependence of Uc2. Uc1 is found to scale linearly with Uc2. I.
The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamic conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition.
For doped two-dimensional Mott insulators in their normal state, the challenge is to understand the evolution from a conventional metal at high doping to a strongly correlated metal near the Mott insulator at zero doping. To this end, we solve the cellular dynamical mean-field equations for the two-dimensional Hubbard model using a plaquette as the reference quantum impurity model and continuous-time quantum Monte Carlo method as impurity solver. The normal-state phase diagram as a function of interaction strength UUU, temperature TTT, and filling nnn shows that, upon increasing nnn toward the Mott insulator, there is a surface of first-order transition between two metals at nonzero doping. That surface ends at a finite temperature critical line originating at the half-filled Mott critical point. Associated with this transition, there is a maximum in scattering rate as well as thermodynamic signatures. These findings suggest a new scenario for the normal-state phase diagram of the high temperature superconductors. The criticality surmised in these systems can originate not from a T === 0 quantum critical point, nor from the proximity of a long-range ordered phase, but from a low temperature transition between two types of metals at finite doping. The influence of Mott physics therefore extends well beyond half-filling.
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 (FE) approach to the 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=4tW=4tW=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±0.05U_{\rm c}/t=4.45 \pm 0.05Uc​/t=4.45±0.05. At U=4.5tU=4.5tU=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 UcU_{\rm c}Uc​.
The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory. The discontinuity in the chemical potential for the change from hole to electron doping is calculated analytically as a function of the on-site Coulomb interaction UUU at the ddd-orbital and the charge-transfer energy ΔΔΔ between the ddd- and ppp-orbitals. Critical behaviour of the quasiparticle weight is also obtained analytically as a function of UUU and ΔΔΔ. The analytic results are in good agreement with the numerical results of the exact diagonalization method.
In this study, the metal-insulator transition in the square-lattice Hubbard model at half-filling is revisited in relation to the DOS and spectral functions by means of the ladder dual fermion approximation (LDFA). For this purpose, a new expression of the two-body Green's function in the form of resolvents is proposed, which provides tractable and efficient means to calculate the local vertex function with the Lanczos exact diagonalization (ED) method. This makes it possible to use the Lanczos ED method as a solver of the effective impurity Anderson model for LDFA, opening up the way to access low temperatures for these perturbative extensions of the dynamical mean-field theory and to obtain accurate DOS and spectral functions on the real frequency axis by a new variant of the maximum entropy method. It is found that for $U\ensuremath{\le}3.5t$, as temperature decreases, the pseudogap formation due to antiferromagnetic correlations in the quasiparticle peak of the spectral function occurs at the XXX point $[\mathbit{k}=(\ensuremath{\pi},0)]$, spreads through the Fermi surface and ends at the M2{M}_{2}M2​ point $[\mathbit{k}=(\ensuremath{\pi}/2,\ensuremath{\pi}/2)]$. The almost simultaneous creation of the pseudogap and the loss of the Fermi liquid feature is consistent with that expected in the Slater regime. Although the pseudogap still appears in the quasi-particle-like single peak for $U\ensuremath{\ge}4.0t$, the Fermi-liquid feature is partially lost on the Fermi surface already at higher temperatures as expected in the Mott-Heisenberg regime, in which local spins are preformed at high temperatures. A sharp crossover from a pseudogap phase to a Mott insulator at finite ${U}^{*}\ensuremath{\approx}4.7t$ is found to occur below the temperature of the pseudogap formation similar to a previous study with the nonlinear $\ensuremath{\sigma}$ model approach.