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arXiv:1611.03455 · Physical review. B./Physical review. B

Doping-driven metal-insulator transitions and charge orderings in the extended Hubbard model

Konrad Jerzy Kapcia, S. Robaszkiewicz, Massimo Capone, A. Amaricci

Published Mar 9, 2017• 39 citations
arXivHTMLPDF

Abstract

We perform a thorough study of the extended Hubbard model featuring local and nearest-neighbor Coulomb repulsion. Using the dynamical mean-field theory we investigated the zero-temperature phase diagram of this model as a function of the chemical doping. The interplay between local and nonlocal interactions drives a variety of phase transitions connecting two distinct charge-ordered insulators, i.e., half filled and quarter filled, a charge-ordered metal and a Mott-insulating phase. We characterize these transitions and the relative stability of the solutions and we show that the two interactions conspire to stabilize the quarter-filled charge-ordered phase.

DOI
10.1103/physrevb.95.125112

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We perform a thorough study of the extended Hubbard model featuring local and nearest-neighbor Coulomb repulsion. Using the dynamical mean-field theory we investigated the zero-temperature phase diagram of this model as a function of the chemical doping. The interplay between local and nonlocal interactions drives a variety of phase transitions connecting two distinct charge-ordered insulators, i.e., half filled and quarter filled, a charge-ordered metal and a Mott-insulating phase. We characterize these transitions and the relative stability of the solutions and we show that the two interactions conspire to stabilize the quarter-filled charge-ordered phase.
We study the extended Hubbard model away from half filling on a two-dimensional square lattice using cluster dynamical mean field theory on clusters of size 8. We show that the model exhibits metallic, compressible charge-ordered, and insulating charge-ordered phases. We determine the location of the charge-ordering phase transition line at finite temperature and the properties of the phases as a function of doping, temperature, local interaction, and nearest-neighbor interaction. An analysis of the energetics of the charge-order transition shows that the charge-ordering transition mainly results in a rearrangement of local and nonlocal potential energy. We show the doping evolution of the spectral function from the isotropic metal via a charge-ordered metal to a charge-ordered insulator with a big gap, and study finite-size effects of the approximation.
We study the half-filled extended Hubbard model on a two-dimensional square lattice using cluster dynamical mean-field theory on clusters of size 8--20. We show that the model exhibits metallic, Mott-insulating, and charge-ordered phases, and determine the location of the charge-ordering phase-transition line and the properties of the phases as a function of temperature, local interaction, and nearest-neighbor interaction. We find strong nonlocal correlations outside the charge-ordered phase and a pronounced screening effect in the vicinity of the phase transition, where nonlocal interactions push the system towards metallic behavior. In contrast, correlations in the charge-ordered phase are mostly local to the unit cell. Finally, we demonstrate how strong nonlocal electron-electron interactions can increase electron mobility by turning a charge-ordered insulator into a metal. We analyze finite-size effects and the convergence of our data to the thermodynamic limit. Control of all sources of errors allows us to assess the regime of applicability of simpler approximation schemes for systems with nonlocal interactions.
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.
Abstract Using the strong coupling diagram technique, we investigate the extended Hubbard model on a two-dimensional square lattice. This approach allows for charge and spin fluctuations and a short-range antiferromagnetic order at nonzero temperatures. The model features the first-order phase transition to states with alternating site occupations (SAO) at the intersite repulsion v = v c . In this work, we show that doping decreases v c . For a nonzero next-nearest neighbor hopping t ′ , less mobile carriers produce a stronger fall in v c . For half-filling and t ′ = 0 , we consider phase diagrams for a fixed temperature T, on-site U, and intersite repulsions. The diagrams contain regions of SAO, Mott insulator, and several metallic states distinguished by their densities of states. Two of them are characterized by a dip and a peak at the Fermi level. The dip originates from the Slater mechanism for itinerant electrons, while the peak to bound states of electrons with localized magnetic moments. The existence of these two metallic regions in the phase diagram is a manifestation of the Pomeranchuk effect. The boundary between these regions reveals itself as a kink in the curve v c (T) and as a maximum in the T dependence of the double occupancy D. Our calculated D for different values of v, U, and T are in semiquantitative agreement with Monte Carlo results.
We derive the disorder vs doping phase diagram of the doped Hubbard model via dynamical mean-field theory combined with typical medium theory, which allows the description of both Mott (correlation driven) and Anderson (disorder driven) metal-insulator transitions. We observe a transition from a metal to an Anderson-Mott insulator for increasing disorder strength at all interactions. In the weak correlation regime and rather small doping, the Anderson-Mott insulator displays properties which are similar to the ones found at half filling. In particular, this phase is characterized by the presence of empty sites. If we further increase either the doping or the correlation, however, an Anderson-Mott phase of a different kind arises for sharply weaker disorder strength. This phase occupies the largest part of the phase diagram in the strong-correlation regime and is characterized by the absence of the empty sites.
The charge ordering transition induced by the nearest-neighbor Coulomb repulsion V in the 1/4-filled extended Hubbard model is investigated using cellular dynamical mean-field theory. We find a transition to a strongly renormalized charge ordered Fermi liquid at V(CO) and a metal-to-insulator transition at V(MI)>V(CO). Short range antiferromagnetism occurs concomitantly with the CO transition. Approaching the charge ordered insulator, V approximately <V(MI), the Fermi surface deforms and the scattering rate of electrons develops momentum dependence on the Fermi surface.