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arXiv:0706.0444 · Physical Review B

Pseudogap and Mott transition studied by cellular dynamical mean-field theory

Yu‐Zhong Zhang, Masatoshi Imada

Published Jul 17, 2007• 89 citations
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Abstract

We study metal-insulator transitions between Mott insulators and metals. The transition mechanism completely different from the original dynamical mean field theory (DMFT) emerges from a cluster extension of it. A consistent picture suggests that the quasiparticle weight $Z$ remains nonzero through metals and suddenly jumps to zero at the transition, while the gap opens continuously in the insulators. This is in contrast with the original DMFT, where $Z$ continuously vanishes but the gap opens discontinuously. The present results arising from electron differentiation in momentum space agree with recent puzzling bulk-sensitive experiments on $\mathrm{Ca}\mathrm{V}{\mathrm{O}}_{3}$ and $\mathrm{Sr}\mathrm{V}{\mathrm{O}}_{3}$.

DOI
10.1103/physrevb.76.045108

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We study metal-insulator transitions between Mott insulators and metals. The transition mechanism completely different from the original dynamical mean field theory (DMFT) emerges from a cluster extension of it. A consistent picture suggests that the quasiparticle weight ZZZ remains nonzero through metals and suddenly jumps to zero at the transition, while the gap opens continuously in the insulators. This is in contrast with the original DMFT, where ZZZ continuously vanishes but the gap opens discontinuously. The present results arising from electron differentiation in momentum space agree with recent puzzling bulk-sensitive experiments on CaVO3\mathrm{Ca}\mathrm{V}{\mathrm{O}}_{3}CaVO3​ and SrVO3\mathrm{Sr}\mathrm{V}{\mathrm{O}}_{3}SrVO3​.
Underdoped Mott insulators provide us with a challenge of many-body physics. Recent renewed understanding is discussed in terms of the evolution of pole and zero structure of the single-particle Green's function. Pseudogap as well as Fermi arc/pocket structure in the underdoped cuprates is well reproduced from the recent cluster extension of the dynamical mean-field theory. Emergent coexisting zeros and poles set the underdoped Mott insulator apart from the Fermi liquid, separated by topological transitions. Cofermion proposed as a generalization of exciton in the slave-boson framework accounts for the origin of the zero surface formation. The cofermion-quasiparticle hybridization gap offers a natural understanding of the pseudogap and various unusual Mottness. Furthermore the cofermion offers a novel pairing mechanism, where the cofermion has two roles: It reinforces the Cooper pair as a pair partner of the quasiparticle and acts as a glue as well. It provides a strong insight for solving the puzzle found in the dichotomy of the gap structure.
We address the nature of the Mott transition in the Hubbard model at half-filling using cluster dynamical mean field theory (DMFT). We compare cluster-DMFT results with those of single-site DMFT. We show that inclusion of the short-range correlations on top of the on-site correlations does not change the order of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical U and modify the shape of the transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition point. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale. The insulating state is characterized by the narrow Mott gap with pronounced peaks at the gap edge.
Filling-control metal-insulator transition on the two-dimensional Hubbard model is investigated by using the correlator projection method, which takes into account momentum dependence of the free energy beyond the dynamical mean-field theory. The phase diagram of metals and Mott insulators is analyzed. Lifshitz transitions occur simultaneously with metal-insulator transitions at large Coulomb repulsion. On the other hand, they are separated each other for lower Coulomb repulsion, where the phase sandwiched by the Lifshitz and metal-insulator transitions appears to show violation of the Luttinger sum rule. Through the metal-insulator transition, quasiparticles retain nonzero renormalization factor and finite quasi-particle weight in the both sides of the transition. This supports that the metal-insulator transition is caused not by the vanishing renormalization factor but by the relative shift of the Fermi level into the Mott gap away from the quasiparticle band, in sharp contrast with the original dynamical mean-field theory. Charge compressibility diverges at the critical end point of the first-order Lifshitz transition at finite temperatures. The origin of the divergence is ascribed to singular momentum dependence of the quasiparticle dispersion.
The recently proposed center-focused post-processing procedure [Phys. Rev. Res. 2, 033476 (2020)] of cellular dynamical mean-field theory suggests that central sites of large impurity clusters are closer to the exact solution of the Hubbard model than the edge sites. In this paper, we systematically investigate results in the spirit of this center-focused scheme for several cluster sizes up to 8×8 in and out of particle-hole symmetry. First we analyze the metal-insulator crossovers and transitions of the half-filled Hubbard model on a simple square lattice. We find that the critical interaction of the crossover is reduced with increasing cluster sizes and the critical temperature abruptly drops for the 4×4 cluster. Second, for this cluster size, we apply the center-focused scheme to a system with more realistic tight-binding parameters, investigating its pseudogap regime as a function of temperature and doping, where we find doping dependent metal-insulator crossovers, Lifshitz transitions and a strongly renormalized Fermi-liquid regime. Additionally to diagnosing the real space origin of the suppressed antinodal spectral weight in the pseudogap regime, we can infer hints towards underlying charge ordering tendencies.
We analyze the effects of the on-site Coulomb repulsion U on a band insulator using dynamical mean field theory (DMFT). We find the surprising result that the gap is suppressed to zero at a critical Uc1 and remains zero within a metallic phase. At a larger Uc2 there is a second transition from the metal to a Mott insulator, in which the gap increases with increasing U. These results are qualitatively different from Hartree-Fock theory which gives a monotonically decreasing but nonzero insulating gap for all finite U.
To gain insight into the physics of the metal-insulator transition and the effectiveness of cluster dynamical mean field theory (DMFT) we have used 1, 2-, and 4-site dynamical mean field theory to solve a polaron model of electrons coupled to a classical phonon field. The metal to polaronic insulator phase boundary is determined along with electron spectral functions and cluster correlation functions. Pronounced cluster size effects occur in the intermediate coupling region in which the cluster calculation leads to a gap and the single-site approximation does not. Differences in spectra (in particular a sharper band edge in the cluster calculation) persist in the strong-coupling regime. A partial density of states is defined encoding a generalized nesting property of the band structure; variations in this density of states account for differences between the dynamical cluster approximation and the cellular-DMFT implementations of cluster DMFT, as well as for differences in behavior between the single-band models appropriate for cuprates and the multiband models appropriate for manganites. A pole or strong resonance in the self-energy is associated with insulating states; the momentum dependence of the pole is found to distinguish between Slater-like and Mott-like mechanisms for metal-insulator transition. Implications for the theoretical treatment of doped manganites are discussed.