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arXiv:cond-mat/0610401 · Physical Review B

Doping-driven Mott transition in the one-band Hubbard model

Philipp Werner, Andrew J. Millis

Published Feb 15, 2007• 77 citations
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Abstract

A powerful diagrammatic impurity solver is shown to permit a systematic study of the doping-driven Mott transition in a one-band Hubbard model within the framework of single-site dynamical mean-field theory. At small dopings and large interaction strengths, we are able to access low enough temperatures that a reliable extrapolation to temperature $T=0$ may be performed, and ground state energies of insulating and metallic states may be compared. We find that the $T=0$ doping-driven transition is of second order and is characterized by an interaction-strength dependent electronic compressibility, which vanishes at the critical interaction strength of the half filled model. Over wide parameter ranges, the compressibility is substantially reduced relative to the noninteracting system. The metal-insulator transition is characterized by the appearance of in-gap states, but these are relevant only for very low dopings of less than 3%.

DOI
10.1103/physrevb.75.085108

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A powerful diagrammatic impurity solver is shown to permit a systematic study of the doping-driven Mott transition in a one-band Hubbard model within the framework of single-site dynamical mean-field theory. At small dopings and large interaction strengths, we are able to access low enough temperatures that a reliable extrapolation to temperature T=0T=0T=0 may be performed, and ground state energies of insulating and metallic states may be compared. We find that the T=0T=0T=0 doping-driven transition is of second order and is characterized by an interaction-strength dependent electronic compressibility, which vanishes at the critical interaction strength of the half filled model. Over wide parameter ranges, the compressibility is substantially reduced relative to the noninteracting system. The metal-insulator transition is characterized by the appearance of in-gap states, but these are relevant only for very low dopings of less than 3%.
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 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.
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.
We have studied the doping-driven orbital-selective Mott transition in multi-band Hubbard models with equal band width in the presence of crystal field splitting. Crystal field splitting lifts one of the bands while leaving the others degenerate. We use single-site dynamical mean-field theory combined with continuous time quantum Monte Carlo impurity solver to calculate a phase diagram as a function of total electron filling N and crystal field splitting Δ . We find a large region of orbital-selective Mott phase in the phase diagram when the doping is large enough. Further analysis indicates that the large region of orbital-selective Mott phase is driven and stabilized by doping. Such models may account for the orbital-selective Mott transition in some doped realistic strongly correlated materials.
We have studied the doping-driven orbital-selective Mott transition in multi-band Hubbard models with equal band width in the presence of crystal field splitting. Crystal field splitting lifts one of the bands while leaving the others degenerate. We use single-site dynamical mean-field theory combined with continuous time quantum Monte Carlo impurity solver to calculate a phase diagram as a function of total electron filling N and crystal field splitting ?. We find a large region of orbital-selective Mott phase in the phase diagram when the doping is large enough. Further analysis indicates that the large region of orbital-selective Mott phase is driven and stabilized by doping. Such models may account for the orbital-selective Mott transition in some doped realistic strongly correlated materials.
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.