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arXiv:1410.4442 · Physical Review B

Nonequilibrium gap collapse near a first-order Mott transition

Matteo Sandri, Michele Fabrizio

Published Mar 2, 2015• 27 citations
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Abstract

We study the nonequilibrium dynamics of a simple model for ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ that consists of a quarter-filled Hubbard model for two orbitals that are split by a weak crystal field. Peculiarities of this model are (1) a Mott insulator whose gap corresponds to transferring an electron from the occupied lower orbital to the empty upper one, rather than from the lower to the upper Hubbard subbands; (2) a Mott transition generically of first order even at zero temperature. We simulate by means of time-dependent Gutzwiller approximation the evolution within the insulating phase of an initial state endowed by a nonequilibrium population of electrons in the upper orbital and holes in the lower one. We find that the excess population may lead, above a threshold, to a gap collapse and drive the insulator into the metastable metallic phase within the coexistence region around the Mott transition. This result foresees a nonthermal pathway to revert a Mott insulator into a metal. Even though this physical scenario is uncovered in a very specific toy model, we argue it might apply to other Mott insulating materials that share similar features.

DOI
10.1103/physrevb.91.115102

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We study the nonequilibrium dynamics of a simple model for V2O3{\mathrm{V}}_{2}{\mathrm{O}}_{3}V2​O3​ that consists of a quarter-filled Hubbard model for two orbitals that are split by a weak crystal field. Peculiarities of this model are (1) a Mott insulator whose gap corresponds to transferring an electron from the occupied lower orbital to the empty upper one, rather than from the lower to the upper Hubbard subbands; (2) a Mott transition generically of first order even at zero temperature. We simulate by means of time-dependent Gutzwiller approximation the evolution within the insulating phase of an initial state endowed by a nonequilibrium population of electrons in the upper orbital and holes in the lower one. We find that the excess population may lead, above a threshold, to a gap collapse and drive the insulator into the metastable metallic phase within the coexistence region around the Mott transition. This result foresees a nonthermal pathway to revert a Mott insulator into a metal. Even though this physical scenario is uncovered in a very specific toy model, we argue it might apply to other Mott insulating materials that share similar features.
We study by dynamical mean-field theory the ground state of a quarter-filled Hubbard model of two bands with different bandwidths. At half-filling, this model is known to display an orbital selective Mott transition, with the narrower band undergoing Mott localization while the wider one being still itinerant. At quarter-filling, the physical behavior is different and to some extent reversed. The interaction generates an effective crystal field splitting, absent in the Hamiltonian, that tends to empty the narrower band in favor of the wider one, which also become more correlated than the former at odds with the orbital selective paradigm. Upon increasing the interaction, the depletion of the narrower band can continue till it empties completely and the system undergoes a topological Lifshitz transition into a half-filled single-band metal that eventually turns insulating. Alternatively, when the two bandwidths are not too different, a first order Mott transition intervenes before the Lifshitz's one. The properties of the Mott insulator are significantly affected by the interplay between spin and orbital degrees of freedom.
We study the Mott transition in the three-orbital Hubbard model. To investigate how the orbital level splitting and the Ising-type Hund's coupling affect the Mott transition in the case of two electrons per site, we use the dynamical mean-field theory combined with continuous-time quantum Monte Carlo simulations. The calculation of the double occupancy reveals that the critical interaction strength separating a metallic phase and two kinds of insulating phases shows a nonmonotonic behavior as a function of the level splitting. We find that this behavior is characteristic for 1/31/31/3 filling, in comparison with the preceding results for different fillings and for two-orbital models. Strong competition between the two insulators results in an intriguing first-order transition to an insulating phase having intermediate characters between Mott and band insulators. It is also found that the two insulators show different behaviors in the phase boundary with the metallic phase in the interaction-temperature plane, which is reflected in a difference in the quasiparticle behavior around the transition. We also discuss the orbital selective Mott transition for larger Hund's coupling, which is compared with previous study at zero temperature.
We investigate the metal-to-insulator phase transition driven by the density-density electronic interaction in the quarter-filled model on a cubic lattice with two orbitals split by a crystal field. We show that a systematic consideration of the non-local collective electronic fluctuations strongly affects the picture of the phase transition provided by the dynamical mean field theory. Our calculations reveal the appearance of metallic and Mott insulating states characterised by the same density but different values of the chemical potential, which is missing in the local approximation to electronic correlations. We find that the region of concomitant metastability of these two solutions is remarkably broad in terms of the interaction strength. It starts at a critical value of the interaction slightly larger than the bandwidth and extends to more than twice the bandwidth, where the two solutions merge into a Mott insulating phase. Our results illustrate that non-local correlations can have crucial consequences on the electronic properties in the strongly correlated regime of the simplest multi-orbital systems.
We investigate a quarter-filled two-band Hubbard model involving a crystal-field splitting, which lifts the orbital degeneracy as well as an interorbital hopping (interband hybridization). Both terms are relevant to the realistic description of correlated materials such as transition-metal oxides. The nature of the Mott metal-insulator transition is clarified and is found to depend on the magnitude of the crystal-field splitting. At large values of the splitting, a transition from a two-band to a one-band metal is first found as the on-site repulsion is increased and is followed by a Mott transition for the remaining band, which follows the single-band (Brinkman-Rice) scenario well documented previously within dynamical mean-field theory. At small values of the crystal-field splitting, a direct transition from a two-band metal to a Mott insulator with partial orbital polarization is found, which takes place simultaneously for both orbitals. This transition is characterized by a vanishing of the quasiparticle weight for the majority orbital but has a first-order character for the minority orbital. It is pointed out that finite-temperature effects may easily turn the metallic regime into a bad metal close to the orbital polarization transition in the metallic phase.
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.