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arXiv:cond-mat/0503759 · Physical Review B

Dynamical behavior across the Mott transition of two bands with different bandwidths

Michel Ferrero, Federico Becca, Michele Fabrizio, Massimo Capone

Published Nov 23, 2005• 88 citations

Abstract

We investigate the role of the bandwidth difference in the Mott metal-insulator transition of a two-band Hubbard model in the limit of infinite dimensions by means of a Gutzwiller variational wave function as well as by dynamical mean-field theory. The variational calculation predicts a two-stage quenching of the charge degrees of freedom, in which the narrower band undergoes a Mott transition before the wider one, both in the presence and in the absence of a Hund's exchange coupling. However, this scenario is not fully confirmed by the dynamical mean-field theory calculation, which shows that, although the quasiparticle residue of the narrower band is zero within our numerical accuracy, low-energy spectral weight still exists inside the Mott-Hubbard gap, concentrated into two peaks symmetric around the chemical potential. This spectral weight vanishes only when the wider band ceases to conduct too. Although our results are compatible with several scenarios---e.g., a narrow-gap semiconductor or a semimetal---we argue that the most plausible one is that the two peaks coexist with a narrow resonance tied at the chemical potential, with a spectral weight below our numerical accuracy. This quasiparticle resonance is expected to vanish when the wider band undergoes the Mott transition.

DOI: 10.1103/physrevb.72.205126

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We investigate the role of the bandwidth difference in the Mott metal-insulator transition of a two-band Hubbard model in the limit of infinite dimensions by means of a Gutzwiller variational wave function as well as by dynamical mean-field theory. The variational calculation predicts a two-stage quenching of the charge degrees of freedom, in which the narrower band undergoes a Mott transition before the wider one, both in the presence and in the absence of a Hund's exchange coupling. However, this scenario is not fully confirmed by the dynamical mean-field theory calculation, which shows that, although the quasiparticle residue of the narrower band is zero within our numerical accuracy, low-energy spectral weight still exists inside the Mott-Hubbard gap, concentrated into two peaks symmetric around the chemical potential. This spectral weight vanishes only when the wider band ceases to conduct too. Although our results are compatible with several scenarios---e.g., a narrow-gap semiconductor or a semimetal---we argue that the most plausible one is that the two peaks coexist with a narrow resonance tied at the chemical potential, with a spectral weight below our numerical accuracy. This quasiparticle resonance is expected to vanish when the wider band undergoes the Mott transition.

We examine whether the Mott transition of a half-filled, two-orbital Hubbard model with unequal bandwidths occurs simultaneously for both bands or whether it is a two-stage process in which the orbital with narrower bandwith localizes first (giving rise to an intermediate ``orbital-selective'' Mott phase). This question is addressed using both dynamical mean-field theory and a representation of fermion operators in terms of slave quantum spins, followed by a mean-field approximation (similar in spirit to a Gutzwiller approximation). In the latter approach, the Mott transition is found to be orbital selective for all values of the Coulomb exchange (Hund) coupling

J

when the bandwidth ratio is small and only beyond a critical value of

J

when the bandwidth ratio is larger. Dynamical mean-field theory partially confirms these findings, but the intermediate phase at

J=0

is found to differ from a conventional Mott insulator, with spectral weight extending down to arbitrary low energy. Finally, the orbital-selective Mott phase is found, at zero temperature, to be unstable with respect to an interorbital hybridization

V

and replaced at small

V

by a state with a large effective mass (and a low quasiparticle coherence scale) for the narrower band.

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

U

at the

d

-orbital and the charge-transfer energy

Δ

between the

d

- and

p

-orbitals. Critical behaviour of the quasiparticle weight is also obtained analytically as a function of

U

and

Δ

. The analytic results are in good agreement with the numerical results of the exact diagonalization method.

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

Δ

, and the charge-transfer energy

d

between the

p

- and

U

-orbitals, transfer integrals

Δ

,

t_{pp}

,

t_{dd}

between

p

-

d

,

p

-

p

and

d

-

d

sites respectively. The critical behaviour of the quasiparticle weight is also obtained analytically.

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 U , and the charge-transfer energy Δ between the d - and p -orbitals, transfer integrals t p d , t p p , t d d between p – d , p – p , and d – d sites respectively. The critical behaviour of the quasiparticle weight is also obtained analytically.

We investigate the Mott transition in a two-band Hubbard-Kanamori model using dynamical mean-field theory with the density matrix renormalization group and the numerical renormalization group (NRG) as impurity solvers. The study focuses on the case where the intraorbital and interorbital Coulomb interactions are equal (

U={U}_{2}

) and the Hund's coupling is absent (

J=0

). Our spectral analysis for this case confirms the absence of an orbital-selective Mott transition (OSMT) even in systems with very distinct bandwidths (

{t}_{1}

and

{t}_{2}

parameters for wide and narrow band, respectively) indicating a simultaneous Mott transition occurring in both bands. Notably, the NRG results show the emergence of a pseudo-gap-like feature and a central peak in the narrow band, whose characteristics depend on the hopping parameter

{t}_{2}

. These spectral features may act as precursors to OSMT in more realistic systems with finite Hund's coupling (

J>0

). Furthermore, in the Mott insulating phase, the self-energies for both bands diverge, indicating that the Mott transition represents a topological phase transition for both bands. Our results underscore the importance of accurate impurity solvers in capturing the density of states and detailed spectral structures.

We study the Mott metal-insulator transition in the two-band Hubbard model with different hopping amplitudes t1 and t2 for the two orbitals on the two-dimensional square lattice by using non-magnetic variational wave functions, similarly to what has been considered in the limit of infinite dimensions by dynamical mean-field theory. We work out the phase diagram at half filling (i.e. two electrons per site) as a function of R = t2/t1 and the on-site Coulomb repulsion U, for two values of the Hund's coupling J = 0 and J/U = 0.1. Our results are in good agreement with previous dynamical mean-field theory calculations, demonstrating that the non-magnetic phase diagram is only slightly modified from infinite to two spatial dimensions. Three phases are present: a metallic one, for small values of U, where both orbitals are itinerant; a Mott insulator, for large values of U, where both orbitals are localized because of the Coulomb repulsion; and the so-called orbital-selective Mott insulator (OSMI), for small values of R and intermediate Us, where one orbital is localized while the other one is still itinerant. The effect of the Hund's coupling is two-fold: on one side, it favors the full Mott phase over the OSMI; on the other side, it stabilizes the OSMI at larger values of R.