arXiv:cond-mat/9811135 · Physical review. B, Condensed matter

Surface metal-insulator transition in the Hubbard model

Michael Potthoff, Wolfgang Nolting

Published Jan 15, 1999• 174 citations

Abstract

The correlation-driven metal-insulator (Mott) transition at a solid surface is studied within the Hubbard model for a semi-infinite lattice by means of the dynamical mean-field theory. The transition takes place at a unique critical strength of the interaction. Depending on the surface geometry, the interaction strength, and the wave vector, we find one-electron excitations in the coherent part of the surface-projected metallic spectrum, which are confined to two dimensions.

DOI: 10.1103/physrevb.59.2549

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arXiv:cond-mat/9811135 · Physical review. B, Condensed matter

Surface metal-insulator transition in the Hubbard model

Michael Potthoff, Wolfgang Nolting

Published Jan 15, 1999• 174 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.59.2549

Related papers

Metallic surface of a Mott insulator–Mott insulating surface of a metal

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The dynamical mean-field theory (DMFT) is employed to study the correlation-driven metal-insulator transition in the semi-infinite Hubbard model at half-filling and zero temperature. We consider the low-index surfaces of the three-dimensional simple-cubic lattice, and systematically vary the model parameters at the very surface, the intralayer and interlayer surface hopping, and the surface Coulomb interaction. Within the DMFT the self-energy functional is assumed to be local. Therewith, the problem is self-consistently mapped onto a set of coupled effective impurity models corresponding to the inequivalent layers parallel to the surface. Assuming that the influence of the high-energy Hubbard bands on the low-energy quasiparticle resonance can be neglected at the critical point, a simplified ``linearized DMFT'' becomes possible. The linearized theory, however, is formally equivalent to the Weiss molecular-field theory for the semi-infinite Ising model. This implies that qualitatively the rich phenomenology of the Landau description of second-order phase transitions at surfaces has a direct analog for the surface Mott transition. Motivated by this formal analogy, we work out the predictions of the linearized DMFT in detail. It is found that under certain circumstances the surface of a Mott insulator can be metallic, while a Mott-insulating surface of a normal metal is not possible. We derive the corresponding phase diagrams, the (mean-field) critical exponents and the critical profiles of the quasiparticle weight. The results are confirmed by a fully numerical evaluation of the DMFT equations using the exact-diagonalization (ED) method. By means of the ED approach, we especially investigate the noncritical parts of the phase diagrams and discuss the U and layer dependence of the quasi-particle weight. For strong modifications of the surface model parameters, the surface low-energy electronic structure dynamically decouples from the bulk.The dynamical mean-field theory (DMFT) is employed to study the correlation-driven metal-insulator transition in the semi-infinite Hubbard model at half-filling and zero temperature. We consider the low-index surfaces of the three-dimensional simple-cubic lattice, and systematically vary the model parameters at the very surface, the intralayer and interlayer surface hopping, and the surface Coulomb interaction. Within the DMFT the self-energy functional is assumed to be local. Therewith, the problem is self-consistently mapped onto a set of coupled effective impurity models corresponding to the inequivalent layers parallel to the surface. Assuming that the influence of the high-energy Hubbard bands on the low-energy quasiparticle resonance can be neglected at the critical point, a simplified ``linearized DMFT'' becomes possible. The linearized theory, however, is formally equivalent to the Weiss molecular-field theory for the semi-infinite Ising model. This implies that qualitatively the rich phenomenology of the Landau description of second-order phase transitions at surfaces has a direct analog for the surface Mott transition. Motivated by this formal analogy, we work out the predictions of the linearized DMFT in detail. It is found that under certain circumstances the surface of a Mott insulator can be metallic, while a Mott-insulating surface of a normal metal is not possible. We derive the corresponding phase diagrams, the (mean-field) critical exponents and the critical profiles of the quasiparticle weight. The results are confirmed by a fully numerical evaluation of the DMFT equations using the exact-diagonalization (ED) method. By means of the ED approach, we especially investigate the noncritical parts of the phase diagrams and discuss the U and layer dependence of the quasi-particle weight. For strong modifications of the surface model parameters, the surface low-energy electronic structure dynamically decouples from the bulk.

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Ohashi, Yasuo, Yoshiaki Ōno

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 $t_{pd}$ , $t_{pp}$ , $t_{dd}$ 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 $t_{pd}$, $t_{pp}$, $t_{dd}$ between $p$-$d$, $p$-$p$ and $d$-$d$ sites respectively. The critical behaviour of the quasiparticle weight is also obtained analytically.

arXiv:cond-mat/0109446Sep 25, 20010 citations

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.

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%.

U

, and the charge-transfer energy

Δ

between the

d

- and

p

-orbitals, transfer integrals

t_{pd}

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.