arXiv:cond-mat/0304624 · Journal of the Physical Society of Japan

Magnetism and Superconductivity in a Two-band Hubbard Model in Infinite Dimensions

Yoshiaki Ōno, Kazuhiro Sano

Published Jan 1, 2002• 1 citation

Abstract

We study a two-band Hubbard model using the dynamical mean-field theory combined with the exact diagonalization method. At the electron density $n=2$, a transition from a band-insulator to a correlated semimetal occurs when the on-site Coulomb interaction $U$ is varied for a fixed value of the charge-transfer energy $Δ$. At low temperature, the correlated semimetal shows ferromagnetism or superconductivity. With increasing doping $|n-2|$, the ferromagnetic transition temperature rapidly decreases and finally becomes zero at a critical value of $n$. The second-order phase transition occurs at high temperature, while a phase separation of ferromagnetic and paramagnetic states takes place at low temperature. The superconducting transition temperature gradually decreases and finally becomes zero near $n=1$ ($n=3$) where the system is Mott insulator which shows antiferromagnetism at low temperature.

DOI: 10.1143/jpsjs.71s.356

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arXiv:cond-mat/0304624 · Journal of the Physical Society of Japan

Magnetism and Superconductivity in a Two-band Hubbard Model in Infinite Dimensions

Yoshiaki Ōno, Kazuhiro Sano

Published Jan 1, 2002• 1 citation

arXiv HTML PDF

Abstract

We study a two-band Hubbard model using the dynamical mean-field theory combined with the exact diagonalization method. At the electron density

n=2

, a transition from a band-insulator to a correlated semimetal occurs when the on-site Coulomb interaction

U

is varied for a fixed value of the charge-transfer energy

Δ

. At low temperature, the correlated semimetal shows ferromagnetism or superconductivity. With increasing doping

|n-2|

, the ferromagnetic transition temperature rapidly decreases and finally becomes zero at a critical value of

n

. The second-order phase transition occurs at high temperature, while a phase separation of ferromagnetic and paramagnetic states takes place at low temperature. The superconducting transition temperature gradually decreases and finally becomes zero near

n=1

(

n=3

) where the system is Mott insulator which shows antiferromagnetism at low temperature.

DOI: 10.1143/jpsjs.71s.356

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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 $U$ 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.

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We investigate the strong correlation effect in the spinless electron-hole two-band Hubbard model using the dynamical mean-field theory. At half filling, both the renormalization factor $Z$ and the number of conduction electrons (valence holes) $n_c$ decrease with increasing the interband Coulomb interaction $U$ down to $Z\sim 0.15$ and $n_c\sim 0.1$ for $U_c \sim \mbox{bandwidth}$ at which the first-order Lifshitz transition occurs from a correlated semimetal with a large effective mass $m^*/m=Z^{-1}$ to a band insulator with a finite gap due to the Hartree shift. A slight hole doping $x$ in the band insulator with a large $U>U_c$ yields a remarkable correlated semimetal with $Z\sim 0.1$ at $x\sim 0.01$ , where in-gap states emerge above the valence band top and those weights increase with increasing $x$ together with the increase in $Z$ similar to the in-gap states observed in doped Mott insulators.We investigate the strong correlation effect in the spinless electron-hole two-band Hubbard model using the dynamical mean-field theory. At half filling, both the renormalization factor $Z$ and the number of conduction electrons (valence holes) $n_c$ decrease with increasing the interband Coulomb interaction $U$ down to $Z\sim 0.15$ and $n_c\sim 0.1$ for $U_c \sim \mbox{bandwidth}$ at which the first-order Lifshitz transition occurs from a correlated semimetal with a large effective mass $m^*/m=Z^{-1}$ to a band insulator with a finite gap due to the Hartree shift. A slight hole doping $x$ in the band insulator with a large $U>U_c$ yields a remarkable correlated semimetal with $Z\sim 0.1$ at $x\sim 0.01$, where in-gap states emerge above the valence band top and those weights increase with increasing $x$ together with the increase in $Z$ similar to the in-gap states observed in doped Mott insulators.

arXiv:2605.24927May 24, 20260 citations

We study a two-band Hubbard model using the dynamical mean-field theory combined with the exact diagonalization method. At the electron density

n=2

, a transition from a band-insulator to a correlated semimetal occurs when the on-site Coulomb interaction

U

is varied for a fixed value of the charge-transfer energy

Δ

. At low temperature, the correlated semimetal shows ferromagnetism or superconductivity. With increasing doping

|n-2|

, the ferromagnetic transition temperature rapidly decreases and finally becomes zero at a critical value of

n

n=1

(

n=3

) where the system is Mott insulator which shows antiferromagnetism at low temperature.

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.

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.

Cooperation and competition between the antiferromagnetic,

d

-wave superconducting, and Mott-insulating states are explored for the two-dimensional Hubbard model including nearest and next-nearest-neighbor hoppings at zero temperature. Using the variational cluster approach with clusters of different shapes and sizes up to 10 sites, it is found that the doping-driven transition from a phase with microscopic coexistence of antiferromagnetism and superconductivity to a purely superconducting phase is discontinuous for strong interaction and accompanied by phase separation. At half-filling the system is in an antiferromagnetic Mott-insulating state with vanishing charge compressibility. Upon decreasing the interaction strength

U

below a certain critical value of roughly ${U}_{c}\ensuremath{\sim}4$ (in units of the nearest-neighbor hopping), however, the filling-dependent magnetic transition changes its character and becomes continuous. Phase separation or, more carefully, the tendency towards the formation of inhomogeneous states disappears. This critical value is in contrast to previous studies, where a much larger value was obtained. Moreover, we find that the system at half-filling undergoes the Mott transition from an insulator to a state with a finite charge compressibility at essentially the same value. The weakly correlated state at half-filling exhibits superconductivity microscopically admixed to the antiferromagnetic order. This scenario suggests a close relation between phase separation and the Mott-insulator physics.

We investigate the strong correlation effect in the spinless electron-hole two-band Hubbard model using the dynamical mean-field theory. At half filling, both the renormalization factor

Z

and the number of conduction electrons (valence holes)

n_c

decrease with increasing the interband Coulomb interaction

U

down to

Z\sim 0.15

and

n_c\sim 0.1

for $U_c \sim \mbox{bandwidth}$ at which the first-order Lifshitz transition occurs from a correlated semimetal with a large effective mass

m^*/m=Z^{-1}

to a band insulator with a finite gap due to the Hartree shift. A slight hole doping

x

in the band insulator with a large

U>U_c

yields a remarkable correlated semimetal with

Z\sim 0.1

x\sim 0.01

, where in-gap states emerge above the valence band top and those weights increase with increasing

x

together with the increase in

Z

similar to the in-gap states observed in doped Mott insulators.