In this work we have considered a two-dimensional two-band Hubbard model (extended Hubbard model) to study the effect of the nonlocal hybridization ${V}_{\mathbf{k}}$ on the superconductivity. In the strong-coupling regime and for a $d$ -wave superconducting gap, we have obtained the superconducting critical temperature ${T}_{c}$ and the zero-temperature superconducting gap ${\ensuremath{\Delta}}_{0}$ for different hybridizations. We have adopted hopping parameters suitable to describe the high-temperature superconductor materials. The results show that for a fixed value of the hybridization and the intraband $d\text{\ensuremath{-}}d$ attractive potential $U$ , the gap increases for low temperatures and diminishes as the temperatures increase toward ${T}_{c}$ . As the hybridization increases both, ${\ensuremath{\Delta}}_{0}$ and ${T}_{c}$ , diminish. For each hybridization, the quantity $2{\ensuremath{\Delta}}_{0}/{k}_{B}{T}_{c}$ increases and saturates in a particular value as $U$ increases. The relation between applied pressure $P$ and hybridization in the strong-coupling regime is also discussed.In this work we have considered a two-dimensional two-band Hubbard model (extended Hubbard model) to study the effect of the nonlocal hybridization ${V}_{\mathbf{k}}$ on the superconductivity. In the strong-coupling regime and for a $d$-wave superconducting gap, we have obtained the superconducting critical temperature ${T}_{c}$ and the zero-temperature superconducting gap ${\ensuremath{\Delta}}_{0}$ for different hybridizations. We have adopted hopping parameters suitable to describe the high-temperature superconductor materials. The results show that for a fixed value of the hybridization and the intraband $d\text{\ensuremath{-}}d$ attractive potential $U$, the gap increases for low temperatures and diminishes as the temperatures increase toward ${T}_{c}$. As the hybridization increases both, ${\ensuremath{\Delta}}_{0}$ and ${T}_{c}$, diminish. For each hybridization, the quantity $2{\ensuremath{\Delta}}_{0}/{k}_{B}{T}_{c}$ increases and saturates in a particular value as $U$ increases. The relation between applied pressure $P$ and hybridization in the strong-coupling regime is also discussed.

Physical Review BJul 1, 20108 citations

Superconductivity of the Two-Dimensional Hubbard Model

Jun Kondo

日本物理學會誌Jul 5, 20010 citations

Energetics of superconductivity in the two-dimensional Hubbard model

Emanuel Gull, Andrew J. Millis

The energetics of the interplay between superconductivity and the pseudogap in high-temperature superconductivity is examined using the eight-site dynamical cluster approximation to the two-dimensional Hubbard model. Two regimes of superconductivity are found: a weak-coupling/large-doping regime in which the onset of superconductivity causes a reduction in potential energy and an increase in kinetic energy, and a strong-coupling regime in which superconductivity is associated with an increase in potential energy and a decrease in kinetic energy. The crossover between the two regimes is found to coincide with the boundary of the normal-state pseudogap, providing further evidence of the unconventional nature of superconductivity in the pseudogap regime. However, the absence, in the strongly correlated but nonsuperconducting state, of discernibly nonlinear response to an applied pairing field suggests that resonating valence bond physics is not the origin of the kinetic-energy driven superconductivity.The energetics of the interplay between superconductivity and the pseudogap in high-temperature superconductivity is examined using the eight-site dynamical cluster approximation to the two-dimensional Hubbard model. Two regimes of superconductivity are found: a weak-coupling/large-doping regime in which the onset of superconductivity causes a reduction in potential energy and an increase in kinetic energy, and a strong-coupling regime in which superconductivity is associated with an increase in potential energy and a decrease in kinetic energy. The crossover between the two regimes is found to coincide with the boundary of the normal-state pseudogap, providing further evidence of the unconventional nature of superconductivity in the pseudogap regime. However, the absence, in the strongly correlated but nonsuperconducting state, of discernibly nonlinear response to an applied pairing field suggests that resonating valence bond physics is not the origin of the kinetic-energy driven superconductivity.

arXiv:1211.3123Physical Review BDec 17, 201286 citations

Magnetic Properties and Superconductivity in the Two-Dimensional Repulsive Hubbard Model

A. Sherman

A new method for estimating the parameter ensuring the fulfillment of the Mermin-Wagner theorem in the strong coupling diagram technique (SCDT) for the two-dimensional Hubbard model is suggested. With the precise parameter value, calculated magnetic quantities are in good agreement with the results of numeric and optical-lattice experiments. Obtained spin and charge vertices are used for investigating superconductivity in the $t$ - $U$ and $t$ - $t'$ - $t"$ - $U$ Hubbard models in the regime of strong correlations. We found no superconducting transition in the $t$ - $U$ model. In the $t$ - $t'$ - $t"$ - $U$ model, the transition occurs for the singlet $d_{x^2-y^2}$ pairing at $T_c\approx0.016t$ . The difference between the two models is in the renormalized hopping describing electron motion in SCDT. In the $t$ - $U$ model, it vanishes for momenta $(π,0)$ , $(0,π)$ of extrema of the $d$ -wave order parameter, while the hopping is finite in the $t$ - $t'$ - $t"$ - $U$ model. In the one-band model, there are optimal values of $t'$ and $t"$ ensuring the highest $T_c$ .A new method for estimating the parameter ensuring the fulfillment of the Mermin-Wagner theorem in the strong coupling diagram technique (SCDT) for the two-dimensional Hubbard model is suggested. With the precise parameter value, calculated magnetic quantities are in good agreement with the results of numeric and optical-lattice experiments. Obtained spin and charge vertices are used for investigating superconductivity in the $t$-$U$ and $t$-$t'$-$t"$-$U$ Hubbard models in the regime of strong correlations. We found no superconducting transition in the $t$-$U$ model. In the $t$-$t'$-$t"$-$U$ model, the transition occurs for the singlet $d_{x^2-y^2}$ pairing at $T_c\approx0.016t$. The difference between the two models is in the renormalized hopping describing electron motion in SCDT. In the $t$-$U$ model, it vanishes for momenta $(π,0)$, $(0,π)$ of extrema of the $d$-wave order parameter, while the hopping is finite in the $t$-$t'$-$t"$-$U$ model. In the one-band model, there are optimal values of $t'$ and $t"$ ensuring the highest $T_c$.

arXiv:2107.06520Journal of the Physical Society of JapanSep 16, 20212 citations

In this work we have considered a two-dimensional two-band Hubbard model (extended Hubbard model) to study the effect of the nonlocal hybridization

{V}_{\mathbf{k}}

on the superconductivity. In the strong-coupling regime and for a

d

-wave superconducting gap, we have obtained the superconducting critical temperature

{T}_{c}

and the zero-temperature superconducting gap ${\ensuremath{\Delta}}_{0}$ for different hybridizations. We have adopted hopping parameters suitable to describe the high-temperature superconductor materials. The results show that for a fixed value of the hybridization and the intraband $d\text{\ensuremath{-}}d$ attractive potential

U

, the gap increases for low temperatures and diminishes as the temperatures increase toward

{T}_{c}

. As the hybridization increases both, ${\ensuremath{\Delta}}_{0}$ and

{T}_{c}

, diminish. For each hybridization, the quantity $2{\ensuremath{\Delta}}_{0}/{k}_{B}{T}_{c}$ increases and saturates in a particular value as

U

increases. The relation between applied pressure

P

and hybridization in the strong-coupling regime is also discussed.

t

U

and

t

t'

t"

U

Hubbard models in the regime of strong correlations. We found no superconducting transition in the

t

U

model. In the

t

t'

t"

U

model, the transition occurs for the singlet

d_{x^2-y^2}

pairing at

T_c\approx0.016t

. The difference between the two models is in the renormalized hopping describing electron motion in SCDT. In the

t

U

model, it vanishes for momenta

(π,0)

(0,π)

of extrema of the

d

-wave order parameter, while the hopping is finite in the

t

t'

t"

U

model. In the one-band model, there are optimal values of

t'

and

t"

ensuring the highest

T_c