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

Superconductivity in the two-dimensional t - t′ -Hubbard model

Andreas Eberlein, Walter Metzner

Using a recently developed renormalization group method for fermionic superfluids, we determine conditions for $d$ -wave superconductivity in the ground state of the two-dimensional Hubbard model at moderate interaction strength, and we compute the pairing gap in the superconducting regime. A pairing instability signaled by a divergent flow in the Cooper channel leads to a superconducting state in all studied cases. The next-to-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ plays a crucial role in the competition between antiferromagnetism and superconductivity. A sizable ${t}^{\ensuremath{'}}$ is necessary to obtain a sizable pairing gap.Using a recently developed renormalization group method for fermionic superfluids, we determine conditions for $d$-wave superconductivity in the ground state of the two-dimensional Hubbard model at moderate interaction strength, and we compute the pairing gap in the superconducting regime. A pairing instability signaled by a divergent flow in the Cooper channel leads to a superconducting state in all studied cases. The next-to-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ plays a crucial role in the competition between antiferromagnetism and superconductivity. A sizable ${t}^{\ensuremath{'}}$ is necessary to obtain a sizable pairing gap.

arXiv:1308.4845Physical Review BJan 17, 201472 citations

Superconductivity in the two-dimensional Hubbard model: One-particle correlation functions

Chien-Hua Pao, N. E. Bickers

The one-particle correlation functions of a ${\mathit{d}}_{\mathit{x}}^{2}$ - ${\mathit{y}}^{2}$ superconducting state in the two-dimensional Hubbard model are investigated within the fluctuation-exchange approximation. This approximation has been previously applied to investigate properties of the Hubbard-model normal state, including incipient instabilities. Results are obtained for the wave vector and temperature dependence of the one-particle energy gap. A miximum gap ratio 2${\mathrm{\ensuremath{\Delta}}}_{\mathit{k}}^{\mathrm{max}}$(T=0)/ ${\mathit{k}}_{\mathit{B}}$ ${\mathit{T}}_{\mathit{c}}$ of order 10 is obtained for intermediate coupling strengths and electron densities near one per site. The potential appearance of spin excitons in two-particle response functions is discussed.The one-particle correlation functions of a ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ superconducting state in the two-dimensional Hubbard model are investigated within the fluctuation-exchange approximation. This approximation has been previously applied to investigate properties of the Hubbard-model normal state, including incipient instabilities. Results are obtained for the wave vector and temperature dependence of the one-particle energy gap. A miximum gap ratio 2${\mathrm{\ensuremath{\Delta}}}_{\mathit{k}}^{\mathrm{max}}$(T=0)/${\mathit{k}}_{\mathit{B}}$${\mathit{T}}_{\mathit{c}}$ of order 10 is obtained for intermediate coupling strengths and electron densities near one per site. The potential appearance of spin excitons in two-particle response functions is discussed.

Physical review. B, Condensed matterJun 1, 199545 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.

Using a recently developed renormalization group method for fermionic superfluids, we determine conditions for

d

-wave superconductivity in the ground state of the two-dimensional Hubbard model at moderate interaction strength, and we compute the pairing gap in the superconducting regime. A pairing instability signaled by a divergent flow in the Cooper channel leads to a superconducting state in all studied cases. The next-to-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ plays a crucial role in the competition between antiferromagnetism and superconductivity. A sizable ${t}^{\ensuremath{'}}$ is necessary to obtain a sizable pairing gap.

The one-particle correlation functions of a

{\mathit{d}}_{\mathit{x}}^{2}

{\mathit{y}}^{2}

superconducting state in the two-dimensional Hubbard model are investigated within the fluctuation-exchange approximation. This approximation has been previously applied to investigate properties of the Hubbard-model normal state, including incipient instabilities. Results are obtained for the wave vector and temperature dependence of the one-particle energy gap. A miximum gap ratio 2${\mathrm{\ensuremath{\Delta}}}_{\mathit{k}}^{\mathrm{max}}$(T=0)/

{\mathit{k}}_{\mathit{B}}

{\mathit{T}}_{\mathit{c}}

of order 10 is obtained for intermediate coupling strengths and electron densities near one per site. The potential appearance of spin excitons in two-particle response functions is discussed.