The relationship between crystal structures and superconducting critical temperatures has attracted considerable attention as a clue to designing higher- $T_{\rm c}$ superconductors. In particular, the relationship between the number $n$ of CuO $_2$ layers in a unit cell of cuprate superconductors and the optimum superconducting transition temperature $T_{\rm c}^{\rm opt}$ is intriguing. As experimentally observed in layered cuprates, $T_{\rm c}^{\rm opt}$ increases when $n$ is increased, up to $n=3$ , and, then, decreases for larger $n$ . However, the mechanism behind the $n$ dependence of $T_{\rm c}^{\rm opt}$ remains elusive although there have been many studies on the $n$ dependence. In this paper, we studied a bilayer $t$ - $t'$ Hubbard model to clarify the effects of the adjacent CuO $_2$ layers on the stability of the superconductivity by using a many-variable variational Monte Carlo method. We calculate the superconducting correlation at long distance and zero temperature, and the amplitude of the superconducting gap functions estimated from the momentum distribution as the observables correlated with $T_{\rm c}^{\rm opt}$ . It is found that the in-plane superconducting correlation is not enhanced in comparison with that in the single-layer $t$ - $t'$ Hubbard model. The superconducting correlations of the bilayer Hamiltonian are significantly small in the overdoped region in comparison with those of single-layer Hamiltonian, which is attributed to the van Hove singularity. In addition, we found that the amplitude of the superconducting gap functions is also similar in both the single-layer and bilayer $t$ - $t'$ Hubbard model at the optimal doping. Therefore, we conclude that the adjacent Hubbard layers are not relevant to the enhancement of $T_{\rm c}^{\rm opt}$ in the bilayer cuprates. Possible origins of the enhanced $T_{\rm c}^{\rm opt}$ other than the adjacent layers are also discussed.The relationship between crystal structures and superconducting critical temperatures has attracted considerable attention as a clue to designing higher-$T_{\rm c}$ superconductors. In particular, the relationship between the number $n$ of CuO$_2$ layers in a unit cell of cuprate superconductors and the optimum superconducting transition temperature $T_{\rm c}^{\rm opt}$ is intriguing. As experimentally observed in layered cuprates, $T_{\rm c}^{\rm opt}$ increases when $n$ is increased, up to $n=3$, and, then, decreases for larger $n$. However, the mechanism behind the $n$ dependence of $T_{\rm c}^{\rm opt}$ remains elusive although there have been many studies on the $n$ dependence. In this paper, we studied a bilayer $t$-$t'$ Hubbard model to clarify the effects of the adjacent CuO$_2$ layers on the stability of the superconductivity by using a many-variable variational Monte Carlo method. We calculate the superconducting correlation at long distance and zero temperature, and the amplitude of the superconducting gap functions estimated from the momentum distribution as the observables correlated with $T_{\rm c}^{\rm opt}$. It is found that the in-plane superconducting correlation is not enhanced in comparison with that in the single-layer $t$-$t'$ Hubbard model. The superconducting correlations of the bilayer Hamiltonian are significantly small in the overdoped region in comparison with those of single-layer Hamiltonian, which is attributed to the van Hove singularity. In addition, we found that the amplitude of the superconducting gap functions is also similar in both the single-layer and bilayer $t$-$t'$ Hubbard model at the optimal doping. Therefore, we conclude that the adjacent Hubbard layers are not relevant to the enhancement of $T_{\rm c}^{\rm opt}$ in the bilayer cuprates. Possible origins of the enhanced $T_{\rm c}^{\rm opt}$ other than the adjacent layers are also discussed.

arXiv:2207.04205Journal of the Physical Society of JapanAug 17, 20228 citations

2D One-Band Hubbard Model for the Cuprates

Silvia B. Bacci, Eduardo R. Gagliano, Richard M. Martin

Springer eBooksJan 1, 19910 citations

Mean field Green function solution of the two-band Hubbard model in cuprates

Gh. Adam, S. Adam

Вестник Российского университета дружбы народов. Серия: Математика, информатика, физикаJan 1, 20100 citations

Interlayer bias effect on time-reversal symmetry breaking in twisted bilayer cuprates

Mathieu Bélanger, David Sénéchal

We study a one-band Hubbard model of twisted bilayer cuprates with a twist angle of $53.{13}^{\ensuremath{\circ}}$. By introducing an interlayer bias, we simulate heterobilayers of different dopings. Using the variational cluster approximation, we probe the effect of this bias on the time-reversal symmetry-breaking (TRSB) phase. Doping differences between layers affect the region where TRSB occurs; we construct a phase diagram mapping out the TRSB phase in the ${n}_{1}\ensuremath{-}{n}_{2}$ plane, with ${n}_{\ensuremath{\ell}}$ being the electron density on layer $\ensuremath{\ell}$. We also map the spontaneous supercurrent on the same plane.We study a one-band Hubbard model of twisted bilayer cuprates with a twist angle of $53.{13}^{\ensuremath{\circ}}$. By introducing an interlayer bias, we simulate heterobilayers of different dopings. Using the variational cluster approximation, we probe the effect of this bias on the time-reversal symmetry-breaking (TRSB) phase. Doping differences between layers affect the region where TRSB occurs; we construct a phase diagram mapping out the TRSB phase in the ${n}_{1}\ensuremath{-}{n}_{2}$ plane, with ${n}_{\ensuremath{\ell}}$ being the electron density on layer $\ensuremath{\ell}$. We also map the spontaneous supercurrent on the same plane.

arXiv:2311.02207Physical review. B./Physical review. BFeb 6, 20244 citations

Variational Cluster Approach to the Bilayer Hubbard Model

Anna Maria Fulterer, Enrico Arrigoni

Jan 1, 20090 citations

Investigation of Strongly Correlated Electron Systems with Cellular Dynamical Mean Field Theory

Marcello Civelli

In this thesis we study the strongly-correlated-electron physics of the longstanding H-Tc-superconductivity problem using a non-perturbative method, the Dynamical Mean Field Theory (DMFT), capable to go beyond standard perturbation-theory techniques. DMFT is by construction a local theory which neglects spatial correlation. Experiments have however shown that the latter is a fundamental property of cuprate materials. In a first step, we approach the problem of spatial correlation in the normal state of cuprate materials using a phenomenological Fermi-Liquid-Boltzmann model. We then introduce and develop in detail an extension to DMFT, the Cellular Dynamical Mean Field Theory (CDMFT), capable of considering short-ranged spatial correlation in a system, and we implement it using the exact diagonalization algorithm . After benchmarking CDMFT with the exact one-dimensional solution of the Hubbard Model, we employ it to study the density-driven Mott metal-insulator transition in the two-dimensional Hubbard Model, focusing in particular on the anomalous properties of the doped normal state close to the Mott insulator. We finally study the superconducting state. We show that within CDMFT the one-band Hubbard Model supports a d-wave superconductive state, which strongly departs from the standard BCS theory. We conjecture a link between the instabilities found in the normal state and the onset of superconductivity.In this thesis we study the strongly-correlated-electron physics of the longstanding H-Tc-superconductivity problem using a non-perturbative method, the Dynamical Mean Field Theory (DMFT), capable to go beyond standard perturbation-theory techniques. DMFT is by construction a local theory which neglects spatial correlation. Experiments have however shown that the latter is a fundamental property of cuprate materials. In a first step, we approach the problem of spatial correlation in the normal state of cuprate materials using a phenomenological Fermi-Liquid-Boltzmann model. We then introduce and develop in detail an extension to DMFT, the Cellular Dynamical Mean Field Theory (CDMFT), capable of considering short-ranged spatial correlation in a system, and we implement it using the exact diagonalization algorithm . After benchmarking CDMFT with the exact one-dimensional solution of the Hubbard Model, we employ it to study the density-driven Mott metal-insulator transition in the two-dimensional Hubbard Model, focusing in particular on the anomalous properties of the doped normal state close to the Mott insulator. We finally study the superconducting state. We show that within CDMFT the one-band Hubbard Model supports a d-wave superconductive state, which strongly departs from the standard BCS theory. We conjecture a link between the instabilities found in the normal state and the onset of superconductivity.

arXiv:0710.2802Oct 13, 20075 citations

The relationship between crystal structures and superconducting critical temperatures has attracted considerable attention as a clue to designing higher-

T_{\rm c}

superconductors. In particular, the relationship between the number

n

of CuO

_2

layers in a unit cell of cuprate superconductors and the optimum superconducting transition temperature

T_{\rm c}^{\rm opt}

is intriguing. As experimentally observed in layered cuprates,

T_{\rm c}^{\rm opt}

increases when

n

is increased, up to

n=3

, and, then, decreases for larger

n

. However, the mechanism behind the

n

dependence of

T_{\rm c}^{\rm opt}

remains elusive although there have been many studies on the

n

dependence. In this paper, we studied a bilayer

t

t'

Hubbard model to clarify the effects of the adjacent CuO

_2

layers on the stability of the superconductivity by using a many-variable variational Monte Carlo method. We calculate the superconducting correlation at long distance and zero temperature, and the amplitude of the superconducting gap functions estimated from the momentum distribution as the observables correlated with

T_{\rm c}^{\rm opt}

. It is found that the in-plane superconducting correlation is not enhanced in comparison with that in the single-layer

t

t'

Hubbard model. The superconducting correlations of the bilayer Hamiltonian are significantly small in the overdoped region in comparison with those of single-layer Hamiltonian, which is attributed to the van Hove singularity. In addition, we found that the amplitude of the superconducting gap functions is also similar in both the single-layer and bilayer

t

t'

Hubbard model at the optimal doping. Therefore, we conclude that the adjacent Hubbard layers are not relevant to the enhancement of

T_{\rm c}^{\rm opt}

in the bilayer cuprates. Possible origins of the enhanced

T_{\rm c}^{\rm opt}

other than the adjacent layers are also discussed.