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Effect of weak inhomogeneities in high temperature superconductivity

D. G. S. P. Doluweera

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

We present results of three studies done using a dynamical cluster quantum Monte Carlo approximation.First, we investigate the d-wave superconducting transition temperature T c in the doped 2D repulsive Hubbard model with a weak inhomogeneity in hopping in the form of checkerboard pattern or a lattice of 2 × 2 plaquettes.Near neighbor hoppings within a plaquette is t and that of between the plaquettes is t ′ .We investigate T c in the weak inhomogeneous limit 0.8t < t ′ < 1.2t.We find inhomogeneity (t ′ = t) suppresses T c .The characteristic spin excitation energy (effective exchange energy) and the strength of d-wave pairing interaction decrease with decreasing T c .The latter observations suggest a strong correlation among effective exchange interaction, T c and the d-wave pairing interaction of the system.Second 1 , we further find that enhancement of effective exchange interaction causes a slight increase in T c of a weakly disordered system with low impurity concentration, compared to the homogeneous system.Here the disorder is introduced to homogeneous repulsive 2D Hubbard model as a weak local potential disorder.Third, we present an improved maximum entropy method to analytically continue quantum Monte Carlo data with a severe sign problem.1 A result from a collaborative study done with A. Kemper of

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We present results of three studies done using a dynamical cluster quantum Monte Carlo approximation.First, we investigate the d-wave superconducting transition temperature T c in the doped 2D repulsive Hubbard model with a weak inhomogeneity in hopping in the form of checkerboard pattern or a lattice of 2 × 2 plaquettes.Near neighbor hoppings within a plaquette is t and that of between the plaquettes is t ′ .We investigate T c in the weak inhomogeneous limit 0.8t < t ′ < 1.2t.We find inhomogeneity (t ′ = t) suppresses T c .The characteristic spin excitation energy (effective exchange energy) and the strength of d-wave pairing interaction decrease with decreasing T c .The latter observations suggest a strong correlation among effective exchange interaction, T c and the d-wave pairing interaction of the system.Second 1 , we further find that enhancement of effective exchange interaction causes a slight increase in T c of a weakly disordered system with low impurity concentration, compared to the homogeneous system.Here the disorder is introduced to homogeneous repulsive 2D Hubbard model as a weak local potential disorder.Third, we present an improved maximum entropy method to analytically continue quantum Monte Carlo data with a severe sign problem.1 A result from a collaborative study done with A. Kemper of
Using a dynamical cluster quantum Monte Carlo approximation, we investigate the ddd-wave superconducting transition temperature Tc{T}_{c}Tc​ in the doped two-dimensional repulsive Hubbard model with a weak inhomogeneity. The inhomogeneity is introduced in the hoppings ${t}^{\ensuremath{'}}$ and ttt in the form of a checkerboard pattern where ttt is the hopping within a $2\ifmmode\times\else\texttimes\fi{}2$ plaquette, and ${t}^{\ensuremath{'}}$ is the hopping between the plaquettes. We find inhomogeneity suppresses Tc{T}_{c}Tc​. The characteristic spin excitation energy and the strength of ddd-wave pairing interaction decrease with decreasing Tc{T}_{c}Tc​, suggesting a strong correlation between these quantities.
It has been argued that inhomogeneity generally can enhance superconductivity (SC) in the cuprate high-Tc{T}_{c}Tc​ materials. To check the validity of this claim, we study ddd-wave SC on the checkerboard Hubbard model on a square lattice using the cellular dynamical mean-field theory method with an exact diagonalization solver at zero temperature. The ddd-wave order parameter is computed for various inhomogeneity levels over the entire doping range of interest in both strong- and weak-coupling regimes. At a given doping, the size of the ddd-wave order parameter manifests itself directly in the height of the coherence peaks and, hence, is an appropriate measure of the strength of SC. The weak-coupling results reveal a suppression of the order parameter in the presence of inhomogeneity for small-to-intermediate hole dopings, while it is enhanced for large dopings. In contrast, for strong coupling, there is a monotonic decrease in the maximum amplitude of the SC order parameter with inhomogeneity over the entire doping range of interest. Furthermore, at moderately high inhomogeneity, the system undergoes a first-order transition from the SC to the normal state in the underdoped regime. In the overdoped regime, the change in the value of the SC order parameter correlates with the height of the lowest-energy peak in the spectral weight of antiferromagnetic spin fluctuations, confirming the connection between antiferromagnetic fluctuations and ddd-wave SC found in earlier papers on the homogeneous case. Our results are benchmarked by comparisons with numerically exact results on the checkerboard Hubbard ladder.
Using a dynamical cluster quantum Monte Carlo approximation, we investigate the effect of local disorder on the stability of ddd-wave superconductivity including the effect of electronic correlations in both particle-particle and particle-hole channels. With increasing impurity potential, we find an initial rise of the critical temperature due to an enhancement of antiferromagnetic spin correlations, followed by a decrease of Tc{T}_{c}Tc​ due to scattering from impurity-induced moments and ordinary pair breaking. We discuss the weak initial dependence of Tc{T}_{c}Tc​ on impurity concentration found in comparison to experiments on cuprates.
Constrained-path quantum Monte Carlo method is applied to study the pairing correlation in the checkerboard Hubbard model with inhomogeneous nearest-neighbor hopping at a low doping of holes. The inhomogeneous hopping can enhance the pairing correlation among different plaquette clusters. An obvious maximum for the pairing correlation is observed at a certain inhomogeneous hopping. The cluster pairing correlation shows the strongest long-range behavior at the optimal inhomogeneity. The enhancement of cluster pairing correlation might be associated with the transition of the Fermi surface structure. This work indicates that the inhomogeneous hopping could tailor the pairing correlation effectively.
Inhomogeneous sss-wave superconductivity is studied in the two-dimensional, square lattice attractive Hubbard Hamiltonian using the Bogoliubov-de Gennes (BdG) mean field approximation. We find that at weak coupling, and for densities mainly below half-filling, an inhomogeneous interaction in which the on-site interaction Ui{U}_{i}Ui​ takes on two values, Ui=0,2U{U}_{i}=0,\phantom{\rule{0.3em}{0ex}}2UUi​=0,2U results in a larger zero temperature pairing amplitude, and that the superconducting Tc{T}_{c}Tc​ can also be significantly increased, relative to a uniform system with Ui=U{U}_{i}=UUi​=U on all sites. These effects are observed for stripe, checkerboard, and even random patterns of the attractive centers, suggesting that the pattern of inhomogeneity is unimportant. Monte Carlo calculations which reintroduce some of the fluctuations neglected within the BdG approach see the same effect, both for the attractive Hubbard model and a Hamiltonian with ddd-wave pairing symmetry.
Using dynamic cluster quantum Monte Carlo simulations, we study the superconducting behavior of a 1/8 doped two-dimensional Hubbard model with imposed unidirectional stripelike charge-density-wave modulation. We find a significant increase of the pairing correlations and critical temperature relative to the homogeneous system when the modulation length scale is sufficiently large. With a separable form of the irreducible particle-particle vertex, we show that optimized superconductivity is obtained for a moderate modulation strength due to a delicate balance between the modulation enhanced pairing interaction, and a concomitant suppression of the bare particle-particle excitations by a modulation reduction of the quasiparticle weight.