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arXiv:1110.5297 · Physical Review B

Coexistence of strong nematic and superconducting correlations in a two-dimensional Hubbard model

Shi-Quan Su, Thomas Maier

Published Dec 22, 2011• 24 citations
arXivHTMLPDF

Abstract

Using a dynamic cluster quantum Monte Carlo approximation, we study a two-dimensional Hubbard model with a small orthorhombic distortion in the nearest-neighbor hopping integrals. We find a large nematic response in the low-frequency single-particle scattering rate which develops with decreasing temperature and doping as the pseudogap region is entered. At the same time, the $d$-wave superconducting gap function develops an $s$-wave component and its amplitude becomes anisotropic. The strength of the pairing correlations, however, is found to be unaffected by the strong anisotropy, indicating that $d$-wave superconductivity can coexist with strong nematicity in the system.

DOI
10.1103/physrevb.84.220506

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Using a dynamic cluster quantum Monte Carlo approximation, we study a two-dimensional Hubbard model with a small orthorhombic distortion in the nearest-neighbor hopping integrals. We find a large nematic response in the low-frequency single-particle scattering rate which develops with decreasing temperature and doping as the pseudogap region is entered. At the same time, the ddd-wave superconducting gap function develops an sss-wave component and its amplitude becomes anisotropic. The strength of the pairing correlations, however, is found to be unaffected by the strong anisotropy, indicating that ddd-wave superconductivity can coexist with strong nematicity in the system.
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.
We investigate the interplay between superconductivity and nematic order in a two-dimensional electron gas with competing pairing and quadrupolar forward-scattering interactions. The model includes both sss-wave and ddd-wave superconducting channels. We compute the mean-field free energy density and determine the phase diagrams as functions of interaction strengths and temperature by solving a set of coupled self-consistent equations. At zero-temperature, we find that the nematic order competes strongly with ddd-wave superconductivity, leading to a direct first-order phase transition, while its interplay with sss-wave pairing allows for a coexistence phase characterized by an anisotropic Fermi surface with a uniform superconducting gap. At finite-temperatures, quadrupolar interactions promote the emergence of additional superconducting components, giving rise to regimes where sss-wave, ddd-wave, and nematic orders coexist. Our results highlight the role of symmetry and interaction strength in shaping the phase structure and provide a minimal framework to describe intertwined nematic and superconducting phases in correlated electron systems.
Dynamic cluster quantum Monte Carlo calculations for a doped two-dimensional extended Hubbard model are used to study the stability and dynamics of ddd-wave pairing when a nearest-neighbor Coulomb repulsion VVV is present in addition to the on-site Coulomb repulsion UUU. We find that ddd-wave pairing and the superconducting transition temperature Tc{T}_{c}Tc​ are only weakly suppressed as long as VVV does not exceed U/2U/2U/2. This stability is traced to the strongly retarded nature of pairing that allows the ddd-wave pairs to minimize the repulsive effect of VVV. When VVV approaches U/2U/2U/2, large momentum charge fluctuations are found to become important and to give rise to a more rapid suppression of ddd-wave pairing and Tc{T}_{c}Tc​ than for smaller VVV.
The two-dimensional Hubbard model exhibits superconductivity with d-wave symmetry even at half-filling in the presence of a next-nearest neighbor hopping. Using plaquette cluster dynamical mean-field theory with a continuous-time quantum Monte Carlo impurity solver, we reveal the non-Fermi liquid character of the metallic phase in proximity to the superconducting state. Specifically, the low-frequency scattering rate for momenta near (π, 0) varies nonmonotonically at low temperatures, and the dc conductivity is T linear at elevated temperatures with an upturn upon cooling. Evidence is provided that pairing fluctuations dominate the normal-conducting state even considerably above the superconducting transition temperature.
We investigate charge fluctuations in the two-dimensional Hubbard model as a function of doping, interaction strength, next-nearest-neighbor hopping, and temperature within the eight-site dynamical cluster approximation. In the regime of intermediate interaction strengths, we find that ddd density wave fluctuations, which had previously been postulated using analytical arguments, are present and strong but cannot be interpreted as the cause of the pseudogap in the model, due to their evolution with doping and interaction strength. For all parameters away from half filling, the charge fluctuations investigated, including ddd density wave fluctuations, are weaker than ddd-wave superconducting fluctuations.
We compute the two-particle quantities relevant for superconducting correlations in the two-dimensional Hubbard model within the dynamical cluster approximation. In the normal state we identify the parameter regime in density, interaction, and second-nearest-neighbor hopping strength that maximizes the d_{x^{2}-y^{2}} superconducting transition temperature. We find in all cases that the optimal transition temperature occurs at intermediate coupling strength, and is suppressed at strong and weak interaction strengths. Similarly, superconducting fluctuations are strongest at intermediate doping and suppressed towards large doping and half filling. We find a change in sign of the vertex contributions to d_{xy} superconductivity from repulsive near half filling to attractive at large doping. p-wave superconductivity is not found at the parameters we study, and s-wave contributions are always repulsive. For negative second-nearest-neighbor hopping the optimal transition temperature shifts towards the electron-doped side in opposition to the van Hove singularity, which moves towards hole doping. We surmise that an increase of the local interaction of the electron-doped compounds would increase T_{c}.