Nature of the Pairing Interaction in the Hubbard Model of High-Temperature Superconductors

Thomas A. Maier (CNMS Staff); Douglas J. Scalapino (CNMS User), University of California, Santa Barbara, and Mark Jarrell (CNMS User) University of Cincinnati

Achievement

The nature of the pairing interaction that mediates superconductivity in the two-dimensional Hubbard model has been addressed numerically in a user project at the Center for Nanophase Materials Sciences. The Hubbard model exhibits several phenomena remarkably similar to what is observed in the cuprate high-temperature superconductors, including superconductivity, antiferromangetism, and the nano-meter scale phase separation present in some underdoped compounds. In this work a combination of numerical dynamic cluster quantum Monte Carlo simulations and diagrammatic techniques revealed the structure and nature of the pairing interaction responsible for superconductivity. This work established that the pairing interaction increases with momentum transfer and decreases when the energy transfer exceeds a scale associated with the antiferromagnetic spin susceptibility. This implies that the pairing interaction is attractive between singlets formed on nearest neighbor sites and that its dynamics is associated with the antiferromagnetic spin fluctuation spectrum. The strength of the pairing interaction is found to peak when the Coulomb repulsion is of the order of the bandwidth, and increases as the system is underdoped. An exact decomposition of the pairing interaction reveals that it is mediated by the exchange of antiferromagnetic spin fluctuations (see attached).

Significance

The relevant parameter region of the Hubbard model to describe the cuprate superconductors is at the crossover region between weak and strong electronic correlations. This makes the study of this model extremely challenging since conventional perturbative approaches fail. Employing a state-of-the-art many-body technique, this work was able to address this region in a controlled way for the first time. This work established that the pairing interaction in the Hubbard model is of magnetic origin. The full characterization of the nature of the pairing interaction is an important step towards the design of materials that become superconducting at even higher temperatures, enabling breakthroughs in real world applications that will benefit from near-ideal conduction of electricity. Moreover, the general concepts developed in this work provide a useful, unbiased method for determining the nature of the leading correlations in interacting many-electron systems and the character of the mechanism responsible for them.

Details of this report can be found in T. A. Maier, M. S. Jarrell, and D. J. Scalapino, "Structure of the Pairing Interaction in the Two-Dimensional Hubbard Model," Phys. Rev. Lett. 96, 4 (2006); T. A. Maier, M. S. Jarrell, and D. J. Scalapino, "Pairing interaction in the two-dimensional Hubbard model studied with a dynamic cluster quantum Monte Carlo approximation," Phys. Rev. B 74, 6 (2006).

ORNL Research by Thomas A. Maier. Co-authors were Douglas J. Scalapino from the University of California, Santa Barbara and Mark Jarrell from the University of Cincinnati. This work was supported by the NSF and enabled by computational resources of the Center for Computational Sciences at Oak Ridge National Laboratory, and was a user project at the CNMS.

Figure

The different contributions to the pairing interaction Vd that leads to superconductivity in the 2D Hubbard model of the high-temperature superconductors. The dominant contribution comes from antiferromagnetic spin fluctuations, while the charge and other fluctuations act to weaken the pairing interaction.