Self-consistent diagrammatics for a correlated superconductor: contrasting two and three dimensions Original Research Article

We use self-consistent diagrammatics to contrast pairing fluctuations in the Attractive Hubbard Model in two and three dimensions. Specifically, we use the self-consistent T-matrix approximation and show that, quite remarkably, this method yields results that are consistent with the exact 2D-XY and 3D-XY critical scaling. We find that dimensionality alone increases the ratio of the mean-field to actual transition temperatures more than 4-fold in 2D, and that the scaling regimes coincide with the normal state pseudogap regime in both 2D and 3D. Together this suggests that the decreasing effective dimensionality when cuprates are underdoped may account for the increasing size of the pseudogap regime.