Pairing glue in the two-dimensional Hubbard model

Cluster dynamical mean-field calculations are used to construct the superconducting gap function of the two-dimensional Hubbard model. The frequency dependence of the imaginary part of the gap function indicates that the pairing is dominated by fluctuations at two characteristic frequencies: one at the scale of the hopping matrix element $t$ and one at a much lower scale. The lower-frequency component becomes more important as the doping is reduced into the pseudogap regime. Comparison to information on the spin-fluctuation spectrum of the model suggests that superconductivity arises from exchange of spin fluctuations. The inferred pairing glue function is in remarkable qualitative consistency with the pairing function inferred from optical conductivity data.

Figure 1

$\Delta \left(i{\omega }_n\right)$ as a function of Matsubara frequency for different dopings at $U=6t$. Left inset: Momentum-space tiling of the DCA cluster used in this Rapid Communication. Right inset: Phase diagram according to Ref. [30].

Figure 2

Main panel: Imaginary part of real frequency gap function computed for different dopings. Dashed curves label dopings within the pseudogap regime and solid curves label dopings outside the pseudogap regime. The vertical dashed line indicates the frequency cutoff chosen in the inset of Fig. 3. Inset: Experimental data reproduced from Ref. [34].

Figure 3

Main panel: Partial integral of $\text{Im}\Delta \left(\omega \right)$ for the dopings of Fig. 1 up to $\Omega =1.6t$. Vertical dashed line: Cutoff frequency used in inset. Inset: Integral over the entire frequency range and over the range of the low-frequency pole, as a function of doping.