Isotope effect in the pseudogap state of high-temperature copper oxide superconductors

We study cuprates within the dynamical cluster approximation and find that the pseudogap displays an isotope effect of the same sign as observed experimentally. Notwithstanding the nonphononic origin of the pseudogap, the interplay between electronic repulsion and retarded phonon-mediated attraction gives rise to an isotope dependence of the antinodal spectra. Due to the strong momentum differentiation, such an interplay is highly nontrivial and leads to the simultaneous presence of heavier quasiparticles along the nodal direction. We predict an isotope effect in electron-doped materials.

Figure 1

(Left-hand side) 16-site clusters considered (the notation is the same as in Ref. 32). (Right-hand side) Corresponding cluster momenta ${\mathbf{K}}_{\mathbf{c}}$ in the BZ. The ${\mathbf{K}}_{\mathbf{c}}$ marked by both the green full square and the red open circle are present in both geometries. The packed circle and checkerboard gray areas denote the coarse graining regions for 16A and B, respectively.

Figure 2

16-site cluster spectra at $T=580$ K for different cluster momenta ${\mathbf{K}}_{\mathbf{c}}$ for hole (a), (b) and $e$ doping (c), (d). $U=8\left|t\right|$, $\left|t\right|=400$ meV, $|t^{\prime }|=120$ meV. ${\omega }_{\text{ph}}=200$ and 100 meV for hole and $e$ doping, respectively. ${\mathbf{K}}_{\mathbf{c}}$-resolved DCA spectra do not depend on any interpolation scheme.

Figure 3

Pseudogap for different values of ${\omega }_{\text{ph}}$ for 5% hole and $e$ doping, upper and lower panels, respectively.

Figure 4

$A_{{\mathbf{K}}_{\mathbf{c}}=(\pi ,0)}(\omega =0)$ for 5% hole doping for both clusters. The dashed black lines show the same quantity obtained for $\lambda =0$ and changing $U$ (upper horizontal scale).