Superfluid stiffness in cuprates: Effect of Mott transition and phase competition

Abstract

Superfluid stiffness ${\ensuremath{\rho}}_{s}$ is a defining characteristic of the superconducting state, allowing phase coherence and supercurrent. It is accessible experimentally through the penetration depth. Coexistence of $d$-wave superconductivity with other phases in underdoped cuprates, such as antiferromagnetism or charge-density waves, may drastically alter ${\ensuremath{\rho}}_{s}$. To shed light on this physics, the zero-temperature value of ${\ensuremath{\rho}}_{s}={\ensuremath{\rho}}_{zz}$ along the $c$ axis was computed for different values of Hubbard interaction $U$ and different sets of tight-binding parameters describing the high-temperature superconductors YBCO and NCCO. We used cellular dynamical mean-field theory for the one-band Hubbard model with exact diagonalization as impurity solver and state-of-the-art bath parametrization. We conclude that Mott physics plays a dominant role in determining the superfluid stiffness on the hole-doped side of the phase diagram. On the electron-doped side, antiferromagnetism wins over superconductivity near half-filling. But, upon approaching optimal electron-doping, homogeneous coexistence between superconductivity and antiferromagnetism causes the superfluid stiffness to drop sharply. Hence, on the electron-doped side, it is competition between antiferromagnetism and $d$-wave superconductivity that plays a dominant role in determining the value of ${\ensuremath{\rho}}_{zz}$ near half-filling. At large overdoping, ${\ensuremath{\rho}}_{zz}$ behaves in a more BCS-type manner in both the electron- and hole-doped cases. We comment on some qualitative implications of these results for the superconducting transition temperature.