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

## TL;DR

This study investigates how Mott physics and phase competition influence the superfluid stiffness in cuprates, revealing dominant effects of Mott physics on hole-doped and antiferromagnetic competition on electron-doped sides.

## Contribution

It provides a detailed computational analysis of superfluid stiffness in cuprates considering Mott transition and phase coexistence using Cellular Dynamical Mean-Field Theory.

## Key findings

- Mott physics dominates superfluid stiffness on hole-doped cuprates.
- Antiferromagnetism suppresses superfluid stiffness near half-filling on electron-doped cuprates.
- Superfluid stiffness approaches BCS behavior at high doping levels.

## Abstract

Superfluid stiffness $\rho_s$ 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 (AF) or charge-density waves (CDW), may drastically alter $\rho_s$. To shed light on this physics, the zero-temperature value of $\rho_s=\rho_{zz}$ 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 $\rho_{zz}$ near half-filling. At large overdoping, $\rho_{zz}$ behaves in a more BCS-like manner in both the electron- and hole-doped cases. We comment on some qualitative implications of these results for the superconducting transition temperature.