# Seminário de Matéria Condensada - 07/06/2018, 11:00, Sala 426 (Torre Nova)

### Correlations among charge order, superconducting interaction, Tc and superfluid density in cuprate superconductors

#### Evandro Vidor de Mello (UFF)

After more than 30 years the problem of high-Tc superconductor is still open. A revealing experiment was the scaling between superfluid density $\rho_{sc}$ and Tc established long ago. The values of $\rho_sc$ are orders of magnitude lower than conventional superconductors, implying that phase fluctuations are important. Another universal feature is the presence of an incommensurate charge order (CO) with $\lambda_{CO}$ wavelength smaller than the superconducting coherence length $\xi$. We simulate CO patterns with a Ginzburg-Landau free energy with $\lambda_{CO}$ modulations. The charge fluctuations yield the superconducting interaction that leads to the amplitudes $\Delta_d({\bf r})$ in the grains. The intergrain Josephson coupling $E_J \propto \rho_{\rm sc}$ establishes long range phase order and is used to derive the $\rho_{sc}(0)-T_c$ for four cuprate families. Through $E_J$ and the resistivity we can infer the real superconducting gap. The method works also with very small charge variations and reproduces the new $\rho_{sc}(0)-T_c$ linear relation on overdoped La$_{2-x}$Sr$_x$CuO$_4$ films, providing a unified approach to under and overdoped cuprates.