Direct theoretical evidence for weaker correlations in electron-doped and Hg-based hole-doped cuprates

Many important questions for high-$T_c$ cuprates are closely related to the insulating nature of parent compounds. While there has been intensive discussion on this issue, all arguments rely strongly on, or are closely related to, the correlation strength of the materials. Clear understanding has been seriously hampered by the absence of a direct measure of this interaction, traditionally denoted by $U$. Here, we report a first-principles estimation of $U$ for several different types of cuprates. The $U$ values clearly increase as a function of the inverse bond distance between apical oxygen and copper. Our results show that the electron-doped cuprates are less correlated than their hole-doped counterparts, which supports the Slater picture rather than the Mott picture. Further, the $U$ values significantly vary even among the hole-doped families. The correlation strengths of the Hg-cuprates are noticeably weaker than that of La$_2$CuO$_4$. Our results suggest that the strong correlation enough to induce Mott gap may not be a prerequisite for the high-$T_c$ superconductivity.