Doping-dependent vortex-state scanning tunneling spectroscopic (STS) studies of cuprate superconductors

We report STS studies of YBa2Cu3O7$-\delta $(Y-123) and Ca-doped Y-123 superconductors as a function of magnetic field ($H)$ and hole doping level ($p)$. Our studies suggest that the origin of the pseudogap (PG) is associated with competing orders (COs), and that the occurrence (absence) of PG above the superconducting (SC) transition $T_{c}$ is associated with a CO energy $\Delta_{CO}$ larger (smaller) than the SC gap $\Delta_{SC}$. We derive $\Delta_{SC}$ and $\Delta_{CO}$ by two approaches. For zero-field STS we apply Green function techniques to fit the ``peak'' features for $\Delta_{SC}$ and the ``kink'' features for $\Delta_{eff} \quad \equiv $ [($\Delta_{SC})^{2}+(\Delta_{CO})^{2}$]$^{1/2}$. For $H$ \textgreater\ 0 we analyze the PG features in the intra-vortex STS for $\Delta_{CO}$ and the peak features in the inter-vortex STS for $\Delta _{SC}$. Both approaches yield consistent results. For optimally and underdoped Y-123, we find that $\Delta_{SC}$ \textless\ $\Delta_{CO}$ with dominant $d_{x^{2}-y^{2}}$-wave pairing, and that $\Delta_{SC}$ decreases with decreasing $p$ while $\Delta_{CO}$ increases. Both $\Delta _{SC}$ and $\Delta_{CO}$ exhibit long-range spatial homogeneity. For Ca-doped Y-123, the substitution of Y by Ca contributes to excess holes and disorder. For $p$ \textgreater\ 0.16, both $\Delta_{SC}$ and $\Delta_{CO}$ decrease with increasing $p$, $\Delta_{CO}$ \textless\ $\Delta_{SC}$ for $p$ \textgreater\ 0.23, and the pairing symmetry becomes ($d_{x^{2}-y^{2}}+s$) with increasing $s$-wave component, implying the diminishing Mott nature in overdoped cuprates. This work was supported by NSF through IQIM at Caltech.