Studies of superconductivity (SC) and competing-order (CO) interplay in cuprates and Fe-base compounds using scanning tunneling spectroscopy (STS)

STS studies of YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ (Y-123) and Ca-doped Y-123 from under- to over-doped regimes demonstrate that the origin of the pseudogap (PG) is due to competing orders (COs), and that the presence (absence) of PG above the SC transition $T_{c}$ is associated with a CO energy $\Delta_{\mathrm{CO}}$ larger (smaller) than the SC gap $\Delta_{\mathrm{SC}}$. We find that for hole doping level $p$ $\le $ 0.16, $\Delta_{\mathrm{CO}}$ \textit{\textgreater } $\Delta_{\mathrm{SC}}$, whereas both $\Delta_{\mathrm{SC}}$ and $\Delta_{\mathrm{CO}}$ decrease with $p$ for $p$ \textgreater 0.16, and $\Delta_{\mathrm{CO}}$ ($\sim$ 10 meV) \textit{\textless } $\Delta_{\mathrm{SC}}$ ($\sim$ 13 meV) at $p$ $\sim$ 0.23. The CO wave-vectors Q$_{\mathrm{CDW}}$ and Q$_{\mathrm{PDW}}$ along the Cu-O bond are determined from Fourier transformation of the STS as a function of $p$, and are found to occur at 1/3 and 2/3 of the reciprocal lattice constant (2$\pi $/$a)$ for $p \quad =$ 0.16. The pairing symmetry also evolves from pure $d_{x^2-y^2}$ to ($d_{x^2-y^2}+s)$ for $p$ \textgreater 0.16, where the $s$-wave component increases with $p$. Moreover, under a finite magnetic field the ratio of the vortex ``halo'' radius ($\xi _{\mathrm{halo}})$ relative to the SC coherence length ($\xi _{\mathrm{SC}})$ decreases with $p$, from $\sim$ 8 for $p \quad =$ 0.16 to $\sim$ 3 for $p \quad =$ 0.216, suggesting PG contributions to the vortex halo. Magnetic resonance mode at $\Omega_{\mathrm{r}}$ $\sim$ 2$\Delta_{\mathrm{SC}}$ is also observed as a function of $p$. Finally, we present comparative STS studies of Fe-based superconductors, including Ba(Fe$_{\mathrm{1-x}}$Co$_{\mathrm{x}})_{2}$As$_{2}$ and Rb$_{0.8}$Fe$_{1.6}$Se$_{2}$. This work was supported by NSF.