Doping-dependent vortex-state scanning tunneling spectroscopic (STS) studies of Ca-doped YBa$_{2}$Cu$_{3}$O$_{7-\delta}$(Y-123)

We present STS studies of Ca-doped Y-123 as a function of magnetic field ($H)$ and hole doping level ($p)$. Our previous STS studies at $H =$ 0 have shown that the origin of the pseudogap (PG) is due to competing orders (COs), and that the presence (absence) of PG above the superconducting (SC) transition $T_{c}$ is associated with a CO energy $\Delta_{\mathrm{CO}}$ larger (smaller) than the SC gap $\Delta_{\mathrm{SC}}$. Moreover, $\Delta _{\mathrm{SC}}$ and $\Delta_{\mathrm{CO}}$ decrease with increasing $p$ for $p$ \textgreater 0.16, and $\Delta_{\mathrm{CO}}$ \textit{\textless } $\Delta _{\mathrm{SC}}$ for $p$ \textgreater 0.23. 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 $p$. Here we investigate the evolution of vortex-state ($H$ \textgreater 0) STS with $p$. For $p =$ 0.21 and $H =$ 3T, STS reveal the presence of vortices with a vortex ``halo'' size $\xi $ $\sim$ 8 nm, smaller than $\xi $ $\sim$ 10 nm for $p =$ 0.16. A PG with $\Delta_{\mathrm{CO}}$ ($\sim$ 11 meV) \textless $\Delta_{\mathrm{SC}}$ ($\sim$ 17 meV) is found inside the vortex core for $p =$ 0.21, which is consistent with the value derived from Green function analysis of the STS in $H =$ 0 and is in contrasts to the finding of an intra-vortex PG $\Delta_{\mathrm{CO}}$ ($\sim$ 32 meV) \textgreater $\Delta_{\mathrm{SC}}$ ($\sim$ 23 meV) for $p =$ 0.16. Fourier transformation of the STS also shows energy-independent wave-vectors Q$_{\mathrm{CDW}}$ and Q$_{\mathrm{PDW}}$ associated with the charge- and pair-density waves, where Q$_{\mathrm{CDW}}$ decreases with $p$ and Q$_{\mathrm{PDW}}$ is $p$-independent.