Alternate cleavage structure and electronic inhomogeneity in Ca-doped YBa$_2$Cu$_3$O$_{7-\delta}$

Abstract

YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) has favorable macroscopic superconducting properties of $T_\mathrm{c}$ up to 93 K and $H_{c2}$ up to 150 T. However, its nanoscale electronic structure remains mysterious because bulk-like electronic properties are not preserved near the surface of cleaved samples for easy access by local or surface-sensitive probes. It has been hypothesized that Ca-doping at the Y site could induce an alternate cleavage plane that mitigates this issue. We use scanning tunneling microscopy (STM) to study both Ca-free and 10% Ca-doped YBCO, and find that the Ca-doped samples do indeed cleave on an alternate plane, yielding a spatially-disordered partial (Y,Ca) layer. Our density functional theory calculations support the increased likelihood of this new cleavage plane in Ca-doped YBCO. On this surface, we image a superconducting gap with average value 24 $\pm$ 3 meV and characteristic length scale 1-2 nm, similar to Bi-based high-$T_\mathrm{c}$ cuprates, but the first map of gap inhomogeneity in the YBCO family.