Possible Nodeless Superconducting Gaps in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ and YBa$_2$Cu$_3$O$_{7-x}$ Revealed by Cross-Sectional Scanning Tunneling Spectroscopy
1State Key Laboratory of Surface Physics, Department of Physics, and Advanced Materials Laboratory, Fudan University, Shanghai 200433 2Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093
Pairing in the cuprate high-temperature superconductors and its origin remain among the most enduring mysteries in condensed matter physics. With cross-sectional scanning tunneling microscopy/spectroscopy, we clearly reveal the spatial-dependence or inhomogeneity of the superconducting gap structure of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212) and YBa$_2$Cu$_3$O$_{7-x}$ (YBCO) along their $c$-axes on a scale shorter than the interlayer spacing. By tunneling into the (100) plane of a Bi2212 single crystal and a YBCO film, we observe both U-shaped tunneling spectra with extended flat zero-conductance bottoms, and V-shaped gap structures, in different regions of each sample. On the YBCO film, tunneling into a (110) surface only reveals a U-shaped gap without any zero-bias peak. Our analysis suggests that the U-shaped gap is likely a nodeless superconducting gap. The V-shaped gap has a very small amplitude, and is likely proximity-induced by regions having the larger U-shaped gap.