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Pairing in the cuprate high-temperature superconductors and its origin remainamong the most enduring mysteries in condensed matter physics. Withcross-sectional scanning tunneling microscopy/ spectroscopy, we clearly revealthe spatial-dependence or inhomogeneity of the superconducting gap structure ofBi$_2$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. Bytunneling into the (100) plane of a Bi2212 single crystal and a YBCO film, weobserve both U-shaped tunneling spectra with extended flat zero-conductancebottoms, and V-shaped gap structures, in different regions of each sample. Onthe YBCO film, tunneling into a (110) surface only reveals a U-shaped gapwithout any zero-bias peak. Our analysis suggests that the U-shaped gap islikely a nodeless superconducting gap. The V-shaped gap has a very smallamplitude, and is likely proximity-induced by regions having the largerU-shaped gap.

chinese physics letters/chinese physics letters

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