Unprecedentedly large gap in HgBa$_2$Ca$_2$Cu$_3$O$_{8+δ}$ with the highest $T_c$ at ambient pressure

Abstract: In cuprate superconductors, the highest $T_c$ is possessed by the HgBa$<em>2$Ca$_2$Cu$_3$O$</em>{8+\delta}$ (Hg-1223) system at ambient pressure, but the reason remains elusive. Here we report the scanning tunneling measurements on the Hg-1223 single crystals with $T_c$ = 134 K. The observed gaps determined from the tunneling spectra (STS) can be categorized into two groups: the smaller gap $\Delta_1$ ranges from about 45 to 70 meV, while the larger gap $\Delta_2$ from about 65 to 98 meV. The STS was measured up to 200 K and the larger gap can persist well above $T_c$, indicating a pseudogap feature which may reflect the strong pairing energy in the inner layer. Interestingly, an extremely strong particle-hole asymmetry is observed in associating with a very robust coherence-like peak at the bias of the larger gap in the hole branch of the Bogoliubov dispersion. We argue that the observed asymmetry results may be from the interplay of a flat band (van Hove singularity) in the electronic spectrum and the large gap in the underdoped (inner) layer. A theoretical approach based on a trilayer model with an interlayer coupling can give a reasonable explanation. Our results provide deep insight into understanding the mechanism of superconductivity in cuprate superconductors.