Unusual Quasiparticle Tunneling in High-$T_c$ Cuprate Superconductors: Evidence for the BCS and Polaronic Multi-Gap Effects on Tunneling Spectra

We propose a model of quasiparticle tunneling across the high-$T_c$ superconductor-insulator-normal metal junction based on the different mechanisms for tunneling of electrons at positive bias and dissociating polaronic Cooper pairs and large polarons at negative bias, and the gap inhomogeneity (i.e., multi-gap) picture. We show that the main features of the tunneling spectra such as low-bias U- and V-shaped features, asymmetry and high-bias dip-hump features, their temperature and doping dependences, and shoulders inside the conductance peaks observed in high-$T_c$ cuprates arise naturally from the model. The experimental tunneling spectra of $\mathrm{B}{\mathrm{a}}_2\mathrm{S}{\mathrm{r}}_2\mathrm{C}\mathrm{a}\mathrm{C}{\mathrm{u}}_2{\mathrm{O}}_{8+\delta }$ are fitted quite well by taking into account the distribution of BCS and polaronic gap values.