Intrinsic Tunneling Spectra of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ near Optimal Doping

We report tunneling spectra of near optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ intrinsic Josephson junctions with area of 0.09 $μ$m$^2$, which avoid some fundamental difficulties in the previous tunneling experiments and allow a stable temperature-dependent measurement. A d-wave Eliashberg analysis shows that the spectrum at 4.2 K can be well fitted by considering electron couplings to a bosonic magnetic resonance mode and a broad high-energy continuum. Above $T_c$, the spectra show a clear pseudogap that persists up to 230 K, and a crossover can be seen indicating two different pseudogap phases existing above $T_c$. The intrinsic electron tunneling nature is discussed in the analysis.