Interplay between Superconducting and Pseudogap States Revealed by Heating-Compensated Interlayer Tunneling Spectroscopy on Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$

The heating-compensated interlayer tunneling spectroscopy is performed on stacks of Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ intrinsic junctions. The high-accuracy spectra without the local heating, for varying temperatures and magnetic fields, reveal that the spectral weight forming the superconducting coherence peak is mainly contributed from the dip position of the hump structure of the pseudogap state. The observed U-shaped subgap structure is consistent with the weighted antinodal tunneling between Cu-O double layers in a junction as suggested in Ref. [17].