Analyzing scanning tunneling spectroscopy for Fe-based superconductor Ba$_{1-x}$K$_x$Fe$_2$As$_2$ and extracting $s$-wave density of states

We extract the density of states (DOS) from the scanning tunneling spectroscopy data for Ba$_{1-x}$K$_x$Fe$_2$As$_2$ superconductor. The obtained sample DOS is composed of two ordinary $s$-wave types from the band at $\Gamma$ point and a linear-like DOS within the $s$-wave gap from the band at M point in the Brillouin zone, and is consistent with the corresponding data from angle-resolved photoemission spectroscopy. We clarify that the major peak of the tunneling conductance is not related to the DOS but is rather the effect of nonequilibrium coherent tunneling including all coherent spins in the tip and sample.