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Microscopic theory of tunneling spectroscopy in Sr$_2$RuO$_4$

We study the surface Andreev bound state (ABS) of superconducting Sr$_2$RuO$_4$, which is a candidate material for the realization of the chiral $p$-wave superconducting state. In order to clarify the role of chiral edge modes as ABSs, the surface density of states and the tunneling conductance is calculated in the normal metal/Sr$_2$RuO$_4$ junction within the framework of recursive Green's function method, while taking into account the orbital degrees of freedom (including Spin-Orbit interactions) with realistic material parameters. In Sr$_2$RuO$_4$, there are two bands $α$ and $β$ originating from quasi-one-dimensional orbitals $d_{yz}$ and $d_{zx}$ and a two-dimensional band $γ$ originating from $d_{xy}$ orbital. We discuss about the contributions of various electronic bands to LDOS and the influence of atomic spin-orbit interaction (SOI). In the light of our calculations, quasi-one-dimensional model with dominant pair potentials in $α$ and $β$ bands is consistent with conductance measurements in Au/Sr$_{2}$RuO$_{4}$ junctions.