Split of zero-bias conductance peak in normal-metal / d-wave superconductor junctions

Effects of impurity scatterings on the conductance in normal-metal / $d$ wave superconductor junctions are discussed by using the single-site approximation. So far, the split of the zero-bias conductance peak has been believed to be an evidence of the broken time reversal symmetry states at the surface of high-$T_c$ superconductors. In this paper, however, it is shown that the impurity scattering near the interface also causes the split of the zero-bias conductance peak. Typical conductance spectra observed in experiments at finite temperatures and under external magnetic fields are explained well by the present theory.