Abstract: Using the extended Blonder--Tinkham--Klapwijk (BTK) theory, this paper calculates the tunnelling conductance in quantum wire/insulator/d_x² -y² + id_xy mixed wave superconductor ( q / I /d_x² -y² + id_xy) junctions. That is different from the case in d- and p-wave superconductor junctions. When the angle $\alpha$  between a-axis of the d_x² -y² wave superconductor and the interface normal is $\pi$ /4, there follows a rather distinctive tunnelling conductance. The zero-bias conductance peak (ZBCP) may or may not appear in the tunnelling conductance. Both the interface potential z and the quasi-particle lifetime factor $\varGamma$ are smaller, there is no ZBCP. Otherwise, the ZBCP will appear. The position of bias conductance peak (BCP) depends strongly on the amplitude ratio of two components for d_x² -y² + id_xy mixed wave. The low and narrow ZBCP may coexist with the BCP in the tunnelling conductance. Using those features in the tunnelling conductance of q / I /d_x² -y² + id_xy junctions, it can distinguish d_x² -y² + id_xy mixed wave superconductor from d- and p-wave one.

Key words: quantum wire, d_{x² -y²} + id_xy mixed wave superconductor, tunneling conductance, quasi-particle lifetime