Tunneling conductance of SIN junctions with different gap symmetries and non-magnetic impurities by direct solution of real-axis Eliashberg equations

Abstract

We theoretically investigate the effect of various symmetries of the superconducting order parameter Δ( ω) on the normalized tunneling conductance of SIN junctions (with no spatial variation of the order parameter in the S electrode) by directly solving the real-axis Eliashberg equations (EEs) for a half-filled infinite band, with the simplifying assumption μ *=0. We analyze six different symmetries of the order parameter: s, d, s+id, s+d, extended s and anisotropic s, by assuming that the spectral function α 2F(Ω) contains an isotropic part α 2F(Ω) is and an anisotropic one, α 2F(Ω) an , such that α 2F(Ω) an =gα 2F(Ω) is , where g is a constant. We compare the resulting conductance curves at T=2 K to those obtained by analytical continuation of the imaginary-axis solution of the EEs, and we show that the agreement is not equally good for all symmetries. Then, we discuss the effect of non-magnetic impurities on the theoretical tunneling conductance curves at T=4 K for all the symmetries considered. Finally, as an example, we apply our calculations to the case of optimally-doped high- T c superconductors. Surprisingly, although the possibility of explaining the very complex phenomenology of HTSC is probably beyond the limits of the Eliashberg theory, the comparison of the theoretical curves calculated at T=4 K with the experimental ones obtained in various optimally-doped copper-oxides gives fairly good results.