Abstract
We study the NIS tunneling spectroscopy in High Tc superconductors using Keldysh formalism (Non equilibrium Green's function) approach. The perturbation series in the tunneling Hamiltonian can be summed to all order. For simple s-wave superconductor it can reproduce the standard BTK results, especially in the ballistic regime where Andreev reflection is important. We apply the method to study the spin fluctuation effect observed in tunneling and ARPES experiments and its manifestation in the ballistic regime such that informations on the anomalous part of the Green's function can be revealed. The high Tc superconductor is modeled by an extended t-t'-J model and calculated with slave-boson mean field theory. The spin fluctuation effect is treated with RPA approximation. We show that in the tunneling limit the quasi-particle tunneling spectra shows peak/dip/hump structure in the [100] direction and the features scale with doping. The scaling of the dip position is different from that observed in tunneling spectra due to band structure effects. In the ballistic regime the dip/hump feature is relatively enhanced and coexist with the Andreev peak. Our approach can also resolve the ky dependence, which is integrated out in the usual tunneling spectra.