Second-quantization description of Andreev reflection and the relation to quasiparticle wave approaches

A second-quantization description is given for Andreev reflection. We introduce an effective interaction Hamiltonian for the interface between the superconductor and the normal metal, which enables us to treat transmission and reflection consistently. The interaction Hamiltonian couples quasiparticles in the normal region (N) and Bogoliubov quasiparticles in the superconducting region (S). It facilitates the description of the elementary excitations of the SN-coupled system, that are generated by Andreev reflections. Moreover, it naturally brings us to the description where the effect of macroscopic quantum fluctuations of the superconducting state on Andreev reflections is considered. This provides a powerful tool for investigating of the mesoscopic aspects of Andreev reflection.