The Importance of Self-Consistency in Determining Interface Properties of SIN and DIN Structures

Abstract We develop a method to solve the Bogoliubov–de Gennes equation for superconductors self-consistently, using the recursion method. The method allows the pairing interaction to be either local or nonlocal corresponding to s-and d-wave superconductivity, respectively. Using this method, we examine the properties of various SIN and DIN interfaces. In particular, we self-consistently calculate the spatially varying density of states and the superconducting order parameter. We see that changing the strength of the insulating barrier at the interface, does not, in the case of an s-wave superconductor, dramatically change the low-energy local density of states in the superconducting region near the interface. This is in stark contrast to what we see in the case of a DIN interface where the local particle density of states is changed dramatically. Hence we deduce that in calculating such properties as the conductance of SIN and DIN structures it is far more important to carry out self-consistent calculations in the d-wave case.