Surface charging in d-wave superconductors

Near surfaces d-wave superconductivity is suppressed and competing order parameters can emerge. Of particular interest is the formation of antiferromagnetism which can be accompanied by a charging of the surface similar to the vortex case. We analyze this scenario for different surface orientations by solving the Bogoliubov-de Gennes equations for a model Hamiltonian with competing antiferromagnetic and d-wave superconducting interactions. In special limits analytical solutions are possible and help to identify the role of Andreev bound states. Finally, we discuss the implications of an angle-dependent surface charge for the critical current through interfaces.