Nonlinear magnetic field dependence of the conductance in d-wave NIS tunnel junctions

The ab-plane NIS-tunnelling conductance in d-wave superconductors shows a zero-bias conductance peak which is predicted to split in a magnetic field. In a pure d-wave superconductor the splitting is linear for fields small on the scale of the thermodynamic critical field. The field dependence is shown to be nonlinear, even at low fields, in the vicinity of a surface phase transition into a local time-reversal symmetry breaking state. The field evolution of the conductance is sensitive to temperature, doping, and the symmetry of the sub-dominant pairing channel.