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.Comment: 4 pages, 4 figure