  The zero-bias conductance peak in d-wave superconductors splits in an applied
magnetic field. In this work, the experimentally observed universal relation
delta ~ B0^(1/2) for strip-shaped samples is derived analytically based on the
long-ranged current contributions from Abrikosov vortices inside the sample.
The result is in full agreement with observed key properties, and features such
as hysteresis effects are made accessible. Employing a magnetically induced
additional order parameter is not necessary for the physical explanation of the
universal relation.
