Effect of the BCS supercurrent on the spontaneous surface flow in unconventional superconductivity with broken time-reversal-symmetry

A spontaneous surface current state is investigated in unconventional superconductivity with broken time-reversal-symmetry. It is shown that a BCS supercurrent lowers the energy of the system in this state. The lowest state has zero total current; it satisfies the Bloch theorem which states absence of the total current in any stable state with no external field. We also show that the magnitude and the direction of the spontaneous current are strongly affected by the detail of the Fermi surface. We explain this effect in connection with a low-energy bound state near the surface originating from the anisotropy of the order parameter.