Tunneling into Current-Carrying Surface States of High T_c Superconductors

Theoretical results for the ab-plane tunneling conductance in the d-wave model for high Tc superconductors are presented. The d-wave model predicts surface bound states below the maximum gap. A sub-dominant order parameter, stabilized by the surface, leads to a splitting of the zero-bias conductance peak (ZBCP) in zero external field and to spontaneous surface currents. In a magnetic field screening currents shift the quasiparticle bound state spectrum and lead to a voltage splitting of the ZBCP that is linear in H at low fields, and saturates at a pairbreaking critical field of order 3 Tesla. Comparisons with recent experimental results on Cu/YBCO junctions are presented.