Tunneling into Current-Carrying Surface States of High-TcSuperconductors

Abstract

Theoretical results for the $\mathrm{ab}$-plane tunneling conductance in the $d$-wave model for high- $T_c$ superconductors are presented. The $d$-wave model predicts surface bound states below the maximum gap. A subdominant 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 bound state spectrum, leading to a splitting of the ZBCP that is linear in $H$ at low fields and saturates at a pair breaking critical field of order $H_c^{*}\simeq 3\mathrm{T}$.