Origin of the zero-bias conductance peaks observed ubiquitously in high-Tcsuperconductors

The midgap surface states predicted previously to exist on non-$\{n0m\}$ surfaces of $d_{x_a^2-x_b^2}$-wave superconductors (SC’s) can be extended to midgap interface states (MIS’s), which exist at almost all interfaces between grains of such SC’s of different principal axes orientations. They can give rise to a zero-bias conductance peak (ZBCP) in quasiparticle tunneling along any axis as shown in our model calculation. When the counterelectrode is a low-$T_c$ SC, its gap is shown to appear as a dip at the center of the (broadened) ZBCP. These and other results support the proposal that such MIS’s are responsible for most if not all of the ZBCP’s observed ubiquitously in tunneling experiments performed on high-$T_c$ SC’s.