Surface states and tunneling spectroscopy of high-Tcsuperconductors

Recent studies of high- T_csuperconductors have clarified new aspects of tunneling spectroscopy. The unconventional pairing states, i.e. d-wave symmetry in these materials have been established through various measurements. Differently from isotropic s-wave superconductors, d-wave pairing states have an internal phase of the pair potential. The internal phase modifies the surface states due to the interference effect of the quasiparticles. Along these lines, a novel formula of tunneling spectroscopy has been presented that fully takes into account of the anisotropy of the pair potential. The most essential difference of this formula from conventional ones is that it suggests the phase-sensitive capability of tunneling spectroscopy. The formula suggests that the symmetry of the pair potential is determined by the orientational dependence measurements of tunneling spectroscopy. Along these lines, several experiments have been performed on high-T_c superconductors. The observation of the zero-bias conductance peaks (ZBCP) on Y Ba₂Cu₃O_7 − δstrongly suggests the d_{x² − y²}-wave pairing states of hole-doped high-T_c superconductors. On the other hand, the absence of ZBCP on (electron-doped)Nd_1.85Ce_0.15CuO_4 − δindicates that the pair potential of this material is a nodeless state. In this paper, recent developments of tunneling spectroscopy for anisotropic superconductors are reviewed both on theoretical and experimental aspects.