Recent studies on high-Tc superconductors
have aroused new interest in tunnelling effects in
unconventional superconductors. Unlike in conventional
s-wave superconductors, the d-wave pairing state in these
materials has an internal phase of the pair potential. The
internal phase as a function of the wavevector of the Cooper
pairs has a large influence on the electric properties of
tunnelling junctions. Important effects of the internal phase on
the Josephson current were first predicted theoretically. The
idea has been established through several experiments using
high-Tc Josephson junctions, which detect π-phase
shift between the a- and b-axis directions and fractional
flux quanta. These results give convincing evidence
for d-wave symmetry in high-Tc superconductors. In
addition, the existence of new interference effects in
the quasiparticle states near surfaces and boundaries has been
suggested through theoretical predictions. Experimentally, a
large number of tunnelling spectroscopy data showed zero-bias
conductance peaks (ZBCPs), the origin of which cannot be
explained in terms of the classical concept that a tunnelling
conductance spectrum is a phase-insensitive probe of the
electronic states. It is clarified theoretically that the
observed ZBCPs reflect the formation of zero-energy states on
the surface due to the π-phase shift of internal phase in
the d-wave pairing symmetry. The formulation developed for
tunnelling spectroscopy suggests that tunnelling spectroscopy is
essentially phase sensitive. In addition, the formation of the
bound states has been shown to have a serious influence on the
electrical properties of Josephson junctions. Several anomalous
properties including strong enhancement of the Josephson current
in the low-temperature region have been predicted theoretically.
In this report, recent developments in tunnelling effects on
surface bound states in unconventional superconductors are
reviewed.