The appearance of the gap nodes intersecting the Fermi surface in Fig. 2(d) of our Letter was due to an error in the final stage of the calculation, i.e., the unitary transformation from the orbital representation (in which we have solved the Eliashberg equation) to the band representation. The correct Fig. 2 is shown below, where the main changes appear in (d), while (a),(b) are the same, and (c),(e) remain essentially unchanged as far as the features on the Fermi surface are concerned. The diagonal elements of the gap in the band representation is fully open on the Fermi surface [schematically the upper panel of Fig. 2(b)], and the off-diagonal elements are less important in this sense. However, the main conclusions of the original Letter related to this figure do remain unaltered in the following sense. (i) The magnitude of the gap along the Fermi surface still varies significantly. (ii) Regarding the way in which the gap nodes intersecting the Fermi surface appear depending on the parameter values, we do find that the nodes in the s-wave gap nearly touch or intersect the Fermi surface for band fillings beyond 6.3, or also when we adopt a band structure obtained for the theoretically optimized lattice parameters. This is consistent with the result recently obtained by Graser et al., who have adopted a five-band model obtained by fitting a band structure of the theoretically optimized lattice structure [1]. In these cases, d wave closely competes with or dominates over s wave. This can be naturally understood as a consequence of the coexistence of (, =2) and (, 0) spin fluctuations as asserted in the original Letter.

No abstract

No abstract

Recent studies on high-T c 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-T c Josephson junctions, which detect π -phase shift between the aand b-axis directions and fractional flux quanta. These results give convincing evidence for d-wave symmetry in high-T c 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 zeroenergy 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.

A topological superconductor (TSC) is characterized by the topologically protected gapless surface state that is essentially an Andreev bound state consisting of Majorana fermions. While a TSC has not yet been discovered, the doped topological insulator Cu(x)Bi(2)Se(3), which superconducts below ∼3 K, has been predicted to possess a topological superconducting state. We report that the point-contact spectra on the cleaved surface of superconducting Cu(x)Bi(2)Se(3) present a zero-bias conductance peak (ZBCP) which signifies unconventional superconductivity. Theoretical considerations of all possible superconducting states help us conclude that this ZBCP is due to Majorana fermions and gives evidence for a topological superconductivity in Cu(x)Bi(2)Se(3). In addition, we found an unusual pseudogap that develops below ∼20 K and coexists with the topological superconducting state.