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.

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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.

For a newly discovered iron-based high Tc superconductor LaFeAsO1−xFx, we have constructed a minimal model, where inclusion of all the five Fe d bands is found to be necessary. Random-phase approximation is applied to the model to investigate the origin of superconductivity. We conclude that the multiple spin fluctuation modes arising from the nesting across the disconnected Fermi surfaces realize an extended s-wave pairing, while d-wave pairing can also be another candidate.

Journal of the Physical Society of Japan FULL PAPERSSuperconductivity is a phenomenon where the macroscopic quantum coherence appears due to the pairing of electrons. This offers a fascinating arena to study the physics of symmetry breaking, i.e., broken gauge symmetry. However, the important symmetries in superconductors are not only the gauge invariance. Especially, the symmetry properties of the pairing, i.e., the parity and spin-singlet / spin-triplet, determine the physical properties of the superconducting state. Recently it has been recognized that there is the important third symmetry of the pair amplitude, i.e., even or odd parity with respect to the frequency. The conventional uniform superconducting states correspond to the even-frequency pairing, but the recent finding is that the odd-frequency pair amplitude arises in the spatially non-uniform situation quite ubiquitously. Especially, this is the case in the Andreev bound state (ABS) appearing at the surface/interface of the sample.The other important recent development is on the nontrivial topological aspects of superconductors. As the band insulators are classified by topological indices into (i) conventional insulator, (ii) quantum Hall insulator, and (iii) topological insulator, also are the gapped superconductors. The influence of the nontrivial topology of the bulk states appears as the edge or surface of the sample, i.e., bulk-edge correspondence.In the superconductors, this leads to the formation of zero energy ABS (ZEABS). Therefore, the ABSs at the surface/interface of the superconductors are the place where the symmetry and topology meet each other which offer the stage of rich physics. In this review, we discuss the physics of ABS from the viewpoint of the odd-frequency pairing, the topological bulk-edge correspondence, and the interplay of these two issues.It is described how the symmetry of the pairing and topological indices determine the absence/presence of the ZEABS, its energy dispersion, and properties as the Majorana fermions. Various related issues such as the Helium 3, transport of Majorana fermions, and tunneling spectroscopies are also briefly discussed.

We study theoretically the transport properties of a normal metal (N)/ferromagnet insulator (FI)/superconductor (S) junction and a S/FI/S junction formed on the surface of a three-dimensional topological insulator, where the chiral Majorana mode exists at the FI/S interface. We find the chiral Majorana mode generated in N/FI/S and S/FI/S junctions is very sensitively controlled by the direction of the magnetization m in the FI region. In particular, the current-phase relation of the Josephson current in S/FI/S junctions has a phase shift of neither 0 nor pi that can be tuned continuously by the component of m perpendicular to the interface.