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.

A dome-shaped superconducting region appears in the phase diagrams of many unconventional superconductors. In doped band insulators, however, reaching optimal superconductivity by the fine-tuning of carriers has seldom been seen. We report the observation of a superconducting dome in the temperature-carrier density phase diagram of MoS(2), an archetypal band insulator. By quasi-continuous electrostatic carrier doping achieved through a combination of liquid and solid gating, we revealed a large enhancement in the transition temperature T(c) occurring at optimal doping in the chemically inaccessible low-carrier density regime. This observation indicates that the superconducting dome may arise even in doped band insulators.

There has been increasing interest in phenomena emerging from relativistic electrons in a solid, which have a potential impact on spintronics and magnetoelectrics. One example is the Rashba effect, which lifts the electron-spin degeneracy as a consequence of spin-orbit interaction under broken inversion symmetry. A high-energy-scale Rashba spin splitting is highly desirable for enhancing the coupling between electron spins and electricity relevant for spintronic functions. Here we describe the finding of a huge spin-orbit interaction effect in a polar semiconductor composed of heavy elements, BiTeI, where the bulk carriers are ruled by large Rashba-like spin splitting. The band splitting and its spin polarization obtained by spin- and angle-resolved photoemission spectroscopy are well in accord with relativistic first-principles calculations, confirming that the spin splitting is indeed derived from bulk atomic configurations. Together with the feasibility of carrier-doping control, the giant-Rashba semiconductor BiTeI possesses excellent potential for application to various spin-dependent electronic functions.