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.

We develop an effective extended Hubbard model to describe the low-energy electronic properties of the twisted bilayer graphene. By using the Bloch states in the effective continuum model and with the aid of the maximally localized algorithm, we construct the Wannier orbitals and obtain an effective tight-binding model on the emergent honeycomb lattice. We found the Wannier state takes a peculiar three-peak form in which the amplitude maxima are located at the triangle corners surrounding the center. We estimate the direct Coulomb interaction and the exchange interaction between the Wannier states. At the filling of two electrons per super cell, in particular, we find an unexpected coincidence in the direct Coulomb energy between a charge-ordered state and a homogeneous state, which would possibly lead to an unconventional many-body state.

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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.

Mazin and Singh argue that the observed peaks in the Fourier transformed spectroscopic maps in Fe(Se,Te) (1) may not be related to the quasi-particle interference (QPI) but would be attributed to the Bragg peaks associated with underlying chalcogen lattice and surface-induced spin-density wave (SDW) (2). They point out that: (i) the observed peaks at q 2 and q 3 are too sharp to be ascribed to the QPI, (ii) q 3 is located at the Bragg point of the chalcogen lattice, (iii) if SDW is induced at the surface and if such an SDW triggers a surface reconstruction, Bragg peak would appear at q 2 , (iv) magnetic field would suppress both superconductivity and SDW, giving rise to the enhancement of the Bragg peak at q 3 at the superconducting (SC) gap energy and suppression of the Bragg peak at q 2 , respectively. We show that these arguments are not relevant in the present case.First, the observed peaks which have been discussed in Ref. 1 are not as sharp as Bragg peak. It is true that q 3 is located at the Bragg point of the chalcogen lattice but the QPI signal is distinct from the lattice Bragg peak. In Fig. 1, we show linecuts from the Fourier-transformed conductance-ratio map Z(q, E), in which QPI peaks appear (1), along the line which passes both q 2 and q 3 . Linecut from the Fourier-transformed topographic image (Fig. 1A of Ref. 1) is also shown to give an idea of the sharpness of the Bragg peak. In the absence of magnetic field (black lines), both peaks at q 2 and q 3 in Z(q, E) are much broader than the Bragg peak. Bragg-like sharp feature emerges at q 3 at high energies but near the SC-gap energy (1 ~ 3 meV), only broad feature dominates. Indeed, the widths of the peaks are comparable to 20 % of the Brillouin zone dimension of 2π/a where a is the inter-chalcogen distance (an arrow in Fig. 1A), as suggested by Mazin and Singh (2).When magnetic field is applied (red lines in Fig. 1A), Bragg-like sharp feature grows at q 3 . Note that the field enhancement of this Bragg-like peak persists well above the SC-gap energy, which clearly suggests that the enhancement can not be explained by the suppression of the SC quasi-particle peak alone. On the contrary, pre-existing broad peak is strongly enhanced only near the SC-gap energy, suggesting that it is related to superconductivity. Namely, features at q 3 consist of two components, a sharp Bragg-like peak and a broad peak. What we ascribed to the QPI peak in Ref. 1 is the latter.Surface reconstruction triggered by surface-induced SDW is an interesting proposal. However, there is no evidence that such a reconstruction or SDW are really induced at the