Discovery of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hat{\boldsymbol{C}}}_2$$\end{document}C^2 rotation anomaly in topological crystalline insulator SrPb

Topological crystalline insulators (TCIs) are insulating electronic states with nontrivial topology protected by crystalline symmetries. Recently, theory has proposed new classes of TCIs protected by rotation symmetries \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat C_n$$\end{document}C^n, which have surface rotation anomaly evading the fermion doubling theorem, i.e., n instead of 2n Dirac cones on the surface preserving the rotation symmetry. Here, we report the first realization of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat C_2$$\end{document}C^2 rotation anomaly in a binary compound SrPb. Our first-principles calculations reveal two massless Dirac fermions protected by the combination of time-reversal symmetry \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat T$$\end{document}T^ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat C_{2y}$$\end{document}C^2y on the (010) surface. Using angle-resolved photoemission spectroscopy, we identify two Dirac surface states inside the bulk band gap of SrPb, confirming the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat C_2$$\end{document}C^2 rotation anomaly in the new classes of TCIs. The findings enrich the classification of topological phases, which pave the way for exploring exotic behavior of the new classes of TCIs.

This paper presents both first-principle calculations and ARPES that SrPb is a topological crystalline insulator protected by time-reversal symmetry and ̂2 rotational symmetry. Based on the results of firstprinciples calculations predicting Dirac cone surface states satisfying ̂2 rotation symmetry in the 2D BZ for (010) surfaces, the authors observe topological Dirac bands satisfying ̂2 rotation symmetry in the Γ ̅ − ̅ line by ARPES. In particular, the ARPES data provide a detailed assignment of the bulk/surface bands through a 3D momentum-resolved observation using VUV incident photon energy dependence, and the data at 200 K clearly extract the characteristics of the Dirac dispersion, which is globally convincing.
I recognize that this manuscript provides new experimental finding in topological materials, which can be definitely a solid piece of new information in this field. On the other hand, we would like to make the following suggestions for a better manuscript.
General comment I personally think impact of this finding is less clear, at least with current written version since plenty of arguments exist on symmetry protection of topological states in recent topological materials search.
Discussion on novel macroscopic property/functionality in SrPb is required to put authors finding significant. Probably related to this, the authors have discussed tunable band structure in SrPb as "If the mirror symmetry is broken while the rotational symmetry is kept by a particular lattice distortion, the surface Dirac points will move to the generic momenta away from the Γ ̅ − ̅ line". In Sn-Te based compound, tunable band nature related to characteristic crystalline symmetry has been already demonstrated in experiments [for example, PRB 87, 155105 (2013)].
Another comments 1. To make findings further solid, spin-polarized arpes experiment is preferred.
2. Is there any particular reason why the authors use 2D curvature did not choose the 2nd. derivative commonly used in conventional method? While this is minor comment, reader may have similar question.

To Referee #1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This work reports the experimental discovery of a C 2 protected TCI, SrPb. This TCI is characterized by two surface Dirac points, which cannot be realized in a standalone 2D system. Though such a C 2 -TCI was proposed in the Bi (ref.29), it was not confirmed in the experiment so far. The present work is the first to discover C 2 -TCI. Thus, I believe this will be an important work in studying new TCI materials. We are very grateful to Referee #1 for his/her high evaluation and recommendation of our work. Following Referee #1's suggestions, we have conducted slab calculations with different terminations at the (010) surface. We consider two possible cleavage positions, as indicated in Fig. R1a,b, which produce two kinds of terminations with different dangling bonds. For termination A, the cleaving breaks one chemical bond for each Sr or Pb atom, while for termination B, the cleaving breaks two chemical bonds for each Sr or Pb atom. R1d are inconsistent. Therefore, we infer that the real cleavage surface should be termination A. We thank again for Referee #1's valuable suggestions.
We have added the calculated results for termination A to Fig. 4h   We are very grateful to Referee #2 for his/her affirmation of our work and valuable suggestions to improve our manuscript. In the previous version, we have proposed that the band structure of SrPb can be tuned by breaking the mirror symmetry, for which the surface Dirac points move away from the Γ − line. As exemplified by Referee #2, tuneable band nature has been already demonstrated in Sn-Te based compounds when the mirror symmetry is preserved, for which the surface Dirac points move along the Γ − line. We have incorporated Referee #2's suggestion into the discussion on page 8. We thank again for Referee #2's valuable suggestions.
Another comments 1. To make findings further solid, spin-polarized ARPES experiment is preferred.
We agree that it is desirable to measure the spin polarization of surface bands by means of spin-resolved ARPES. To observe the surface states of SrPb, which lie around the Fermi level, ARPES measurements have to be performed at high temperatures. We found that the lifetime of the electronic states of SrPb was short at high temperatures. Since spin-resolved spectra have much lower signals compared with spin-integrated spectra, it will take much longer time in spin-resolved ARPES measurements. The lifetime is not enough to collect high signal-to-noise ratio data to clarify the spin polarization of surface bands. We hope that the Referee understands the difficulty.