Distinct multiple fermionic states in a single topological metal

Among the quantum materials that have recently gained interest are the topological insulators, wherein symmetry-protected surface states cross in reciprocal space, and the Dirac nodal-line semimetals, where bulk bands touch along a line in k-space. However, the existence of multiple fermion phases in a single material has not been verified yet. Using angle-resolved photoemission spectroscopy (ARPES) and first-principles electronic structure calculations, we systematically study the metallic material Hf2Te2P and discover properties, which are unique in a single topological quantum material. We experimentally observe weak topological insulator surface states and our calculations suggest additional strong topological insulator surface states. Our first-principles calculations reveal a one-dimensional Dirac crossing—the surface Dirac-node arc—along a high-symmetry direction which is confirmed by our ARPES measurements. This novel state originates from the surface bands of a weak topological insulator and is therefore distinct from the well-known Fermi arcs in semimetals.


Reviewer 2:
Hosen and co-authors present an ARPES and ab initio calculation study of Hf2Te2P. They observe multiple Dirac point nodes and a Dirac node arc, and a combination of both theory and experiment is used to argue for the coexistence of both strong and weak topological surface states. This work is an important development in the field. The richness of topological surface states observed and predicted in this one material, as well as the capability of this material to yield very sharp ARPES spectra, will prompt many followup studies. I feel that the authors have done an adequate job responding to my earlier referee report, and I recommend this paper for publication in Nature Communications.
Authors: We would like the thank the reviewer for his/her time and recommending our manuscript for publication in Nature Communications. Authors: We wish to thank the reviewer for this comment. We have modified our Fig. 5 to represent our data better. We respect the reviewer's opinion; however, we think that it might help the reader in some extent to visualize our data and wish to keep this figure. The new Fig. 5 looks as follows:

Reviewer 3:
The authors have improved and clarified their manuscript in response to the referee reports. However, the definition and explanation of the Dirac arc is still not clear. Since it is one of the main observations of the paper, it must be completely clear. I can envision two possibilities: 1. The Dirac arc is actually a Dirac point with a near-zero dispersion in one direction. This requires no symmetry. This has been observed in Ru2Sn3 (see Gibson, et al, Scientific Reports vol. 4, Article number: 5168 (2014)).
2. The Dirac arc is a two-fold degenerate set of bands that remain two-fold degenerate along some line/path in the surface Brillioun zone. The latter possibility requires symmetry to protect, which is referred to as "in-plane time reversal symmetry" in Ref. 33. The authors refer to this symmetry but do not explain why their system possesses it. I believe this could arise the product of time reversal and a mirror symmetry, but if the authors rely on this symmetry, the need to explain what it is and why their system has it.
The authors must clarify which of these possibilities (or perhaps something else) describes their Dirac arc.
Authors: We thank the reviewer for appreciating our efforts to improve the manuscript. To address the point of the reviewer regarding the origin of the observed Dirac node arc we have added a further text part in the Discussion section. First, in the introduction a few words were added to explain that the Dirac node arc is a line segment along which there is a Dirac crossing in one direction. Second, the Dirac arc that we discuss is different from the situation discussed for Ru 2 Sn 3 by Gibson et al (Sci. Rep. 4, 5168 (2014)). In that paper there is a single Dirac crossing at the Gamma point and a gapped surface state at other momenta along a high-symmetry line. Our observed Dirac node arc consists of ungapped Dirac crossings along a line in momentum space. Moreover, neither the actual Dirac crossing is observed (as it is above EF) nor the top of the gapped of the gapped Dirac cones. In our work we observe both experimentally and theoretically gapless Dirac crossings along a line in the surface Brillouin zone.
The situation at hand in Hf 2 Te 2 P is more closely described by the 2nd possibility mentioned by the reviewer. We have added a further analysis to the Discussion section, which follows up on this aspect. We had already mentioned previously the "in-plane time-reversal symmetry" in relation to the work of Ref. 33; in the revised version we now clarify its origin in more detail.
I would like to reiterate from my previous report that the experimental data and DFT results are very nice.
Authors: We would like to thank the reviewer for finding our experimental data and calculated results very nice.