Polar and phase domain walls with conducting interfacial states in a Weyl semimetal MoTe2

Much of the dramatic growth in research on topological materials has focused on topologically protected surface states. While the domain walls of topological materials such as Weyl semimetals with broken inversion or time-reversal symmetry can provide a hunting ground for exploring topological interfacial states, such investigations have received little attention to date. Here, utilizing in-situ cryogenic transmission electron microscopy combined with first-principles calculations, we discover intriguing domain-wall structures in MoTe2, both between polar variants of the low-temperature(T) Weyl phase, and between this and the high-T higher-order topological phase. We demonstrate how polar domain walls can be manipulated with electron beams and show that phase domain walls tend to form superlattice-like structures along the c axis. Scanning tunneling microscopy indicates a possible signature of a conducting hinge state at phase domain walls. Our results open avenues for investigating topological interfacial states and unveiling multifunctional aspects of domain walls in topological materials.

Reply to the comments of reviewers. The new aspects and novelty of our results are clearly stated in our revised manuscript. All changes in the manuscript and supplementary information are highlighted in blue.

Reviewer #1
(1) "The authors report on a detailed electron microscopy and first-principles calculations study on the domain-wall structures in MoTe2. Given the recent interest in metals without inversion symmetry, particularly concerning Weyl physics and "ferroelectric metallicity," I find that the paper does not provide significantly new contributions to these fields to warrant publication in Nature Communications. First, the major claim is the discovery of "intriguing" DWs in the low-T phase of Weyl MoTe2, which is not too surprising given the fact that they are been proposed to tune the topological invariants, make our current work timely. However, he/she raised questions on the novelty of our work in a not-so-clear manner.
First, we fully agree that domains and DWs are required to appear by symmetry breaking -space inversion symmetry breaking in MoTe 2 . As stated in the introduction, the symmetry argument was one of the motivating factors of our work. Since Weyl semimetals must have broken space inversion or time reversal symmetry, they must have domains and domain walls. However, numerous papers on Weyl semimetals in highly prestigious journal In this work, we provide the first experimentally demonstration of phase domains/DWs as well as polar domains/DWs in polar Weyl semimetal MoTe 2 . The demonstration is not just finding domains/DWs, but also brings new surprisingly insights into unveiling the intriguing Weyl physics. For example, we found the presence of conducting hinge states in those phase DWs where phase DWs are the interfaces between "topologically distinct" phases: topologically nontrivial WSM and high-order topological phases (i.e. T d /1T' superlattice structures along the c axis). The presence of the topological hinge states makes the reported phase DWs unique and fundamentally important. In contrast to phase DWs, polar DWs are the interfaces between "topologically identical" phase. Since T d ↑ and T d ↓ polar phases are related by the space-inversion symmetry, Weyl points in these phases will have the same location in the energy and momentum space, but opposite chirality and are hence considered "topologically identical." One naturally expects quantum phenomena occurring due to the projection of opposite pairs of Weyl points and the resulting Fermi arc patterns at the T d ↑/T d ↓ polar DWs. For example, as we tune this interlayer displacements parameter, λ, opposite Weyl points move towards each other in the momentum space, and finally mutually annihilate at λ = 0, i.e. no Weyl points for the T 0 phase. A similar manipulation of Weyl point separation and Weyl point number by interlayer displacements has been discussed in WTe 2 31 . In addition, these polar domains and DWs can be still controllable. We emphasize that those discoveries provide new research opportunities not only on a large number of polar topological semimetals (e.g. hexagonal ABC compound such as LiZnBi, doped HgCr 2 (Se,Te) 4 and Ta 3 S 2 , Cd 2 As 3 , TaIrTe 4 , (W, Mo)(Te,P) 2 , family, (Ta, Nb)(As, P) and RAlGe family) but also on chiral and/or magnetic topological materials owing to the ubiquitous symmetry breaking nature. The broad impacts of our work in searching for "new topological interfacial states" of domains/DWs are highly anticipated.
On the other hand, he/she made the following unclear comparisons with Ca 3 Ru 2 O 7 , "this study is not so different from two previous studies on DWs in the polar metal Ca3Ru2O7." We, first, thank the reviewer for bringing out Ca 3 Ru 2 O 7 and two mentioned papers which are closely related to one of our core topics-polar semi(metal). Beyond just citing these papers, we highlight the achievements of these works in the introduction of our revised manuscript.
However, we emphasize that the origins of ferroelectricity between Ca 3 Ru 2 O 7 and MoTe 2 are fundamentally distinct. Ca 3 Ru 2 O 7 belongs to a hybrid "improper" ferroelectric (HIF) family with polarity as a secondary effect, whereas T d -MoTe 2 can be referred to a "proper" Next, we do not understand the meaning of these statements: "In particular, the junction in fig. 4  interesting." As we explained in the above reply, our work paves the way for gaining an even Solving the Weyl equation under the experimentally known DW geometry is highly desired." In page 8, "We next consider the T 0 , 1T' and Td phases from the view of symmetry. Figure 3d illustrates the MoTe 2 "family-tree" of the crystallographic group-subgroup relations 57 . The 1T' and T d phases reveal that a proper transition drives from the high-symmetric T 0 upon the Г 4 + or Г 2 zone center instabilities, which is consistent with the phonon dispersion shown in Supplementary Fig.   S7. A detailed symmetry analysis further indicates that Pm (space group #6) is a subgroup of both 1T' (P2 1 /m) and T d -MoTe 2 (Pmn2 1 ) and it is expected to link the 1T' and T d phases as shown in Fig. 3d. Space group Pm is, indeed, the symmetry to describe those superlattice-like structures appearing across transition ( Supplementary Fig. S4), providing a complete unified symmetry description of MoTe 2 ." In page 9-10, "First, notably, the T d polar phases of MoTe 2 host topologically non-trivial Weyl points 16,17,40,41 .
Since T d ↑ and T d ↓ polar phases are related by the space-inversion symmetry, Weyl points in these phases will have the same location in the energy and momentum space (but opposite chirality), and are hence considered "topologically identical." One naturally expects quantum  (1) I liked this paper quite a bit and I think it should be published. Just a few comments: Reply: We appreciate the reviewer's comments on our manuscript. Thank you!
(2) There were a few English related typos that should be fixed.
Reply: We sincerely thank the reviewer for this suggestion. The manuscript was significantly revised to reflect the reviewer's requests and read by a native English speaker.
(3) The authors seemed to be treating the Fe substitution quite trivially. Is this really the case?
where does the Fe go and how does it behave electronically? Some explanation for this should be given. After this, the paper seems to be in good shape.
Reply: Regarding the Fe effect, we used a nominal ratio of 30% Fe sources in the starting material prior to the flux growth. However, we estimated the real composition of Fe impurities in grown crystals to be only ~1.06% (359 Fe atoms in a 50×50 nm 2 shown below). Fe doping effect is observable in transport properties. As shown below, the polar phase transition Fe atoms in a 50×50 nm 2 square area).

Reviewer #3
( Reply: We appreciate the reviewer's nice summary on our manuscript. Thank you! (2) The discussion of the structure is hard to follow. In Figure 1, I might suggest adding "x" for inversion centers, so we can see where they are present and where they are broken.
Reply: We have now marked the inversion centers in the revised Figure 1. The readability has also been improved in the resubmitted manuscript. Thanks for pointing it out.
Revised Figure 1