Oscillating edge states in one-dimensional MoS2 nanowires

Reducing the dimensionality of transition metal dichalcogenides to one dimension opens it to structural and electronic modulation related to charge density wave and quantum correlation effects arising from edge states. The greater flexibility of a molecular scale nanowire allows a strain-imposing substrate to exert structural and electronic modulation on it, leading to an interplay between the curvature-induced influences and intrinsic ground-state topology. Herein, the templated growth of MoS2 nanowire arrays consisting of the smallest stoichiometric MoS2 building blocks is investigated using scanning tunnelling microscopy and non-contact atomic force microscopy. Our results show that lattice strain imposed on a nanowire causes the energy of the edge states to oscillate periodically along its length in phase with the period of the substrate topographical modulation. This periodic oscillation vanishes when individual MoS2 nanowires join to form a wider nanoribbon, revealing that the strain-induced modulation depends on in-plane rigidity, which increases with system size.

Point-by-point response to "Article ID: NCOMMS-16-12106-T, Title: Oscillating Edge States in One-dimensional MoS 2 Nanowires" Reviewers' comments: Reviewer #1 (Remarks to the Author): The manuscript reports the preparation of MoS2 nanowire and nanoribbon on a vicinal Au substrate. The strain induced morphology corrugation and associated edge state modulation were revealed very clearly by using STM/STS combined with first principles calculations. The data and analysis are clean and convincing. However I feel that the reported result is conceptually not new, and not so important to stimulate a general interest. Edge state is commonly observed on surface steps and 1D structures, and strain modulation due to lattice mismatch is very natural. It is not surprising to observe such phenomena. The authors claim that such modulation along 1D wire may tune the 1D transport property, which is of course interesting if the authors can demonstrate it. But that is totally another story. For the present work, I feel it more suitable for a more specific journal such as physical review B.

Response to first referee's comments:
Although edge state are commonly observed on surface steps and 1D structure, this is the first time that edge states from a single molecular scale MoS 2 wire with extremely narrow width (0.6 nm width) are studied experimentally. We showed convincingly how such ultrathin nanowires can be prepared with a high coverage on Au surface. Due to the extreme width of such nanowires, the property of the MoS 2 nanowire is dictated by its edge states. There are several key features which distinguishes the current work from any previous reports (if any) 1. The oscillation of edge states has not been reported thus far. In fact this is true not just for MoS 2 , but for any form of semiconductor or metallic nanowires. Our work reported such oscillation for the first time in an ultra-narrow nanowire.
2. The dependence of the conductance oscillation of this edge state on system size has never been systematically studied and verified, and we did so in this work. We showed that this oscillation is active only when the system size is reduced to a single molecular wire.
3. We have obtained direct atomic visualization of how 2 adjacent nanowires fuse to form 1 twin wire.
Recently, there are lots of interests on the edge states of graphene ribbon (GNR) and TMDs because of their influence on the electronic and magnetic properties of 1-D system 1-2 . There have been many theoretical studies but not enough experimental verifications on whether such single wires can be grown. In this work, we present an atom-resolved STM/AFM and STS study of MoS 2 nanowires, which helps us to understand the relationship between electronic structure and local atomic geometry. Our results are also important for theoretical studies of TMDS nanoribbon structures, since no ultra-narrow MoS 2 nanowires were ever grown by a bottom up method before. It has important relevance to 1-D materials as a whole, especially when reduced to very fine dimensions, where edge states dominate the properties.
Reviewer #2 (Remarks to the Author): The manuscript reports the synthesis and characterization of different new MoS2 nanowires (around 200 nm long) grown by molecular beam epitaxy using gold substrates. The nanowires/nonoribbons grow at the steps of Au (755) surface. In particular, the thinnest nanowire exhibits a structural and electronic modulation due to the edge interaction with the Au substrate. As the nanowires get wider, the modulation vanishes since the interaction with the substrate changes. Different characterization techniques are used to analyze the properties of these MoS2 naowires such as STM, NC-AFM, XPS and HREELS. Additionally, the authors have performed first principles calculations to support their findings. The results look correct, interesting, useful to experimentalists and theorists, and could lead to the controlled synthesis of other semiconducting transition metal dichalcogenides (STMD) nanowires/nanoribbons, similar in structure (trigonal prismatic), such as WS2, MoSe2 and WSe2. I recommend the publication of the manuscript after the authors address the following points: 1. How stable would the MoS 2 nanowires be if these are exposed to air?
Response: Due to the reactive nature of the edges of such ultra-narrow wires, the nanowire will react with oxygen. However, the structural integrity of the wire is kept as we can still observe it under STM. The thicker wires are less reactive than the thinner ones, due to the higher ratio of basal plane atoms to edge atoms.

2.
Can the authors comment about the possibility of releasing the nanowires from the gold substrate to use them in other applications? Is this possible?
Response: In this paper, our samples were prepared on the single crystal gold substrate, so it is costly to peel out the MoS 2 nanowires by chemically etching the gold. In future, we will attempt to synthesize the nanowires on Au or Cu foils. Alternatively it is possible to prepare epitaxial gold films on mica surface for the growth of the MoS 2 nanowires, and the ultrathin gold film can be etched when we transferred the wires using the polymer stamp approach, similar to transferring graphene. In this way, the nanowires may be delaminated from the gold substrate.
Due to the technical challenge involved in these steps, they are not attempted in the current study which has its focus on the atomic structures of these wires.
3. According to the authors DFT calculations, the suspended thinnest nanowire possesses a band gap of 0.14 eV. Since DFT always underestimates the band gap, the authors should mention this in the text. Can the authors provide a theoretical realistic value of this band gap for the suspended system?

Response:
The referee is correct to point out that in most cases, DFT significantly underestimates bandgaps of semiconducting materials by 50% due to the neglect of strong correlations in XC functionals.
However, MoS 2 is an exceptional case that DFT is able to generate reasonably good bandgap.  To further address the issue, we also did the so-called DFT+U calculations where the effects of strong correlations are introduced through the Hubbard U. DFT+U method was designed to fix the underestimated bandgap by DFT. We found that for monolayer MoS 2 , (unlike other materials) the inclusion of U decreases the bandgap which can be seen from Fig. 2. We therefore concluded that the DFT prediction of 0.14 eV for the thinnest MoS 2 wire we synthesized is reasonable. We have added this comment in supporting file. Response: Yes, we think our findings can be applicable to the synthesis of other TMDs nanowires, such as WS 2 and WSe 2 . The lattice constant of the MoS 2 (a=3.183Å) is close to that of WS 2 (a=3.182Å). Due to the larger spin orbit coupling, the bandgap of the monolayer WS 2 and WSe 2 are normally larger than that of MoS 2 and MoSe 2 respectively. If strains are exerted on the TMDS nanowires by the substrate, the strains will modulate the coupling strengths of the orbital through the structural relaxations, which result in the change of the band gap. According to DFT calculations, the reduction rate of bandgap in WS 2 (WSe 2 ) is slower than that of MoS 2 ( MoSe 2 ) under a systematic increase of strains(Phys. Rev. B88, 195420, 2013). Furthermore, it was found that the magnetic moment in WS 2 is larger than the that of MoS 2 when the nanoribbons get wider (Applied Surf.Sci.371, 376, 2016) . The concept of half-metallicity can be explored in these 1-D TMD wires. It has been predicted by theoretical calculations that bare zigzag MoS 2 nanoribbons become half-metallic as a result of the (2x1) reconstruction of edge atoms and are semiconductor for minority spins, but metallic for the majority spins (J.Phys. Chem.C115, 3934,2011). These effects may be accentuated in other TMDs with larger spin orbit coupling. Rui-lin Chu recently predicted from their first-principles calculations that TMD provide a very good platform for Majorana fermions based on its edge states with strong spin-orbit coupling. As a result, the proximity induced superconducting pairing and the associated Majorana fermions can be robust against disorders (see Rui-lin Chu, "Spin oribit-coupled quantum wires and Majarona fermions on zigzag edges of monolayer TMD", Physical Review B, 89, 155317 (2014)).

Action:
We have added the following in the discussion section of the paper "It has been predicted by theoretical calculations that zigzag MoS 2 nanoribbons become halfmetallic as a result of the (2×1) reconstruction of edge atoms and are semiconductor for minority spins, but metallic for the majority spins 35. Using first-principles calculations 20 , Chu et. al. predicted that chalcogen-terminated zigzag edges support edge bands with strong Rashbatype spin orbit coupling which are well separated from the bulk bands; the edge modes can be topological although the bulk semiconductor is non-topological. These effects are expected to be accentuated in TMDs with large spin orbit couplings. The potential modulation and charge ordering observed here could result in the peculiar spin texture and coherent spin dynamics for spin manipulation and detection in these wires."

Reviewer #3 (Remarks to the Author):
Mainly with the STM, Authors studied one-dimensional MoS2 grown at the step edge of Au surface, found a periodical oscillation. The observation is original and interest, although this phenomenon is very similar to 2D moire pattern. the data were collected carefully and analyzed reasonable, the presentation is clear, the conclusions sound right and useful. There are a few points should be considered before publication.
Response to third referee's comments: 1. The treatment of uncertainties. Authors mentioned the period is 4.4 ± 0.2 nm, but I cannot find why is ±0.2, please specify it.

Response:
The period is measured by analyzing the line section profiles of 30 dI/dV maps of MoS 2 nanowires, taking the statistical mean of their period. The uncertainty arises from the standard deviation of this mean period.
2. Line 151,152. "On the other hand, it is noted that a peak with similar position as P2 has been reported on the edges of MoSe2". I do not understand why authors mentioned a MoSe2 peak.
The materials are different; it is useless to compare two STS peaks from two materials.
Response: Yes, we agree, this sentence has been deleted in the text.
3. Line 168, 169. "This asymmetric behaviour is similar to the moire pattern inversion between the filled and empty electronic states in monolayer MoS2/Au system." Please give a Ref.

article.
Response: Actually, this is a typo error, we have changed this sentence to "This asymmetric behaviour is similar to the moiré pattern inversion between the filled and empty electronic states in monolayer grapehene/Ru system (Phys.Rev. Lett.100, 056807,2008)." In Gr/Ru system, the STS recorded on the top of the "high" and "low" regions are obviously different due to inhomogeneities in charge distribution due to electron doping from Ru substrate. This is analogous to the observation in our MoS 2 nanowires 4. In this manuscript, Line 118, the edge of MoS2 was considered to be terminated by mono-S. Do Authors check the edge be terminated by dimer-S?

Response:
We did not observe dimer-S on ultranarrow MoS 2 wire. However we do observe a bright-dark alternating pattern along the edge of tooth-saw like nanoribbons as shown in Fig. 3, in which a periodicity is twice the lattice of MoS 2 (3.15Å). This 2× period is typical characteristic of S2 dimer terminated zigzag Mo edge (Nat Nanotechnol 2, 53,2007). It is not clear to us at this stage how the terminations differ, but it may be related to fluctuations in chemical potential of S and Mo during growth. Response: For systems under study, it is difficult to compare the simulated STM images with experiments because for such ultra-thin wires, the STM tip induced local field normally has great effects, while in simulations, STM tip is not included and the STM image is approximated by ground-state surface local DOS. To demonstrate this, we conducted DFT calculations to simulate the STM image of the single wire. Results are shown in Fig. 4. As expected, although we do see the variation of DOS along the wire, but it is hard to compare simulations with experiments.
Actually, in this case, in our opinion, it may make more sense to relate the charge redistribution ( Fig. 3g in the paper) with experimentally observed STM image. The charge redistribution mainly happens at the contact region between MoS 2 and Au substrate, which does not affect much the surface local dos, but surely have great effects on electron tunneling from the Au substrate to the STM tip that will be reflected in observed STM images. On the other hand, we fully agree with the referee that it would be nice to be able to directly explain the observed STM images from theory. This will have to be done by more advanced calculation that fully takes into account the STM-tip induced nonequilibrium effects. We plan to do this using the recently proposed steady-state DFT that is good for nonequilibrium quantum systems (Sci. Rep. 5, 15386 (2015)) to address this issue in our future study. We have added more discussions for this in the resubmitted paper.