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C: Physical Processes in Nanomaterials and Nanostructures

Deconstruction of the electronic properties of a topological insulator with a two-dimensional noble metal-organic honeycomb-Kagome band structure Hao Sun, Shijing Tan, Min Feng, Jin Zhao, and Hrvoje Petek J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03353 • Publication Date (Web): 22 Jul 2018 Downloaded from http://pubs.acs.org on July 23, 2018

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The Journal of Physical Chemistry

Deconstruction of the electronic properties of a topological insulator with a two-dimensional noble metal-organic honeycomb-Kagome band structure Hao Sun,1‡ Shijing Tan, 2‡ Min Feng,2 Jin Zhao1,2,3*, and Hrvoje Petek2* 1

ICQD/Hefei National Laboratory for Physical Sciences at Microscale, and Key Laboratory of

Strongly-Coupled Quantum Matter Physics, Chinese Academy of Sciences, and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China 2

Department of Physics and Astronomy and Pittsburgh Quantum Institute, University of

Pittsburgh, Pittsburgh PA 15260, United States 3

Synergetic Innovation Center of Quantum Information & Quantum Physics, University of

Science and Technology of China, Hefei, Anhui 230026, China

KEYWORDS: Topological insulator, metal-organic lattice, molecular self-assembly, Rashba effect

ABSTRACT: Some metal-organic (MO) lattices with strong spin-orbit coupling (SOC) have been predicted to behave as two-dimensional topological insulators (2D-TIs). The polarization of metallic edge states with the opposite electron spin in 2D-TIs, in otherwise insulating 2D MO sheets, is interesting for spintronic technology. The 2D-TI character of MO lattices, however, has

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not been confirmed by experiment. The main challenge has been that MO lattices usually selforganize on metal substrates, which can introduce interactions that modify and can even suppress the topological character. We calculate the topological properties of 2D metal-organic honeycomb lattice composed of noble metal atom vertices and bidentate 1,4-phenylene diisocyanide (PDI) linkers, which form honeycomb-Kagome band structure (MOHKLs), free and on metal substrates. The selection of vertices and linkers can independently tune the SOC and transport properties. Calculations predict that unsupported 2D MOHKLs indeed possess SOCinduced gaps between the Dirac bands at the K points. Furthermore, nanoribbons of such MOHKLs are calculated to possess metallic spin-polarized edge states. Supporting MOHKLs on a metal substrate, however, introduces an electric potential giving rise to Rashba SOC, which can collapse the band gaps. Molecule-resolved measurements by scanning tunneling microscopy and spectroscopy test the electronic properties of Ag-PDI MOHKL self-assembled on Ag(111) surface, but find no evidence of the 2D-TI electronic band structure. Releasing MOHKLs from the electronic and chemical influences of substrates to preserve their TI properties remains a challenge. The Rashba SOC provides an additional tool for designing 2D-TI band structures.

I.

INTRODUCTION

The discovery of topological phenomena in the condensed phase has opened up new design principles for quantum materials with intriguing electronic structures that impart novel spindependent surface and bulk transport properties.1-4 Intense interest in topological insulator (TI) materials,5-7 whose electronic structure is characterized by Z2 topological invariance under the time-reversal symmetry,5,

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has encouraged the exploration and characterization of novel

quantum materials. In addition to the bulk TI materials, which have gapless (metallic) surface


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states and insulating bulk, 2D-TIs have also been of keen interest because their linearly dispersive Dirac bands and dispersionless flat bands near the Fermi level can be modified by the relativistic SOC to acquire metallic, spin-polarized, one-dimensional edge states and sheet band gaps. These electronic properties potentially give rise to exotic phenomena such as quantum spin-Hall effect, ferromagnetism, superconductivity, Wigner crystal phases, etc.9-30 In addition to inorganic materials,11-12, 20, 22-23, 28-29 a new class 2D-TIs materials, which form 2D-MO lattices,31-32 has been predicted by theory.15-18, 25, 33-34 Such materials, if they could be synthesized and their intrinsic properties harnessed, would have advantages of low cost, economical use of rare elements, easy fabrication, broad tunability by organic functionalization, mechanical flexibility, etc. Liu and coworkers have predicted several kinds of 2D-TIs based on hexagonally tessellated MO lattices, where either each metal atom forms an apex between three phenyl rings in a honeycomb structure,15, 17-18 or Kagome lattices where each organic molecule forms an apex between three metal atoms.16, 25, 33-35 Most theoretical predictions of MO 2D-TIs have been based on calculations for free-standing, single-layer materials, but their realization and application, necessarily involves a substrate support; incisive examination of TI properties of the supported 2D-MOHKLs is still lacking. In this study, we combine first-principles theoretical design and electronic structure characterization of a new class of 2D-TI materials based on MO lattices forming honeycombKagome structures, with their experimental synthesis and molecule-resolved electronic structure evaluation.36-37 The 2D-TI martial design is motivated by tendency of 1,4-phenylene diisocyanide (PDI) molecules to form MO films on noble metal substrates.38-40 A specific successful 2D-TI film synthesis described herein combines the propensities of Ag adatoms on Ag(111) surface to form covalent bonds with –NC groups of three PDI molecules, with those of


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PDI molecules for bidentate bonding with two metal adatoms, which are the key features for self-assembly into the theoretically studied MOHKLs with potentially TI properties. With two Ag atoms per unit cell donating their single valance electrons to the lattice, first-principles calculations predict the unsupported Ag-PDI MOHKL to have 1) half-filled Dirac bands crossing at the Fermi level (EF); and 2) a flat band above them becoming nearly degenerate at the Γ point. Introducing the relativistic SOC dominantly from the metal atoms causes band gaps to form within the sheet, and spin polarized edge states to appear at the Dirac band crossings at the K and Γ points. Specifically, the relativistic SOC affects the Dirac bands, which cross at the K point in its absence, but in its presence form two bands, one fully occupied and the other unoccupied, which are separated by an SOC strength dependent band gap. Calculation of the Z2=1 index of the topological invariance and edge states of MOHKL ribbons within the SOC gaps, predicts unsupported noble metal atom-PDI MOHKLs to embody the intrinsic TI properties.41 We also calculate the electronic structure of the Ag-PDI MOHKL on the Ag(111) support, and predict that the electric potential gradient at the surface, which produces an electric field and thereby causes the Rashba SOC,42 is sufficiently strong to collapse the relativistic SOC gap at the K points, but not at the Γ point. The Rashba SOC arises from the surface normal electric field, which together with the in-plane electron velocity, creates a surface normal magnetic field. This magnetic field causes a splitting of the otherwise degenerate spin bands for electron momentum ≠ 0 . Our results show that such previously unexplored interactions could quench 2D-TI properties at MOHKL/metal substrate interfaces. The predicted Ag-PDI MOHKL is synthesized by self-assembly upon dosing PDI molecules onto an Ag(111) surface, and its molecular and electronic structures are evaluated by moleculeresolved low-temperature scanning tunneling microscopy (LT-STM) and spectroscopy (STS).


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STS measurements find no sign of 2D-TI properties, e.g., the Dirac and flat bands, and their edge states. The contact between the MOHKL and its metal substrate creates inevitable electrostatic and chemical interactions, which quench the TI properties. To overcome perturbations by the substrate, we attempt Ag-PDI MOHKL synthesis on an NaCl film, but find its self-assembly to be suppressed. Our study deconstructs the challenges of realizing practical 2D-TI MO films.

II.

THEORETICAL AND EXPERIMENTAL METHODS

The first-principles calculations are based on spin-polarized density functional theory (DFT) using Perdew-Burke-Ernzerhof (PBE) exchange-correlation generalized gradient approximation (GGA) functional43, as implemented in the VASP code.44-46 The projected augmented wave method is used with plane wave basis sets and energy cutoff of 500 eV.47 The calculations use 3×3×1 K points for the structure optimization and 9×9×1 K points for the self-consistent band calculations. To fully characterize the topological properties, we use a tight binding (TB) model, which is similar to that proposed by Kane for graphene1, 8. The Hamiltonian is written as: =

+ ,

≪ ,≫

(, × , ) ⋅ "#,# , $ % , (4)

where t is the hopping term, and is the strength of intrinsic SOC. i, j are lattice site indices, which refer to different onsite orbitals, and ( , s are the spin index and Pauli matrices, respectively. Vectors d1 and d2 in the second term refer the direction vectors between the two next nearest lattice sites, and

and are the electron creation and annihilation operators. The

parameters in the TB Hamiltonian are obtained by fitting the DFT band structure. The TB terms t


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are set to 0.6 eV for hopping, and to =0.006 eV for the relativistic SOC parameter for the AuPDI simulation. To confirm the topological nature of the band gaps, we calculate the Z2 invariant by calculating the Pfaffian of time reversal matrix of eigenvalues at each time reversal invariant momentum (TRIM) with the expression:5

) =

*det./(Γ )1 , 4 , (5) = 67 (−5)9Θ97 (5); (5) 23./(Γ )1 @

(−1)> = ? ) (6)

where 7 (5) is the electron wave function, 4 , (5) is the matrix element obtained by the inner product of eigenvectors, and Θ is the time reversal operator. Then ν, the Z2 number, is obtained from eq. (6). Because the unsupported MOHKL also has space inversion symmetry, the Z2 invariant calculations can be simplified by calculating the parity at each TRIM using the formula:5

(−1)>

@

= ? E (7)

where E is the parity of electron wave functions at TRIM. The value of (-1)ν we calculate at the flat band and the bottom Dirac band equals to -1, which leads to the nonzero Z2=ν=1. The STM/STS measurements are performed in an Omicron LT-STM chamber at 6×10-11 mBar pressure. The noble metal samples are cleaned by cycles of Ar+-ion sputtering and 800 K annealing. The PDI molecules are dosed as described in our previous studies.39-40 The STM


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images are obtained at 77 K in a constant current mode, and STS is measured at 4.7 K using a lock-in technique with modulation at 731 Hz.

III.

RESULTS AND DISCUSSION

A. The topological band structure of free-standing 2D MOHKLs. 2D-TI band structures have been predicted for honeycomb or Kagome lattices that combine metal vertices with organic linkers and possess extended π-bonding networks.15-16, 18, 30, 33-34, 48 We begin by considering interactions of PDI molecules with noble metal atoms because of their known propensity to self-organize into π-bonded MO chains on single crystal Au surfaces.38 PDI molecules deposited on Au(111) and Au(001) surfaces at submonolayer coverages incorporate Au adatoms as covalently bound bridging ligands to form 1D MO chains.38-40 The chain formation arises from the proclivity of Au adatoms for double coordination, especially by forming covalent bonds with the cyano or carbene/zwitterion ligands.49-51 Exceptionally, on the three-fold symmetric Au(111) surface, Au adatoms can accept a third ligand to form vertices connecting three linear chains that grow along the symmetry axes, thereby exhibiting a weak tendency to form 2D reticulated structures.40 Molecules, such as 4,4-biphenyl diisocyanide also form linear MO chains on Au(111),52 suggesting other potential molecular ligands for the synthesis of MO lattices. Based on this potential to form 2D MO structures, we calculate the electronic properties of unsupported noble metal-PDI MOHKLs. As an example, Figure 1a shows the molecular structure of a possible Au-PDI lattice, where Au atoms form the honeycomb lattice and PDI molecules link them to form a Kagome electronic network. Calculating the free-standing Au-PDI


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MOHKL geometry shows that a planar structure is created without steric hindrance between molecules causing out-of-plane distortions, contrary to the previously calculated MOHKLs based on phenyl ring linkers, which possessed stronger repulsive interactions.15, 17-18 Such distortions may affect electron delocalization, and hence impact the charge transport in MO polymers. Each unit cell of Au-PDI MOHKL is a parallelogram with lattice constants of ~20 Å (Figure. 1a), which consists of two Au aadtoms bonded covalently to C atoms of –NC groups of three PDI molecules. The Au atoms donate two 6s electrons to the G bonding network of the PDI linkers to produce the density functional theory (DFT) band structure in Figure 1b. Without inclusion of SOC, the band structure has typical features of a Kagome lattice: two half-filled Dirac bands, which intersect at the Dirac points that coincide with EF at the K points, and ~0.5 eV above EF, the Dirac bands disperse to a flat band at the Γ point..26, 48, 53-56 This is most likely a Chern flat band with a bandwidth of 17.1 meV, which could impart many-body ferromagnetic properties, if it were occupied.17 The density of states (DOS) shown in Figure 1c suggest that the Dirac and the flat bands are mostly contributed by the π* orbital of the PDI molecule. The pz orbitals of Au atoms that connects the PDI molecules contribute to the inter-molecule hopping term. Introducing the relativistic SOC to the calculation imparts topological properties to the band structure this MOHKL in Figure 1d. The relativistic SOC of Au atoms causes gaps of 11.8 meV (Eg1) and 37.9 meV (Eg2) to open at the Dirac points and between the flat band and the Dirac band. The band structures Ag-PDI and Cu-PDI have the same topological properties, albeit with smaller gaps that follow from the relativistic SOC of the lighter noble metals. Table 1 reports the calculated gaps Eg1 and Eg2 for MOHKLs composed of various noble metal atoms.


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Figure 1. (a) The molecular structure of the 2D noble metal-PDI MOHKLs. The blue dashed quadrangle shows a unit cell of the 2D MOHKL. (b) and (c) The band structures of Au-PDI MOHKL calculated without and with the relativistic SOC, respectively. The blue and orange lines identify the Dirac bands, and red the flat band.


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TABLE 1. The relativistic SOC induced gaps, effective electron masses (m*) at the Dirac point and threshold external electric fields (Eth) for closing the gaps at Dirac points by the Rashba SOC effect for the noble metal-PDI MOHKLs.

MOHKL

Eg1 (meV)

Eg2 (meV)

m*(10-4me)

Eth (mV/Å)

Au-PDI

11.8

37.9

2.76

1.84

Ag-PDI

3.3

9.1

2.32

0.36

Cu-PDI

2.0

5.7

1.70

0.12

The topological character of the bands in Figure 1d is confirmed by calculating the Z2=1. For a 2D topological material, ribbons formed from the MOHKL are expected to have spin-polarized metallic edge states within the SOC band gaps, where electrons of the opposite k-vector propagate with the opposite spin. To model a finite system that could support such spin-polarized metallic edge states, we calculate the band structure of an Au-PDI nanoribbon with a tightbinding (TB) model, which is adopted because a DFT calculation of the electronic properties of an MOHKL ribbon requires a large unit cell, and therefore impractical computational resources. First, we use TB model for a 2D Au-PDI MOHKL as shown in Figure 2a and obtain the TB parameters in Figure 2b by requiring that the model reproduce the DFT band structure in Figure 1d. Next, using the TB parameters we calculate the band structure of a nanoribbon with a 40 unit cell (2D film) width, which predicts the expected metallic edge states within the sheet relativistic SOC band gaps between the Dirac bands and the Dirac and flat band, as can be seen in Figure 2c.


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Figure 2. (a) Schematic illustration of the tight-binding model, in which PDI molecule and Au atom are treated using single orbitals. (b)The band structure of Au-PDI MOHKL calculated by the TB model. The Dirac bands are shown by the blue and orange lines, while the flat band is shown in red. (b) The metallic edge states (brown) calculated by the TB model with SOC for an Au-PDI nanoribbon 40 unit cells wide. The non-metallic (green) bands are in the ribbon interior.

B. Rashba SOC effect on supported MOHKLs In addition to the relativistic SOC, if the mirror symmetry is broken, such as at a surface, a Rashba SOC term is turned on by presence of the surface normal field and may affect the band structures of MOHKLs. Like in graphene, the Rashba SOC term arises due to the overlap of the G and ( orbitals, which creates a dipole moment;57-58 its effect on the band structure depends linearly on the electric field perpendicular to the MOHKL. Such a field exists at any surface because of the surface normal electrical potential. The Rashba SOC shifts bands with the opposite sign of parallel momentum, k||, in the opposite direction, which may close the band gap at the Dirac point.2, 4 Because the Rashba SOC can eliminate the 2D-TI properties,58-59 it is important to calculate its magnitude for supported MOHKLs.


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To evaluate the effect of the Rashba SOC, we again turn to a TB approach. The z component of the Rashba term (normal to the surface) is added to the Hamiltonian by considering the nearest neighbor hopping sites as follows:8, 42 HI = HI

, $ %

$ J" × , K % (1) L

where " is a Pauli matrix, and , , a directional vector from site i to the nearest site j. HI is the Rashba SOC strength, which is proportional to the existing surface normal electric field E. According to the 2D electron gas approximation:2, 4, 42 HI =

ℏ% |O| R , (2) 4P∗ % %

In Figure 3a-c, one can see that increasing the E field, increases HI causing progressive closing of the relativistic SOC gap at the Dirac point, but not between the flat band and the Dirac bands at the Γ point. At the K point, the Rashba SOC shifts the Dirac bands along the energy axis, whereas at the Γ point they mainly shift in the ±k directions, as shown in the insets of Figure 3ac and Supporting Information Figure S1. Therefore, the Rashba SOC will modulate and possibly close the topological gap at the K point, but not at the Γ point. More details on how the Rashba SOC modifies the bands is discussed in the Supporting Information I.


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(a)

(c)

(b)

Figure 3. (a-c) TB band structures of a 2D Ag-PDI film with the relativistic SOC causing the splitting between the Dirac bands producing a band gap, and the Rashba SOC effect, with an increasing the ratio UVW = 0.5, 1.0, 2.0 from (a) to (c) causing the band gap to close. The insets show expanded bands at the K U XY

point. Including the Rashba SOC, cause the splitting of the bands with different spin (removes the twofold degeneracy of the blue and orange Dirac bands): two of the four bands are shifted towards each other along the energy axis (black bands) possibly closing the topological gap at the K point.

The Rashba SOC causes the band gap Eg1 to be modified according to: R[ = R[$ − 2HI \ = R[$ −

ℏ% |O| || R , (3) 2P∗ % %

where k|| is the surface parallel momentum. Using eq. 3, we estimate the threshold electric fields (Eth) that are necessary to close the relativistic SOC band gaps and report them for each noble metal substrate in Table I. The calculations show a range of Eth from 0.12 to 1.84 mV/Å, whereas the expected fields for the supported MOHKLs on noble metals are about thousand times larger. This result predicts that the Rashba SOC effect will in fact suppress the 2D-TI properties of the Dirac bands at the K points of noble metal MOHKLs when they are supported on the noble metal substrates. The above calculations and Figure 3 show that supporting an MOHKL on a metal will create an orthogonal field that may collapse the relativistic SOC induced band gap at Dirac point with


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concomitant extinction of the corresponding edge states. The band gap at the Γ point, however, will remain with its edge states preserved, though its energy relative to EF makes it unlikely to affect the electronic transport. The combined effects of the relativistic and Rashba SOC on the band structure of graphene has been thoroughly studied.1, 57-61 The noble metal-PDI MOHKLs also have Dirac bands, which undergo similar modifications to graphene, but the methodology for controlling the electronic properties though the Rashba SOC have not yet been developed.59-60 The manipulation of the Rashba SOC can be accomplished by applying an external electric field, rotating a magnetic field, or by introducing a local curvature through external stress; in the case of graphene, such manipulations have been investigated for the purpose of controlling the spintronic properties as well as realizing Majorana fermions.58, 62-63

C. Synthesis and electronic structure of an Ag-PDI To synthesize a 2D MOHKL lattice and probe its electronic properties, we investigate the self-assembly of PDI on Au(111), Au(001), Ag(111), and Cu(110) surfaces under ultrahigh vacuum (UHV) conditions within a low temperature STM chamber. As alredy noted, on Au and Cu surfaces PDI molecules predominantly self-assemble into linear noble metal-PDI chains,38-40 but only on Ag(111) the three-fold coordination predominates, forming nearly perfect MOHKLs. We therefore describe the synthesis and molecule resolved electronic structure of the Ag-PDI MOHKL. The self-assembly of the Ag-PDI lattice depends on the synthesis conditions. Depositing PDI molecules onto Ag(111) substrate at below 150 K causes assembly of PDI into a close-packed


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layer with a 0.76 nm periodicity in a √7 × 2√7 superstructure, which is consistent with an upright geometry most likely involving monodentate bonding of the –NC groups to the terrace Ag atoms (Figure 4a, b). The DFT calculations confirm monodentate PDI asssembly into a √7 × 2√7 superstructure, as shown in Figure 4c. In the molecular electronics literature, such upright PDI bonding has been considered in the context of single-molecule conductivity, and its existance is hereby confirmed.64-68 When the temperature is increased to around 200 K, a highly ordered Ag-PDI MOHKL forms on the Ag(111) with its lattice aligned to the high symmetry directions of the substrate and a period of 1.96 nm, as shown in Figure 4d, e. Each hexagon side, representing an Ag-PDI-Ag unit, has a length of 1.15 nm, corresponding to approximately four times the Ag-Ag interatomic distance of Ag(111). This is to be compared with 1.21 nm for an unsupported Ag-PDI MOHKL, which suggests that the Ag-C-N-bonds bend out-of-plane to enable Ag atoms of the MOHKL to bond epitaxially with its supporting lattice.39 The self-organization process of a MOHKL most likely involves the formation at and dissociation from the Ag(111) step edges of monodentate Ag-PDI complexes, enabling Ag adatoms to suppport and transport their PDI molecule on Ag(111) terraces. Transport of the monodentate Ag-PDI complexes occurs until they encounter each other enabling one to combine with the other through bidentate PDI bonding, which eventually grows a MOHKL film. The MOHKL grows, by itinerant monodentate Ag-PDI complexes adding to recumbent monodentate PDI molecules that form the bearded framework edges, such as seen in Figure 4d. The self-assembly terminates when the itinerant monodentate Ag-PDI complexes are consumed to form a MOHKL lattice, with the recumbent PDI molecules at the edge, as can be seen in Figure 5a. The beard edge molecules appear to bind with one of their –NC groups to terrace Ag atoms, which are not imaged, rather than to Ag adatoms, which


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appear as bright spots in the STM images. Increasing the temperature to above 250 K, destroys the Ag-PDI MOHKLs when a disordered, difficult to characterize structure, forms (Supporting Information II). The focus of our experiments is on the intermediate temperature Ag-PDI MOHKL on Ag(111) surface and its electronic structure. With a special STM tip condition, a molecular resolution STM image is obtained (Figure 4f), which clearly shows the intramolecular contrast of PDI, with the Ag adatoms at vertices appearing as triply coordinated points. The experimentally observed MOHKL structure is anticipated by the calculated one for the unsupported Au-PDI MOHKL in Figure 1a, and is confirmed by the simulated STM image of a supported Ag-PDI MOHKL in Figure 4g. The predicted 2D-TI band stucture of an unsupported Ag-PDI MOHKL in Figure 2b can in principle be confirmed by showing that the Ag-PDI MOHKL on an Ag(111) surface has an intrior insulating sheet and conducting edges. Therefore, we measure dI/dV spectra with our STM at different locations across an edge of a honeycomb layer to map how the electronic structure of a MOHKL evolves form the Ag(111) substrate to the sheet interior. Figure 5 shows how the measured dI/dV spectra change from the bare Ag(111) surface over an MOHKL edge. The dI/dV spectra of the bare Ag(111) surface have a strong step-like transition at the threshold for tunneling into its Shockley surface (SS) state at about -64 meV below EF.69-71 As the dI/dV measurements approach the MOHKL, the SS DOS in the spectra is pushed to higher energy as can be expected from confinement, and sharp features become washed out possibly because of enhanced scattering at the MOHKL boundary. Above the MOHKL, the most significant DOS appears as a broad peak at +0.3 V above the hexagons, which is most likely a


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vestige of SS, which is pushed up in energy and broadened because of quantum confinement within the hexagons.71-73 We search for the predicted band gap opening in the sheet interior, metallic edge states at the island perifery, and the flat band at ~0.5 eV above EF, but find no evidence for such diagnostic electronic electronic structures of the TI properties of the MOHKL partial monolayer. Apparently, the MOHKL is strongly coupled to the Ag(111) substrate and its density of states is too low to distinguish its characteristic bands. This is most likely because the Ag atoms of a MOHKL are chemically bonded to the Ag(111) substrate; this distinguishes Ag-PDI MOHKL from van der Waals bonded 2D materials like graphene, which retain most of their intrinsic propertiesand merely are doped when coupled with a metal surface. Based on first-principles calculaitons, the electric field at the Ag-PDI/Ag(111) interface is estimated to be 1.3 V/Å (Supporting Infomration III), which exceeds the Eth for eliminating the relativistic gap of the TI band structure by the Rashba SOC (Table 1).

Figure 4. (a) The close packed monodentate PDI film grown on Ag(111) surface with substrate temperature at 150 K (imaged at -0.9 V and 0.06 nA). (b) The height profile along the blue line marked in (a). (c) The calculated top and side views of the optimized close-packed √7 × 2√7 PDI structure on


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Ag(111) corresponding to the structure in (a). (d) The Ag-PDI MOHKL grown on Ag(111) substrate at 200 K (imaged at -0.2 V and 0.1 nA). (e) The corresponding line profile along the position marked by the green line in (d). (f) A high resolution STM image of Ag-PDI MOHKL with a special STM tip (imaged at 2.0 V and 0.13 nA, size: 4.5×4.4 nm2). (g) The simulated STM image of an Ag-PDI MOHKL corresponding to the high-resolution experimental image in (f).

Figure 5. (a) STM image showing the edge of a hexagonal Ag-PDI MOHKL lattice. (b) The dI/dV spectra obtained at the corresponding positions across the edge marked in (a) by colored dots and numbers for −0.5-1.0 eV (left panel) and ±30 meV (right panel). The colors indicate: gray dashed lines, the 0 levels; red (dots and lines), the dI/dV measurements above the Ag(111) surface; yellow, the MOHKL Ag adatoms; blue, the PDI molecules; and green, the hollow hexagon centers; the measurements are performed for ranges of −0.5-1.0 eV and ±30 meV.

To ameliorate the interfering interactions with the metal substrate, with a goal of protecting the 2D-TI properties, we attempt to grow Ag-PDI MOHKLs on semi-insulating substrates, specifically a NaCl(100) bilayer film grown on Ag(111) substrate,74 which may have reduced


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Rashba SOC and chemical perturbations. A previous report of formation of Au-PDI chains on Au cluster decorated mica surface suggested that a synthesis of a MOHKLs on an insulating substrate might be feasible,75 and MO building blocks have been imaged on NaCl films.76 Unfortunately, different attempts to encourage Ag-PDI lattices onto NaCl films by migration from Ag terraces, or by direct growth from Ag clusters deposited onto NaCl films fail, as shown in the Supporting Information IV. There are several potential reasons why the MOHKLs do not appear on the NaCl substrate. First, the square lattice of NaCl(100) may not be favorable for growing hexagonal MO lattices. Second, the corrugated potential landscape of the ionic NaCl(100) surface probably suppresses the diffusion of Ag atoms or their complexes, which we think is essential for the MOHKL growth. Third, PDI molecules probably do not adsorb on NaCl films at temperatures required for the Ag-PDI MOHKL growth, and therefore have little chance to form complexes with Ag adatoms under UHV conditions. The growth might occur at higher PDI pressures and surface temperatures that favor the Ag-PDI complex formation and diffusion. We note that others have also challenged to isolate MO layers from perturbations by metal surfaces. For example, 2D or 1D MO lattices have been successfully synthesized on insulating substrates by simultaneously dosing organic molecules and metal atoms.75,

77

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reported synthesis of a free-standing, monolayer MO sheet at an air/water interface.78 In the studies of edge states of the bottom-up synthesized graphene nanoribbons, the strong covalent CC bond in graphene made it possible to use STM tip to move its nanoribbon segments onto a post-deposited NaCl islands.79 Unfortunately, Ag-PDI bonding is relatively weak, such that above 250 K the Ag-PDI MOHKL is destroyed (Supporting Information II). Attempts to move Ag-PDI MOHKLs by STM manipulation fail and other mechanical methods to isolate the Ag-


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PDI MOHKL turn out to be even more challenging.80-81 Thus, further efforts in synthesis and isolation are necessary to realize and characterize the predicted 2D-TI properties of Ag-PDI MOHKLs.

Figure 6. (a) Optimized geometrical structure (Ag-PDI-BN_1) of Ag-PDI on h-BN sheet with the lattice constant of 20.89 Å. (b) The optimized structure of Ag-PDI on h-BN sheet with the lattice constant of 20.09 Å (Ag-PDI-BN_2), where the Ag-PDI layer is strongly distorted by compression. (c) The energy levels at the Dirac points for illustrating the influence of the relativistic and Rashba effects for the free Ag-PDI MOHKL and on an h-BN sheet. The Fermi levels are set to 0; yellow dots represent the four degenerate bands at the Dirac points of the free Ag-PDI without SOC; green dots indicate the gap opening from the relativistic SOC; dark red dots correspond to the Ag-PDI-BN_1 system with the weak Rashba SOC; and blue dots show the effect of stronger Rashba SOC for the Ag-PDI-BN_2 system.

We also note that it has been claimed based on theory that when a MOHKL is prepared on an insulating substrate, such as hexagonal-BN (h-BN) monolayer, it can maintain its TI properties. Zhang et al. performed DFT band structure calculations for a Cu-dicyanoanthracene (Cu-DAC) hexagonal lattice with similar characteristics to the Ag-PDI lattice.48 In this MOHKL, the Cu atoms are bound by dicyano linkers in a very similar fashion as Ag atoms are bound by the isocyanide groups of PDI molecules. This MOHKL system is predicted to have a topological band structure for a free Cu-DAC sheet and for a Cu-DAC on an h-BN substrate.23 Therefore, we


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performed periodic band structure calculations for the free Ag-PDI MOHKL and on an h-BN sheet (Figure 6), which illustrate the different effects of the relativistic and Rashba SOC. For the free Ag-PDI sheet, the relativistic SOC causes a band splitting of ~3 meV at the Dirac point (Figure 6c). The calculations assume either that the Ag-PDI/h-BN system periodicity is that of the unsupported Ag-PDI or that of the h-BN lattice (20.89 Å) The former structure causes the hBN lattice to expand by 3.98% and Ag-PDI to remain planar above it at a distance of ~0.40 nm (Figure 6a; structure Ag_PDI-BN_1). For such large interplane distance, the Rashba interaction at the Ag-PDI MOHKL that is caused by the h-BN substrate is relatively weak (3 meV) of bands with the opposite spin is sufficiently large to close the band gap at the Dirac point. Thus, the stratagem of depositing a 2D-TI on a 2D insulting substrate may protect the TI properties from quenching, but the outcome depends on the chemical interactions between the sheets.

IV

CONCLUSIONS We have investigated by theory and experiment the TI properties of noble metal-PDI HKL

lattices. DFT and tight-binding calculations show that the free-standing noble metal-PDI


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MOHKLs have 2D-TI electronic structures. The calculations predict a Dirac point exactly at EF, and a topological Chern flat band above the Dirac bands. Relativistic SOC induced band gaps and edge states exist between the flat band and Dirac bands at the Γ point, and the Dirac bands at the Dirac point. The TI properties are confirmed by the calculation of Z2=1. Theoretical investigations based on DFT and tight-binding model show that the Rashba SOC introduced by supporting the 2D-TI on a substrate can easily close the relativistic SOC induced gap at the Dirac point, and therefore the predicted metallic edge states and sheet gaps may not exist for most supported MOHKLs. The edge states at the Γ point, however, that are protected by time reversal invariant momenta, have potential applications in electronic transport. We have also successfully synthesized Ag-PDI MOHKL on the Ag(111) substrate enabling investigation of its edge and sheet molecular and electronic structures with molecular resolution by STM. STS measurements, however, do not find evidence for the 2D-TI electronic bands that are predicted by theory. Most likely, the TI properties are suppressed by the Rashba SOC effect at the MOHKL/metal interface and strong electronic coupling between the MOHKL and the Ag(111) substrate. The synthesis of such MOHKL on NaCl surface is unsuccessful, highlighting the challenges of realizing 2D-TI MO lattices and bringing them to practical applications. Our theoretical and experimental studies show that the 2D-TI properties of MOHKLs are fragile, and can be easily suppressed by interactions with supporting substrates.

AUTHOR INFORMATION Corresponding Authors *Email: [email protected], [email protected] Author Contributions ‡H. S. and S. T. contributed equally to this work


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Orcid Jin Zhao: 0000-0003-1346-5280 Hrvoje Petek: 0000-0001-9605-2590 Conflicts of Interest The authors declare no conflicts of interest.

Acknowledgements H. P. and J. Z. acknowledge the support from DOE-BES Division of Chemical Sciences, Geosciences, and Biosciences Grant No. DE-SC0002313. J. Z. acknowledges the support of National Key R&D Program of China (2016YFA0200604 and 2017YFA0204904), National Natural Science Foundation of China, Grant No. 11620101003, 21373190, 21421063; the Fundamental Research Funds for the Central Universities WK3510000005. Calculations are performed at Environmental Molecular Sciences Laboratory at the PNNL, a user facility sponsored by the DOE Office of Biological and Environmental Research.

Notes and references

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