Hidden Order and Haldane-Like Phase in Molecular Chains

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Hidden Order and Haldane-Like Phase in Molecular Chains Assembled from Conformation-Switchable Molecules Jialiang Deng, Aidi Zhao,* Ruiqi Zhang, Huan Shan, Bin Li,* Jinlong Yang, and Bing Wang

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Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, No. 96 Jinzhai Road, Hefei, Anhui 230026, P. R. China S Supporting Information *

ABSTRACT: Topological properties of matters have attracted tremendous interest in the past years due to the scientific and technological importance. It is of great interest to discover the analogs of topological phases in molecular architectures, if the key constituents of the phases are properly mimicked. Using scanning tunneling microscopy, we demonstrate that quasi-1D molecular chains assembled from conformation-switchable dibenzo[g,p]chrysene molecules show hidden antiparallel order analogous to the hidden antiferromagnetic order in the Haldane phase, a known topological phase of quantum spin-1 chains. This is realized by mimicking the spin degree of freedom with the intramolecular helicene chiral switches and by emulating the interspin antiferromagnetic coupling with intermolecular homochiral coupling. The discovery of the molecular analog of topological matters may inspire the search of molecular architectures with nontrivial topological properties. KEYWORDS: scanning tunneling microscopy, molecular chain, molecular switch, aromatic coupling, topological order

E

no apparent magnetic order in the chain, there exists a nonlocal hidden antiferromagnetic order with hidden symmetry breaking.14−17 Here “hidden” means that although there is no apparent local order, there exists a nonlocal order hidden behind the seeming randomness (the length of the spins with SZ = 0 is arbitrary). In this work, we show that the conformation-switchable dibenzo[g,p]chrysene (DBC) molecules adsorbed on Cu(111) exhibit rich topological morphologies at different coverages owing to the interplay between intermolecular interactions and intramolecular conformational changes. At a coverage of 0.6 monolayer (ML), the DBC molecules self-assemble into molecular chains possessing topological characters similar to the valence-bond solid (VBS) configuration in Haldane chain and also show hidden antiparallel order analogous to the hidden antiferromagnetic order in Haldane phase. Such a molecular chain represents the direct molecular analog of symmetry-protected topological matters.

ngineering molecular architectures with desired topological properties is formidably challenging in chemistry. In the past years, the synthesis of complex molecular knots and links of specific topologies,1,2 for example, Möbius strips3 and Borromean rings,4 has been successfully realized, and their topological properties were demonstrated. However, efforts were scarcely made to the discovery of topological phases in transformable molecular collective systems. This necessitates the utility of both intramolecular conformational changes and intermolecular interactions with extraordinarily high precision. Nontrivial topological phases of matters have been demonstrated in various quantum or classical systems.5−8 The question is raised whether molecular architectures consisting of conformation-switchable units may have similar topological characters if the units are specifically designed analogous to those in the known topological matters, starting from the simplest 1D cases. A representative 1D topological phase is the Haldane phase of a quantum S = 1 antiferromagnetic spin chain, namely the Haldane chain. It was proposed by Duncan Haldane in a conjecture and partly won him a share of the 2016 Nobel Prize in Physics.9,10 The Haldane phase of the chain was recently identified as a 1D symmetry-protected topological phase by Gu and Wen,11 and the relevant symmetry protection was interpreted.12,13 The most striking topological character is that even though there is © 2018 American Chemical Society

Received: January 7, 2018 Accepted: June 19, 2018 Published: June 19, 2018 6515

DOI: 10.1021/acsnano.8b00146 ACS Nano 2018, 12, 6515−6522

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Cite This: ACS Nano 2018, 12, 6515−6522

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Figure 1. Topological properties of individual DBC molecules. (a) Helicene’s notation of the DBC molecule. The DBC can be regarded as the combination of two [4]Helicene molecules. (b) Each helicene part has a Fjord region where the two hydrogen atoms (H1 and H2, from the benzene lobes 1 and 2, respectively) are repulsed and shift upward and downward (red arrows), leading to the doubly degenerated chirality m (left-handed helicity) and p (right-handed helicity). (c) Symbolized representation consisting of a pair of plus and minus signs to denote the conformational property of the molecules. The conformation of DBC molecule can be defined by the discrete displacement of the two upper lobes, σ1L and σ1R. (d) The combinations of m and p helicene part leads to four conformers: M and P represent the two chiral enantiomers of DBC with left-handed and right-handed chirality, respectively. A and A′ represent the meso-isomer of DBC with opposite orientations. (e) The corresponding symbolic representation of the four conformers. (f) Theoretically simulated STM images for the four conformers adsorbed on Cu(111).

Figure 2. Coverage dependence of the morphology of DBC on Cu(111). (a−d) STM images of the same sample taken at increased molecular coverage of 0.09, 0.6, 0.9, and 1 ML, respectively. Here 1 ML refers to the surface that is fully covered by one layer of closest-packed DBC molecules. The substrate temperature was kept at room temperature during deposition. Scale bars, 2 nm. The observed conformers at each coverage are listed below the STM images, indicating a strong dependence on the coverage and intermolecular interactions.

RESULTS AND DISCUSSION

viewed as the combination of two chiral [4]Helicene ([4H]) molecules with the center-overlapped naphthalene units. The [4H] molecule has two chiral enantiomers (m and p) which are differentiated in the Fjord region. The two benzene lobes 1 and 2 are shifted either upward or downward due to the repulsion of the conflicting hydrogen atoms H1 and H2, endowing the molecule with helical chirality (Figure 1b). The [4H] can be switched between its two chiral enantiomers (m and p) with a low-energy barrier of racemization,21 making a typical molecular chiral switch. The different [4H] combina-

Topological Characteristics of DBC Molecules. DBC, the conformation-switchable molecule we investigated in this study, is a helicene derivative with a double-helicene structure. It has long been known as a kind of overcrowded nonplanar polycyclic hydrocarbon and has been investigated as a typical chiral core for liquid crystal studies.18−21 The structural feature and the conformational changes of DBC molecules can be well understood under the framework of helicene’s notation, as illustrated in Figure 1. The chemical structure of DBC can be 6516


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Figure 3. Intermolecular homochiral coupling in the molecular chains. (a) STM image (V = −2 V, I = 100 pA) shows DBC molecules are self-assembled into quasi-1D stripes at a coverage of ∼0.6 ML. Scale bar, 3 nm. (b, d) STM images of two types of intermolecular helical coupling motifs designated by λ (m−m, left-handed) and ρ (p−p, right-handed). (c, e) Corresponding structural models and the symbolic representation of both types of intermolecular coupling. The coupling is via aromatic interaction of the helicene parts, and the interacting benzene lobes from each helicene part are shifted upward (+) and downward (−).

eV (39 kJ/Mol) (Supporting Information, Figure S1 and Table S1), which is on the energy scale with the helical aromatic coupling (several kcal mol−1).22 That is to say, the energy barrier may be overcome by such intermolecular coupling, and the DBC molecules on Cu(111) may adopt all the four conformers in the self-assembled molecular chains or arrays where intermolecular interactions play important roles. Evolution of the Morphology of DBC Molecules Deposited on Cu(111). The above speculation was examined in our experiments of depositing DBC on Cu(111). Figure 2a−d shows the coverage dependence of the morphology of DBC on Cu(111). All observable conformers for each coverage are listed below and can be readily identified by comparing their STM images to the simulated STM images in Figure 1f. The A and A′ conformers show mirror structure with C2h symmetry, while the M and P conformers show brighter diagonal protrusions with D2 symmetry. At very low coverage of 0.1 ML, the DBC molecules are isolated, and all DBC molecules are in the A(A′) conformation (Figure 2a). When the coverage is elevated to about 0.6 ML, the DBC molecules are self-assembled into quasi-1D molecular chains with serpentine arrangement (Figure 2b). Interestingly, we found numerous chiral conformers P and M emerge in the molecular chains. Further increasing the coverage leads to the formation of a 2D molecular array consisting of DBC molecules all in the achiral A(A′) conformation. At coverage of about 0.9 ML, the Cu surface is covered fully by 2D molecular array (Figure 2c). It is found that in this self-assembled domain, the DBC molecules keep the serpentine arrangement in one direction and adopt linear arrangement in another direction. More interestingly, when the coverage reaches 1 ML, all the DBC molecules change from A(A′) to M(P) and the surface is fully covered by a racemic molecular array consisting of equal amounts of P and M conformers. The unusual evolution of the conformations from 0D molecules to 1D chains then to 2D arrays further confirms that the energy barriers for the racemization among different conformers of adsorbed DBC

tions can lead to four different DBC conformers, represented by A(p + m), M(m + m), P(p + p), and A′(m + p), respectively. Here “M” and “P” denote two chiral enantiomers, and “A(A′)” is an achiral meso-isomer (Figure 1d). These conformations can transform into each other by switching the chirality of the helicene parts. A and A′ are conformers with inverse orientation which are same in free-space but are differentiated in a molecular chain due to the broken rotational symmetry. In order to depict the topological characteristics of the four conformers, the displacement of the benzene lobe 1 (red arrows in Figure 1b,c) σ1 is employed as the variable, and the orientations of σ1 are denoted by plus and minus signs. The four-fold degeneracy of DBC can be described by a pair of two signs (σ1L, σ1R), where σ1L, σ1R ∈ {+, − }. The four conformers A, A′, P, and M can therefore be symbolically represented as (+, + ), (− − ), (+ − ), and (− + ), respectively (Figure 1e). Previous studies18,20 has shown that the ground state of a free DBC molecule is the chiral conformer P or M, and the energy of the achiral conformer A(A′) is much higher, which is confirmed by our calculations based on density functional theory (DFT). However, the energy diagram changes dramatically when the DBC molecules are deposited on Cu(111) surface, as indicated by our calculations (Supporting Information, Figure S1). The calculated ground states of DBC molecules adsorbed on Cu(111) are the A and A′ conformers, whose total energy is about 0.062 eV (6.0 kJ/Mol) lower than the chiral enantiomers M and P. The convergences of this energy difference with respect to the used basis-set size, k-point grid, number of metal layers, and size of the vacuum gap in the slab model have been checked, and the results show that the calculated relative stability for the achiral A(A′) and chiral M(P) adsorbed on Cu(111) surface is credible. The theoretically simulated scanning tunneling microscopy (STM) images for the four adsorbed conformers are shown in Figure 1f. The topological properties of each conformers can be directly identified from the contrast of the benzene lobes in STM images, in accordance to Figure 1e. The energy barrier from the adsorbed M or P to A(A′) is calculated to be ∼0.40 6517


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Table 1. Conformations, Intermolecular Distance (Dmole), Total Energy (Edimer) and Interaction Energy Related to Respective Molecules (Eint) of Various DBC Dimers in Gas Phase Eint

conformation of dimers dimers

symbolic representation

coupling motif

relative shift along molecular long axis

Dmole (Å)

Edimer (eV)

(eV)

(kJ/mol)

A′ A (A A′)

(− − ) (+ + ) or (+ + ) (− − )

homochiral

A A (A′ A′)

(− − ) (− − ) or (+ + ) (+ + )

heterochiral

A M (P A)

(+ + ) (− + ) or (+ − ) (+ + )

homochiral

A′ M (P A′)

(− − ) (− + ) or (+ − ) (− − )

heterochiral

M M (P P)

(− + ) (− + ) or (+ − ) (+ − )

homochiral

M P (P M)

(− + ) (+ − ) or (+ − ) (− + )

heterochiral

no yes no yes no yes no yes no yes no yes

10.90 10.00 11.40 10.96 10.51 10.07 10.59 10.24 10.20 10.26 10.86 10.92

−512.169 −512.217 −512.112 −512.130 −512.423 −512.486 −512.368 −512.417 −512.644 −512.646 −512.561 −512.583

−0.137 −0.185 −0.080 −0.098 −0.170 −0.233 −0.115 −0.164 −0.170 −0.172 −0.087 −0.109

−13.2 −17.8 −7.7 −9.5 −16.3 −21.0 −11.1 −16.3 −16.4 −16.5 −8.4 −10.5

Figure 4. Hidden antiparallel order in the DBC chains. (a, c) Two typical DBC chains containing random chiral DBC molecules. (b, d) The corresponding symbolic and spin-1 representations of the chains in (a) and (c). The blue arrows represent the S = 1 spins with SZ = ± 1, and “0” denotes S = 1 spins with SZ = 0. The molecular chains thus show a hidden antiparallel order similar to that in the VBS state of a Haldane chain.

molecules are fairly low, which can be readily overcome by intermolecular interactions, in consistent with our calculations. Among all the morphologies, the molecular chains in Figure 2b are particularly interesting because all the four conformers can be observed in a single chain. The arrangement of the four conformers in a chain seems fairly random without a longrange positional order; the chiral P or M molecules are randomly intercalated in the A(A′) chain. However, we will show in the following sections that there exists a hidden order in the chain which has not been revealed in previous studies of conformation-nonswitchable molecular chains. Intermolecular Homochiral Coupling in the Molecular Chains. To better understand the topological properties of the quasi-1D molecular chains at the coverage of 0.6 ML, we investigated the intermolecular interactions in the chains. Figure 3a shows a large-area STM image of a number of quasi1D molecular chains. The interchain and intermolecular

distances are about 1.6 and 1 nm, respectively. The vertical quasi-equidistant ordering can be attributed to similar repulsive electrostatic interactions,23 while the smaller horizontal distance indicates a stronger intermolecular coupling via the Fjord regions.22 Although all four conformers exist randomly in the chains, we found that all DBC molecules are coupled via a same coupling rule, that is, the homochiral aromatic coupling, owing to the chiral nature of the helicene parts. In Figure 3b,d, we list the detailed STM image for all eight coupling configurations between the adjacent conformers. We found that all of them can be categorized into two homochiral aromatic coupling motifs, m−m and p−p. We use λ and ρ to designate the left-handed and right-handed helical coupling motifs. Heterochiral coupling motifs (m−p and p−m) are not observed, which can be readily understood with higher energy due to steric repulsion effect. This is a typical example of chiral recognition. Such a homochiral coupling rule has been 6518


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Such a hidden antiparallel order has not been observed in any known molecular chains even for those conformationswitchable molecules with only one chiral switch. It should be a specific topological phenomenon for conformation-switchable molecules with two symmetric chiral switches. In Figures 1 and 3, we have employed a symbolic representation to depict the topological properties of individual DBC molecules and the intermolecular coupling motifs. Here we can also plot the corresponding symbolic representation of the whole chains, as shown in Figure 4b,d. Interestingly, we found that the hidden antiparallel order represents an exact analog to the hidden antiferromagnetic order in a Haldane chain if we define all the pairs (+ + ), (− − ), (− + ), and (+ − ) as the four states of a pseudospin S = 1. In the lower panels of Figure 4b,d, we plot the corresponding VBS representation of the two chains in which the upward and downward blue arrows represent analogs of the two states of S = 1 spins with SZ = ± 1, and 0 represents analogs of state of S = 1 spins with SZ = 0. The green lines are guiding lines that indicate the antiparallel arrangement of A and A′ molecules remains across the intercalation of one and two M or P molecules. It can be readily derived that the alternating arrangement of the A and A′ molecules will not be changed if more M(P) molecules are intercalated. We call the diluted antiparallel phase of the DBC chains the Haldane-like phase, and it has been observed in all DBC chains. Analogy between the DBC Chain and the Spin-1 Haldane Chain. A Haldane chain is a quantum S = 1 antiferromagnetic spin chain in the Haldane phase. The most striking topological character of the Haldane phase is that even though there is no apparent magnetic order in the chain, there exists a nonlocal hidden antiferromagnetic order.14−17 The key insight to the nature of Haldane phase has been given in the Affleck−Lieb−Kennedy−Tasaki (AKLT) model14 in which the spin-1 is treated as a combination of two s = 1/2 spins (Supporting Information, Figure S3) in a so-called VBS configuration. The ground state of the Haldane phase has been proved to be the VBS state.15,16 In the VBS state, two essential constituents are required, the spin-1 unit at each site consisting a pair of s = 1/2 spins and the intersite valence bonds (equivalent to spin singlets) (Figure 5a). Each pair of spin-1/2 can be symbolically represented by a pair of two signs (+, + ), (− − ) and (+ − )/(− + ) (the spin-1/2 variables are denoted by plus and minus signs), corresponding to the S = 1 spins with SZ = +1, −1, and 0, respectively. And each valence bond is represented by a pair of coupled opposite signs “+)(−” and “−)(+” (Figure 5b). To verify if the DBC molecular chain can indeed be interpreted as a molecular analog of the Haldane chain, it is necessary to check carefully the analogy between the topological properties of DBC chains and the spin-1 chain in VBS state. In Supporting Information, Figure S1, we establish a full mapping between the spin-1 Haldane chain and the DBC molecular chain. DBC molecules have two symmetric parts, and each part is able to switch between two degenerated ground states in analog to s = 1/2 spin up and spin down. The four-fold degeneracy of DBC can thus be described in VBS representation (the spin-1/2 variables are denoted by plus and minus signs) as we have depicted in Figure 1c,e. The DBC molecules then mimic the spin-1 unit of the spin-1 chain in the VBS state. The next step toward the further mimic of the VBS state is to emulate the antiferromagnetic coupling between neighboring S = 1 spins, that is, the antiparallel valence bonds

previously demonstrated to play a key role in constructing chiral supramolecular architectures.23 Following the symbolic representation in Figure 1, these two motifs can be symbolically represented by a pair of coupled opposite signs “+)(−” and “−)(+”. In this sense, the intermolecular homochiral coupling can thus be regarded as valence bonds as indicated by the blue lines in Figure 3c,e. In order to understand and validate the experimental results, especially that the homochiral aromatic coupling is the energyfavorable ground state, we have also performed DFT calculations for the dimers with various combinations of A(A′) and M(P). Since the calculations of dimers on Cu substrate exceed our current capacities, dimers in gas phase are simulated as a simple evaluation of the interaction between the DBC molecules in the molecular chain on Cu surface, and the possible relative shift along the molecular long axis between the two molecules is considered (Supporting Information, Figure S2). Based on the symmetry, all of these configurations can be transferred into the 12 ones in Table 1. Here the interaction energy related to respective molecules Eint is defined as the difference between total energy of dimer [X Y] and total energies of X and Y (X, Y = A, A′, M, P). We may find that all dimers with homochiral intermolecular coupling are indeed more energetically favorable than their corresponding ones with heterochiral intermolecular coupling, and the interaction energy Eint of the former is almost twice as large as the latter for some cases. Therefore, the DBC molecules should prefer interacting via homochiral intermolecular coupling. For the dimers in the eight types of intermolecular helical coupling motifs in Figure 3, the ones with a small relative shift (∼1.1 Å) along the molecular long axis between two molecules are more energetically favorable than those without any relative shift, in agreement with the serpentine arrangement of molecular chain in the experiment. The underlying mechanism should be the steric repulsion effect in the xy-plane, which does not influence the chiral intermolecular coupling related to the steric repulsion effect in the z-direction and the hidden antiparallel order in the molecular chain according to our experimental results. The distance between the centers of two molecules Dmole is 10.00 and 10.07 Å for the most energetically favorable dimers [A′ A] and [A M], respectively. All of the above calculated results of DBC dimers are consistent with our experimental observations. Hidden Antiparallel Order in DBC Molecular Chains. In the above investigation, we have shown that the DBC molecular chains consist of conformation-switchable molecules via a homochiral coupling rule. An identical coupling rule in self-assembled molecular chains usually leads to uniform chains with long-range positional order. However, in this case, we found an ordered arrangement of the molecules in a chain which has not been previously reported. In Figure 4a,c, the STM images of two typical DBC chains with a couple of chiral M and P molecules randomly intercalated in the chains of achiral A and A′ molecules are presented as representative examples. The symbolic representation of the conformation for each DBC molecule is superimposed on the STM images. The most interesting topological phenomenon is that achiral A and A′ molecules appear in an alternating manner in every chain, despite of the random intercalation of M or P or their dimers! That is to say, the seemly random molecular chains are not really random, they show a hidden antiparallel order across the intercalated M or P molecules. 6519


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with slight vertical shift. Unlike the Haldane-like phase in the isolated molecular chain in Figure 3, this phase is topologically trivial because it can be regarded as a perfectly antiparallel Néel phase which can be expressed in terms of a local order parameter, different from the Haldane-like phase (Supporting Information, Figure S5). For the coverage of 1 ML, all DBC molecules are switched to be chiral, and the adjacent DBC molecules are of opposite chirality (M and P) and in perpendicular orientation. The recovery of molecular chirality and change of assembly structure when the coverage is increased to 1 ML can be understood by combining analyses of the steric repulsion effect and the DFT calculations (Supporting Information, Figure S6).

Figure 5. VBS state in AKLT model of Haldane phase and VBS representation of DBC molecular chains. (a) AKLT model of Haldane phase of antiferromagnetic S = 1 spin chain. Each site consists of two symmetrized s = 1/2 spins, and the neighboring sites are bonded by a spin singlet, the so-called valence bond. (b) A typical VBS state of a chain within the AKLT model showing the hidden antiferromagnetic (antiparallel) order. The S = 1 spins are denoted by pairs of spin-1/2 variables (+ +), (− −) or (+ −)/(− +). The blue arrows represent the S = 1 spins with SZ = 1, and “0” denotes S = 1 spins with SZ = 0. The configurations have previously been discovered in a classical system with the DOF phase of crystal surfaces that also shows the hidden antiparallel order.15 The analogy between the VBS state of spin-1 chain and the DOF phase of crystal surface is shown in (b) (following Figure 15 in ref 15).

CONCLUSIONS In summary, we have shown that the conformation-switchable DBC molecules adsorbed on Cu(111) exhibit rich topological morphologies at different coverages owing to the interplay between intermolecular interactions and intramolecular conformational changes. At a coverage of 0.6 ML, the DBC molecules self-assemble into molecular chains which act as a molecular analog of the VBS state of the S = 1 Haldane spin chain. One of the main topological characters of the Haldane phase, the hidden antiparallel order, are effectively resembled by the molecular chains with intramolecular conformational changes and intermolecular homochiral couplings. The realspace demonstration of the hidden topological order in DBC chains suggests that molecular systems with rich topological features may help to comprehend the topological properties of their quantum counterparts. Our findings in this work demonstrate that the conformational degree of freedom of a molecule can be abstracted to be pseudospin and effectively mimic the spin degree of freedom of quantum spins. Inspired by this fact, one would expect more phenomena of quantum spin may be effectively emulated by pseudospins in molecular systems in the future, for example, spinons, double exchange, superexchange, etc. Moreover, this study provides a representative example that bridges the gap between topological molecular chemistry and topological physics and may stimulate the search of more molecular system like biomolecular complexes with nontrivial topological properties.

in the VBS state.14−17 As shown in Figure 3, the homochiral coupling motifs can also be properly represented by a pair of coupled opposite signs “+)(−” and “−)(+”, which resemble the valence bonds in the VBS state in AKLT model. From the above analysis, we have shown that the DBC chains reproduce the apparent topological characteristic of VBS state, which is the ground state of a spin-1 Haldane chain. The Haldane-like phase in DBC chains can be regarded as a world line of its quantum counterpart. Such a classical analog of Haldane phase has been theorectically proposed for the disordered flat (DOF) phase in crystal surfaces described in ref 15. Here the DBC chains present an experimental example of the analog of Haldane phase. The most intriguing topological characteristic of the Haldane phase, that is, the hidden antiparallel order, is preserved in the DBC chains owing to the fact that the symmetry responsible for the hidden order is similarly presented in the DBC chains. The hidden order in a spin-1 Haldane chain is protected by a D2 (equal to Z2 × Z2) symmetry,12−17 which is a dihedral group of π rotations of the spin about two orthogonal axes. This hidden order in the DBC chains is also protected by a Z2 × Z2 symmetry which comes from the product of the flip degeneracy of two helicene parts. Besides the hidden antiparallel order, another key topological character of the Haldane phase, that is, the doubly degenerate nearly free edge states (either + or − ), can also be evidenced at the ending helicene parts of the DBC molecular chains (see Supporting Information, Figure S4). This is not surprising since the DBC chains in the Haldane-like phase inherit all topological characters including the edge states from the VBS state of a quantum Haldane chain. In addition to the above-mentioned isolated molecular chains, we also observe molecular chains in 2D arrays. As we shown in Figure 2, at a coverage of 0.9 ML, all DBC molecules become achiral, and the 2D domain consisting of dense pack of zigzag molecular chains in which achiral A and A′ molecules appears alternately in an antiparallel manner. In each chain the adjacent molecules are also coupled via homochiral coupling

METHODS Experimental Methods. The experiment was performed with a low-temperature STM (Omicron GmbH) with a base pressure of 5 × 10−11 mbar. The Cu(111) single crystal was cleaned by repeated cycles of Ar+ sputtering and annealing (to 700 K) to obtain atomically flat clean surface. DBC molecules (crystalline powder, purity >98%, purchased from Tokyo Chemical Industry Co., Ltd.) are evaporated from a quartz crucible heated to 105 °C in an organic evaporator (OME, MBE-Komponenten GmbH) with a deposition rate of 0.03 ML/min. Here 1 ML refers to the surface is fully covered by one layer of closest-packed DBC molecules. The Cu(111) surface was held at room temperature during the evaporation. All the STM images are acquired with constant current mode under LHe (5 K) temperature. An electrochemical etched and well-cleaned tungsten tip is used. The polarity of the applied voltage refers to the sample bias with respect to the tip. DFT Calculations. The first-principles simulations of the DBC molecules adsorbed on Cu(111) and their dimers are based on the DFT and implemented in the VASP package.24,25 The generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE)26 and projector augmented wave (PAW) potentials are used. In all computations, the kinetic energy cutoff is set to be 520 eV in the plane-wave expansion. All the geometry structures are fully relaxed 6520


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ACS Nano until total energy and forces are converged to 10−5 eV and 0.02 eV/Å, respectively. In order to calculate the total energies of free DBC molecules and their dimers, we place them in a 30 Å × 30 Å × 30 Å grid, which is big enough to avoid interaction between two adjacent periodic images, and use only Γ point for k-point grid. To simulate single DBC adsorption on Cu(111) surface, we adopted a repeated slab geometry with three layers of copper and a large unit cell of 17.96 Å × 17.77 Å × 22.19 Å, and a denser k-point grid of 3 × 3 × 1 is used. Effect of van der Waals (vdW) interaction is accounted for by using the vdW-DF functional.27,28 The STM image is simulated using an isovalue image based on Tersoff and Hamann’s formula and its extension.29

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ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.8b00146. Supplemental STM data and theoretical calculations; convergence tests of the calculations; mapping between the spin-1 chain and the DBC molecular chain (PDF)

AUTHOR INFORMATION Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Aidi Zhao: 0000-0002-6546-4610 Ruiqi Zhang: 0000-0002-7820-6020 Bin Li: 0000-0003-0115-4047 Jinlong Yang: 0000-0002-5651-5340 Bing Wang: 0000-0002-2953-2196 Author Contributions

A.Z. and B.W. conceived the project and designed the experiments. J.D., A.Z., and H.S. performed the STM experiments. A.Z. and J.D. analyzed the STM results. R.Z., B.L., and J.Y. performed theoretical calculations. A.Z. and B.L. wrote the manuscript. All the authors discussed the results and commented on the manuscript. Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by the National Key R&D Program of China (grant nos. 2016YFA0200603, 2017YFA0204904), the “Strategic Priority Research Program (B)” of CAS (XDB01020100), the National Natural Science Foundation of China (grant nos. 91321309, 21473174, and 21421063), the Anhui Initiative in Quantum Information Technologies, and the Fundamental Research Funds for the Central Universities (grant nos. WK2060190084, WK2340000074). A.Z. acknowledges a fellowship from the Youth Innovation Promotion Association of CAS (2011322). REFERENCES (1) Gupta, S.; Saxena, A. A Topological Twist on Materials Science. MRS Bull. 2014, 39, 265−279. (2) Lukin, O.; Vögtle, F. Knotting and Threading of Molecules: Chemistry and Chirality of Molecular Knots and Their Assemblies. Angew. Chem., Int. Ed. 2005, 44, 1456−1477. (3) Han, D.; Pal, S.; Liu, Y.; Yan, H. Folding and Cutting DNA into Reconfigurable Topological Nanostructures. Nat. Nanotechnol. 2010, 5, 712−717. 6521


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ACS Nano (25) Makov, G.; Payne, M. C. Periodic Boundary Conditions in ab initio Calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 1995, 51, 4014−4022. (26) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (27) Dion, M.; Rydberg, H.; Schroder, E.; Langreth, D. C.; Lundqvist, B. I. Van der Waals Density Functional for General Geometries. Phys. Rev. Lett. 2004, 92, 246401. (28) Klimeš, J.; Bowler, D. R.; Michaelides, A. Van der Waals Density Functionals Applied to Solids. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83, 195131. (29) Tersoff, J.; Hamann, D. R. Theory of the Scanning Tunneling Microscope. Phys. Rev. B: Condens. Matter Mater. Phys. 1985, 31, 805−813.

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Hidden Order and Haldane-Like Phase in Molecular Chains

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