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 ACS Nano, Just Accepted Manuscript • Publication Date (Web): 19 Jun 2018 Downloaded from http://pubs.acs.org on June 19, 2018

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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 Hefei National laboratory for Physical sciences at the Microscale and Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, No. 96 Jinzhai Road, Hefei, Anhui 230026, P. R. China. *E-mail: [email protected]; *E-mail: [email protected] Keywords: STM, molecular chain, molecular switch, aromatic coupling, topological order

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 (DBC) 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 inter-spin antiferromagnetic coupling with intermolecular homochiral coupling.

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The discovery of the molecular analog of topological matters may inspire the search of molecular architectures with nontrivial topological properties.

Engineering molecular architectures with desired topological properties is formidable challenging in chemistry. In the past years, the synthesis of complex molecular knots and links of specific topologies,1,2 for examples, 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 win 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 Wen11 and the relevant symmetry protection was interpreted.12,13 The most striking topological character is that even though there is 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 exist a non-local 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 DBC


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molecules adsorbed on Cu(111) exhibit rich topological morphologies at different coverages owing to the interplay between intermlecular interactions and intramolecular conformational changes. At a coverage of 0.6 ML, the DBC molecules self-assemble into molecular chains possessing topological characters similar to the 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.

Results and Discussion 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 non-planar 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 Fig. 1. The chemical structure of DBC can be viewed as the combination of two chiral [4]Helicene ([4H]) molecules with the center-overlapped naphthalene units. [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 upwards or downwards due to the repulsion of the conflicting hydrogen atoms H1 and H2, endowing the molecule with helical chirality (Fig. 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] combinations 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 (Fig. 1d). These conformations can transform into each


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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 Fig. 1b and 1c) 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 (Fig. 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 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, Fig. 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 enatiomers M and P. The convergences of this energy difference with respect to the used basis-set size, kpoint 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 STM images for the four adsorbed conformers are shown in Fig. 1f. The topological properties of each conformers can be directed identified from the contrast of the benzene lobes in STM images, in accordance to Fig. 1e. The energy barrier from the adsorbed M or P to A(A′) is calculated to be ~ 0.40 eV (39 kJ/Mol) (Supporting Information, Fig. 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


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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.

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


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conformers. (f) Theoretically simulated STM images for the four conformers adsorbed on Cu(111). 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). Fig. 2a to 2d shows the coverage dependence of the morphology of DBC on Cu(111). All observable conformers for each coverage are listed below which can be readily identified by comparing their STM images to the simulated STM images in Fig. 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 (Fig. 2(a)). When the coverage is elevated to about 0.6 ML, the DBC molecules are self-assembled into quasi-1D molecular chains with serpentine arrangement (Fig. 2(b)). 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 (Fig. 2(c)). 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 molecules are fairly low which can be readily overcome by intermolecular interactions, in consistent with our calculations.


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Among all the morphologies, the molecular chains in Fig. 2b are particular 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 long-range 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-non-switchable molecular chains.

Figure 2. Coverage dependence of the morphology of DBC on Cu(111). (a-d) are STM images of a 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 is fully covered by one layer 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. 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


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investigated the intermolecular interactions in the chains. Figure 3a shows a large-area STM image of a number of quasi-1D molecular chains. The inter-chain and intermolecular distances are about 1.6 nm 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, i.e., the homochiral aromatic coupling, owing to the chiral nature of the helicene parts. In Fig. 3b and 3d, 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 due to the much higher energy due to steric repulsion effect. This is a typical example of chiral recognition. Such a homochiral coupling rule has been previously demonstrated to play a key role in constructing chiral supramolecular architectures.23 Following the symbolic representation in Fig. 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 valance bonds as indicated by the blue lines in Fig. 3c and 3e.


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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 (monolayer). 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 intramolecular coupling. The coupling is via aromatic interaction of the helicene parts and the interacting benzene lobes from each helicene parts are shifted upwards (+) and downwards (−). In order to understand and validate the experimental results, especially that the homochiral aromatic coupling is the energy-favorable 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, Fig. S2). Based on the symmetry, all of these


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configurations can be transferred into the twelve 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. So the DBC molecules should prefer interacting via homochiral intermolecular coupling. For the dimers in the eight types of intermolecular helical coupling motifs in Fig. 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 xyplane, 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 Å 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. Table 1. Conformations, intermolecular distance (Dmole), total energy (Edimer) and interaction energy related to respective molecules (Eint) of various DBC dimers in gas phase.

Conformation of dimers dimers

Symbolic representation

Coupling motif

A′′ A (A A′′)

(− −) (+ +) or (+ +) (− −)

homochiral

Relative shift along molecular long axis

Dmole

Edimer

(Å)

(eV)

(eV)

(kJ/Mol)

No

10.90

−512.169

−0.137

−13.2

Yes

10.00

−512.217

−0.185

−17.8


Eint

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A A (A′′ A′′)

(− −) (− −) or (+ +) (+ +)

heterochiral

A M (P A)

(+ +) (− +) or (+ −) (+ +)

homochiral

A′′ M (P A′′)

(− −) (− +) or (+ −) (− −)

heterochiral

M M (P P)

(− +) (− +) or (+ −) (+ −)

homochiral

(− +) (+ −) or (+ −) (− +)

heterochiral

M P (P M)

No

11.40

−512.112

−0.080

−7.7

Yes

10.96

−512.130

−0.098

−9.5

No

10.51

−512.423

−0.170

−16.3

Yes

10.07

−512.486

−0.233

−21.0

No

10.59

−512.368

−0.115

−11.1

Yes

10.24

−512.417

−0.164

−16.3

No

10.20

−512.644

−0.170

−16.4

Yes

10.26

−512.646

−0.172

−16.5

No

10.86

−512.561

−0.087

−8.4

Yes

10.92

−512.583

−0.109

−10.5

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 Fig. 4a and 4c, 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 showing a hidden antiparallel order across over the intercalated M or P molecules.


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Such a hidden antiparallel order has not been observed in any known molecular chains even for those conformation-switchable molecules with only one chiral switch. It should be a specific topological phenomenon for conformation-switchable molecules with two symmetric chiral switches. In Fig. 1 and Fig. 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 Fig. 4b and 4d. Interestingly, we found that the hidden antiparallel order represent 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 Fig. 4b and 4d, we plot the corresponding VBS representation of the two chains in which the upwards and downwards 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.


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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. 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


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Information, Fig. S3) in a so-called valance-bond solid (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 inter-site valance bonds (equivalent to spin singlets) (Fig. 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 valance bond is represented by a pair of coupled opposite signs “ +)(−” and “ −)(+” (Fig. 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, Fig. 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 Fig. 1c and 1e. The DBC molecules then mimic the spin-1 unit of the spin-1 chain in the VBS state. The next step towards the further mimic of the VBS state is to emulate the antiferromagnetic coupling between neighboring S = 1 spins, i.e., the antiparallel valance bonds in the VBS state.14-17 As we show in Fig. 3, the homochiral coupling motifs can also be properly represented by a pair of coupled opposite signs “ +)(−” and “ −)(+”, which resemble the valance bonds in the VBS state in AKLT model.


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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 valance 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 has 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 the Fig. 15 in Ref. 15). 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


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characteristic of the Haldane phase, i.e., 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 (equals 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, i.e. the doubly-degenerate nearlyfree edge states (either + or −), can also be evidenced at the ending helicene parts of the DBC molecular chains (See Supporting Information, Fig. 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 Fig. 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 appear alternately in an antiparallel manner. In each chain the adjacent molecules are also coupled via homochiral coupling with slight vertical shift. Unlike the Haldane-like phase in the isolated molecular chain in Fig. 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, Fig. 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


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to 1 ML can be understood by combining analyses of the steric repulsion effect and the DFT calculations (Supporting Information, Fig. S6).

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 intermlecular 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 suggest 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 examples, 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.

METHODS


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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 are set to be 520 eV in the plane-wave expansion. All the geometry structures are fully relaxed 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 gird, 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


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Waals (vdW) interaction is accounted for by using 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

ASSOCIATED CONTENT Supporting Information Available: Supplemental STM data and theoretical calculations; convergence tests of the calculations; mapping between the spin-1 chain and the DBC molecular chain. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]; *E-mail: [email protected] 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


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This work was supported by the National Key R&D Program of China (Grants nos. 2016YFA0200603, 2017YFA0204904), the “Strategic Priority Research Program (B)” of CAS (XDB01020100), the National Natural Science Foundation of China (Grants nos. 91321309, 21473174, and 21421063), the Anhui Initiative in Quantum Information Technologies, and the Fundamental Research Funds for the Central Universities (Grants 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. (4) Chichak, K. S.; Cantrill, S. J.; Pease, A. R.; Chiu, S.-H.; Cave, G. W. V.; Atwood, J. L.; Stoddart, J. F. Molecular Borromean Rings. Science 2004, 304, 1308–1312. (5) Topological Insulators. In Contemporary Concepts of Condensed Matter Science Vol. 6; Franz, M., Molenkamp, L., Eds.; Elsevier: Oxford, 2013; pp 1–324. (6) Wen, X.-G. Colloquium: Zoo of Quantum-Topological Phases of Matter. Rev. Mod. Phys. 2017, 89, 041004. (7) Süsstrunk R.; Huber, S. D. Observation of Phononic Helical Edge States in a Mechanical Topological Insulator. Science 2015, 349, 47–50.


20

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(8) Nash, L. M.; Kleckner, D.; Read, A.; Vitelli, V.; Turner, A. M.; Irvine, W. T. M. Topological Mechanics of Gyroscopic Metamaterials. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, 14495–14500. (9) Haldane, F. D. Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State. Phys. Rev. Lett. 1983, 50, 1153–1156. (10) “The Nobel Prize in Physics 2016 - Scientific background: Topological phase transitions and topological phases of matter”. Nobelprize.org. Nobel Media AB 2014. Web site. http://www.nobelprize.org/nobel_prizes/physics/laureates/2016/advanced.html (accessed Jan 07, 2018). (11) Gu Z.-C.; Wen, X.-G. Tensor-Entanglement-Filtering Renormalization Approach and Symmetry-Protected Topological Order. Phys. Rev. B 2009, 80, 155131. (12) Pollmann, F.; Turner, A. M.; Berg, E.; Oshikawa, M. Entanglement Spectrum of a Topological Phase in One Dimension. Phys. Rev. B 2010, 81, 064439. (13) Pollmann, F.; Berg, E.; Turner, A. M.; Oshikawa, M. Symmetry Protection of Topological Phases in One-Dimensional Quantum Spin Systems. Phys. Rev. B 2012, 85, 075125. (14) Affleck, I.; Kennedy, T.; Lieb, E. H.; Tasaki, H. Rigorous Results on Valence-Bond Ground States in Antiferromagnets. Phys. Rev. Lett. 1987, 59, 799–802. (15) den Nijs, M.; Rommelse, K. Preroughening Transitions in Crystal Surfaces and ValenceBond Phases in Quantum Spin Chains. Phys. Rev. B 1989, 40, 4709–4734. (16) Kennedy, T.;

Tasaki,

H.

Hidden

Z2×Z2

Symmetry Breaking

in

Haldane-Gap

Antiferromagnets. Phys. Rev. B 1992, 45, 304–307.


21

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(17) Affleck, I. Quantum Spin Chains and the Haldane Gap. J. Phys.: Condens. Matter 1989, 1, 3047–3072. (18) Herbstein, F. H.; Schmidt, G. M. J. The Structure of Overcrowded Aromatic Compounds. Part IV. The crystal Structure of Tetrabenzonaphthalene. J. Chem. Soc. 1954, 0, 3314–3319. (19) Yamaguchi, S.; Swager, T. M. Oxidative Cyclization of Bis(biaryl)acetylenes: Synthesis and Photophysics of Dibenzo[g,p]chrysene-Based Fluorescent Polymers. J. Am. Chem. Soc. 2001, 123, 12087–12088. (20) Nagayama, H.; Varshney, S. K.; Goto, M.; Araoka, F.; Ishikawa, K.; Prasad, V.; Takezoe, H. Spontaneous Deracemization of Disc-Like Molecules in the Columnar Phase. Angew. Chem. Int. Ed. 2010, 49, 445–448. (21) Gingras, M.; Félix, G.; Peresutti, R. One Hundred Years of Helicene Chemistry. Part 2: Stereoselective Syntheses and Chiral Separations of Carbohelicenes. Chem. Soc. Rev. 2013, 42, 1007–1050. (22) Treier, M.; Ruffieux, P.; Gröning, P.; Xiao, S.; Nuckolls, C.; Fasel, R. An Aromatic Coupling Motif for Two-Dimensional Supramolecular Architectures. Chem. Commun. 2008, 4555–4557. (23) Shchyrba, A.; Nguyen, M.-T.; Wäckerlin, C.; Martens, S.; Nowakow-ska, S.; Ivas, T.; Roose, J.; Nijs, T.; Boz, S.; Schär, M.; Stöhr, M.; Pignedoli, C. A.; Thilgen, C.; Diederich, F.; Passerone, D.; Jung, T. A. Chirality Transfer in 1D Self-Assemblies: Influence of HBonding vs Metal Coordination between Dicyano[7]helicene Enantiomers. J. Am. Chem. Soc. 2013, 135, 15270–15273. (24) Kresse, G.; Hafner, J. Ab initio Molecular Dynamics for Liquid Metals. Phys. Rev. B 1993, 47, 558–561.


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(25) Makov, G.; Payne, M. C. Periodic Boundary Conditions in ab initio Calculations. Phys. Rev. B 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 2011, 83, 195131. (29) Tersoff, J.; Hamann, D. R. Theory of the Scanning Tunneling Microscope. Phys. Rev. B 1985, 31, 805–813.

Table of Contents

Quasi-1D molecular chains assembled from conformation-switchable dibenzo[g,p]chrysene (DBC) molecules show hidden antiparallel order analogous to the hidden antiferromagnetic order in the Haldane phase, a known topological phase of spin-1 chains. This is realized by mimicking the spin-1 degree of freedom with the intramolecular helicene chiral switches and by emulating the inter-spin antiferromagnetic coupling with intermolecular homochiral coupling.


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Hidden Order and Haldane-Like Phase in Molecular Chains

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