A topological FB, resembling a Landau level, presents an exotic Bloch state but without band dispersion. It arises from destructive interference (phase cancelation) of wave functions1–3, differing from topologically trivial FBs of highly localized atomic orbitals, such as f-orbitals4 and dangling bonds5, and the FBs resulted from Moiré band folding of twisted bilayer graphene6. The phase cancelation renders the FB to be inherently topologically nontrivial without band inversion7–9. On the other hand, different from a topological insulator or semimetal of single-particle physics, the completely quenched electron kinetic energy in a FB magnifies the electron-electron interaction, leading to a range of many-body quantum phases when it is partially occupied, such as fractional quantum Hall effect10, Wigner crystallization11, ferromagnetism3,12, superconductivity13 and excitonic insulator state14. Recent discovery of superconductivity in twisted bilayer graphene has further boosted the interest in FBs15.
Theoretically, lattice models of desired lattice and/or orbital symmetries have been shown to inherently exhibit a FB, based on which various 2D FB-materials have been predicted from first-principles. These include 2D metalorganic frameworks (MOFs)16–19, covalent organic frameworks (COFs)12,20,21 and inorganic 2D material22. Experimentally, some indicative signatures have been attributed to FB in thin films23–28 with a layered structure which contains one atomic layer manifesting a 2D FB lattice model, such as Kagome lattice. But in such systems the FB is inevitably overlapping with many dispersive bands from other atomic layers, and/or was not truly flat in the whole BZ. In general, experimental realization of topological FBs has been very challenging because of lack of FB materials, and especially remained elusive in the ideal platform of monolayer materials where they have been originally proposed based on destructive quantum interference in 2D lattice models. To date, there is no monolayer material that has been synthesized to enable direct observation of FB. The closest is a recent experiment that has successfully grown π-conjugated polymer monolayers of tribromotrioxaazatriangulene and tribromotrioxoazatriangulene on Au(111) substrate29, enabling a clear observation of Dirac bands by ARPES. However, the FB, which was thought to be present with a Kagome sublattice29, cannot be actually accessed or seen in this organic monolayer because it is located ~ 1.0 eV above Fermi level21.
Here, we report direct observation of topological FB in a self-assembled monolayer of 2D H-bond HOF of THPB on Au(111) surface. Formation of mesoscale, uniform domains of THPB are seen by STM/STS, whose long-range order and lattice symmetry are further confirmed by low-energy electron diffraction (LEED). Remarkably, a perfect FB over the whole BZ is clearly observed by ARPES. Interestingly, DFT calculations reveal that the FB arises from a hidden electronic breathing-Kagome sublattice of corner benzene rings (CBRs) of THPB encoded in the HOF, and hence topological non-trivial, but atomically the THPB molecules sit in a triangle lattice while their three CBRs accidentally form a perfect Kagome lattice without breathing bonds. The electronic breathing effect is shown to be caused by different inter-CBR hopping mediated by H-bonds versus covalent bonds. Furthermore, the most salient features of H-bonds are characterized by high-resolution STM/STS, Raman spectroscopy and DFT calculations.
Experimental growth and structural characterization of mesoscale, highly-ordered and uniform 2D HOF of THPB
Instead of realizing FB-lattices using candidates of MOF16–19 and COFs12,20,21 predicted by existing theory, we have taken a different approach to grow HOFs, to take the advantage of H-bonds which are weaker but more flexible than the organo-metallic and covalent bonds, in order to assemble large-scale monolayer structures of high uniformity. Here, we use THPB as a model molecule which are deposited onto Au(111) substrate at room temperature30,31 (see Methods for sample preparation). The H-bond assisted self-assembly turned out to be very successful as evidenced in Fig. 1.
Figure 1a and 1b show large-scaled STM images of 2D crystalline domains of THPB monolayer film at the coverage of 0.75 ML, where THPB molecules aggregate into a triangle lattice with long-range order. In Fig. 1b, the crystalline orientations of Au\(\left[1\stackrel{-}{1}0\right]\) and \(\left[11\stackrel{-}{2}\right]\) are determined by visualizing the well-known herringbone reconstruction of Au(111) surface32. Domain walls are also observed with adjacent domains being mirror-symmetric with each other (see Fig. S1). The THPB-HOF lattices have been fabricated successfully over the entire substrate surface and remain intact across surface steps (see Fig. 1a and 1b).
High-resolution STM image (Fig. 1c) distinguishes clearly each individual THPB molecule consisting of three bright protrusions corresponding to three CBRs, and reveals the self-assembled trigonal THPB lattice having a lattice constant of 14.6 ± 0.2 Å. Accordingly, a schematic lattice model is constructed as shown in Fig. 1d. The THPB molecules aggregate via formation of three H-bonds, rotated by 120° with each other, between the hydroxyl groups at the corner of THPB. The orientation of THPB-HOF lattice is determined whose lattice vectors a1 (a2) are aligned ~ 20º from the close-packed \(\left[1\stackrel{-}{1}0\right]\) direction of Au surface. Consequently, the BZ of HOF lattice and that of Au(111) surface rotate away from each other by ~ 20º, as shown in Fig. 1e; the former is also ~ 5 times smaller than the latter. These relations are used for analyzing their respective ARPES spectra later.
The long-range order of THPB-HOF lattice is further confirmed by LEED, displaying clearly diffraction spots from a periodic superstructure (Fig. 1g). It confirms again the HOF domains are aligned in the same orientation, with a trigonal lattice rotated by 20° from that of the Au(111) surface (Fig. 1f). The lattice constant of HOF is extracted to be ~ 1.5 nm from LEED, in very good agreement with STM. These findings demonstrate that epitaxial growth of 2D HOFs offers a viable approach to synthesize organic 2D materials, especially monolayer HOFs with desirable electronic properties, such as the FB as demonstrated below.
ARPES observation of flat band
The mesoscale size and mono-orientation of 2D THPB-HOF has enabled the characterization of its band structure by ARPES. As a reference, the ARPES of the bare Au(111) surface was measured first (Fig. 2a). The well-known Shockley surface states with a parabolic valley at -0.5 eV are clearly observed. In addition, the parabolic Au surface sp band having the bottom of valley at ~ -3.6 eV and some bulk bands lying at the lower energies are also visible, in good agreement with previous reports33,34. The d band of Au locates below − 3.8 eV.
We have grown 2D THPB-HOFs from ~ 0.5 monolayer (ML) to nearly-full coverage on Au(111) surface with their long-range order all confirmed by STM and LEED. Figure 2b shows the ARPES measured from one of the 0.5 ML samples, along the KAu-Г-KAu direction of the Au(111) BZ. Remarkably, a perfect FB can be clearly seen at the energy of -2.62 eV. The Au Shockley surface state is no longer observable upon molecular coverage, while its sp surface bands and bulk d bands remain visible but become weaker. The FB is more prominent in the second-derivative intensity plot (middle panel of Fig. 2b), which gives rise to a distinct peak in the density of state (DOS) plot (right). The position of FB at -2.62 eV provides an indirect measure of the bandgap for the HOF lattice to be 5.24 eV, as shown in Fig. 2c. Considering Au-HOF forming a typical metal-semiconductor heterojunction, the Fermi level of Au is aligned with the middle-gap position of HOF. Therefore, the FB band, which is the valence band maximum (VBM) of HOF, appears below the Au Fermi level at an energy equaling to half of the gap.
To confirm the FB exists in the whole 2D BZ, we conduct low-temperature ARPES measurement at 12 K on a sample of nearly-full coverage of THPB-HOF. The constant-energy contour (CEC) at -2.67 eV is shown in Fig. 2d, which signifies the presence of a FB. Besides the circular Au sp band appearing near the zone boundary, a broad hexagonal ring is visible around the zone center, indicating the existence of FB over the whole first BZ of HOF.
Furthermore, to reveal the truly flatness of FB, three line-cuts are taken along momentum paths of Γ-KHOF, Γ-KAu and MHOF-Γ-MHOF, as indicated by yellow-black dashed lines in Fig. 2d. The cut 1 (Fig. 2e) and 2 (Fig. 2f) are taken with the energies from − 2.2 to -3.4 eV. Two bands can be distinguished in both intensity (left panel) and second-derivative (right panel) plots: a perfectly FB (band 1) in touch with a weakly dispersive band (band 2) at the Γ point. Note that there is also a parabolic Au surface sp band intersects with these two HOF bands. The spectrum of cut 3 is shown in Fig. 2g, and interestingly, a third strongly dispersive band shows up below the above-mentioned two bands. This third band is further confirmed by the energy distribution curves (EDC) measured from − 0.39 to 0.39 Å−1 (Fig. 2h). By deconvoluting these three bands, the FB energy is found at -2.57 eV, slightly different from its apparent position of -2.62 eV in Fig. 2b. Overall, the band dispersions are clearer in Fig. 2g than those in Fig. 2e and 2f, partly because the cut 3 is outside the circular Au sp band at the zone boundary, as shown in Fig. 2d. Consequently, the Au sp band sits above without overlapping with the FB. More line-cut spectra are available in SI, Fig. S2.
Origin of topological FBs from a hidden breathing-Kagome sublattice in THPB-HOF.
Taking the whole THPB as one molecular basis, the HOF has an apparent triangle lattice, as shown in Fig. 1d, which is not expected to host FB. In order to reveal the origin of the observed FB by ARPES, we have performed DFT calculations. The optimized lattice structure and the calculated band structure are shown in Fig. 3a and 3b, respectively. Indeed, Fig. 3b shows that the THPB-HOF is a semiconductor having a FB below the Fermi level as the VBM, consistent with the experimental observation (see Fig. 2b and 2c). We note the calculated gap of ~ 3.0 eV from local-density-approximation (LDA) is corrected to ~ 4.0 eV by Heyd-Scuseria-Ernzerhof (HSE) functional, which is ~ 1.0 eV smaller than the experimentally derived value in Fig. 2b. This difference is reasonable considering there could be some charge transfer from Au surface to HOF to shift the Fermi level of HOF above its mid-gap position so that the FB would appear farther below the Au Fermi surface and/or that the HSE gap can still be an underestimation35.
Figure 3b also shows that the FB touches with a slightly dispersive band below, as observed in ARPES. A checkerboard lattice could have such a two-bands configuration36, but the THPB-HOF lattice does not have a square symmetry. So, one more dispersive band below, as also seen in ARPES, is included for the analysis, and we realized that it resembles the typical three-bands structure of a breathing-Kagome lattice which has a trigonal lattice symmetry as the HOF has37. However, a quick inspection of lattice structure (Fig. 3b) finds no breathing bonds. To resolve this inconsistency, we plot the charge density of the designated three bands overlaid on the lattice in Fig. 3a, which are mainly contributed by C and O pz orbitals (Fig. S4). Then, we realized that a sublattice of effectively breathing-Kagome type is formed by three CBRs of THPB molecules via two different inter-CBR hopping, namely the H-bonds mediated by O/H atoms versus the covalent bonds mediated by the center benzene ring in THPB. Consequently, an interesting scenario of “a breathing-Kagome lattice without breathing” is accomplished, with the effect of breathing achieved electronically by different lattice hopping strength via H-bond (tH) and covalent bond (tC), as indicated in Fig. 3a and illustrated in Fig. 3c.
To further confirm the above identification of FB, we have fit the three DFT-LDA bands of interest with a tight-binding (TB) breathing-Kagome lattice Hamiltonian, as shown in Fig. 3d. One sees that the TB bands (red-dotted line) agree well with the DFT bands (blue solid lines) using only two fitting parameters of tH = 0.05 eV and tC = 0.26 eV, and the former is much smaller than the latter indicating a strong electronic breathing effect. Using the TB model, we also calculated the compact localized state (CLS) and noncontractible loop state (NLS) in real space to illustrate the nontrivial FB topology, which is confirmed by calculation of topological invariant (see Fig. S4). Moreover, we made a Wannier fitting of the DFT-LDA bands (cyan-dotted lines in Fig. 3d), and simulated the ARPES spectra using a long pulse (Fig. 3e) to mimic the continuous light source used in experiments (see Methods), as shown in Fig. 3f along the K-Γ-K and M-Γ-M paths in the BZ of THPB-HOF. The Wannier band dispersions along three paths, Γ to KHOF, Γ to KAu and MHOF-ΓHOF-MHOF are also calculated as black-dashed lines overlaid on the experimental spectra in Fig. 2e-2g, respectively. We note that we used DFT-LDA results for fitting the three breathing-Kagome bands because they agree better with experiments, possibly because LDA gives a better description of H-bonds, i.e. tH. Qualitatively, it does not affect the assessment of the origin of FB.
Further experimental evidence of H-bond and breathing Kagome lattice
To better resolve the H-bond, we performed differential conductance (dI/dV) mapping along with STM imaging, to visualize the local charge DOS. Figure 4a and 4b shows the topographic STM image and the dI/dV image, respectively. One clearly sees that the local DOS of covalent C-C bonds bridging the CBRs within a THBP molecule is much higher than that of H-bonds bridging the CBRs in between the THBP molecules. This indicates that the sublattice of all CBRs forms an effective breathing-Kagome hopping pattern, because the intra-THBP CBR-CBR hopping (tC in Fig. 4b) via covalent bonds is much stronger than the inter-THBP CBR-CBR hopping (tH in Fig. 4b) via H-bonds, even though the measured intra-THBP CBR-CBR distance (dC = 7.4 Å) is about the same as the inter-THBP CBR-CBR distance (dH = 7.2 Å), as show in Fig. 4a. This leads to a breathing-Kagome band structure with a high degree of breathing of electronic hopping but without a breathing atomic structure. The DFT-LDA calculated inter-THPB distance is 14.7 Å, in excellent agreement with the experimental value of 14.6 Å; the H-bond length is on average ~ 1.65 Å, slightly shorter than that in water of 1.97 Å38.
Further evidence for the presence of H-bonds is collected from the in-situ Raman spectroscopic measurement (see Methods). Figure 4c shows the spectrum under a 532 nm laser excitation. Above 1000 cm− 1, there are clearly four prominent Raman peaks located at 1495, 2308, 3110 and 3225 cm− 1, respectively. To assign their origin, we performed DFT calculations of the off-resonant Raman spectrum of THPB-HOF monolayer, as shown in Fig. 4d and S7. One sees that the calculation reproduces three experimental Raman peaks (1594, 3135 and 3474 cm− 1), except the one at 2308 cm− 1. The vibration modes of the three reproduced peaks are examined (see Fig. S5), and their atom-resolved contributions agree with the results of projected phonon DOS (SI, Fig. S6). The peak at 3474 cm− 1 is identified from the H-O vibration, whose position is indicative of the H-bond strength39. To confirm this, we also calculated the Raman spectrum of the THPB-HOF under a 2% biaxial tensile strain (see Fig. S7). The position of the H-O peak of the strained HOF changes to 3584 cm− 1, indicating a blueshift of 110 cm− 1 due to the weakened H-bonds, while the other peaks remain almost intact. This allows us to assign the experimental peak at 3225 cm− 1 to the H-O vibration, which is redshifted from that in water at ~ 3400 cm− 1 40. It suggests that the H-bond strength in the THPB-HOF is stronger than that in water, consistent with the H-bond length difference mentioned above.
In conclusion, we have observed for the first time a topological FB arising from single atomic-layer 2D materials of THPB-HOF. The successful fabrication of self-assembled mesoscale, highly-ordered and uniform HOF films has enabled the STM, APRES and LEED characterization. DFT calculations have revealed that the FB is originated from electronically a hidden breathing-Kagome lattice without structurally breathing bonds. Our findings pave the way to future realization of 2D topological and FB materials by the demonstrated approach of self-assembly of HOFs, for which a wide range of possible molecular precursors and different substrates can be explored.