Growth of Mesoscale Ordered Two-Dimensional Hydrogen-Bond Organic Framework with the Observation of Flat Band

Flat bands (FBs), presenting a strongly interacting quantum system, have drawn increasing interest recently. However, experimental growth and synthesis of FB materials have been challenging and have remained elusive for the ideal form of monolayer materials where the FB arises from destructive quantum interference as predicted in 2D lattice models. Here, we report surface growth of a self-assembled monolayer of 2D hydrogen-bond (H-bond) organic frameworks (HOFs) of 1,3,5-tris(4-hydroxyphenyl)benzene (THPB) on Au(111) substrate and the observation of FB. High-resolution scanning tunneling microscopy or spectroscopy shows mesoscale, highly ordered, and uniform THPB HOF domains, while angle-resolved photoemission spectroscopy highlights a FB over the whole Brillouin zone. Density-functional-theory calculations and analyses reveal that the observed topological FB arises from a hidden electronic breathing-kagome lattice without atomically breathing bonds. Our findings demonstrate that self-assembly of HOFs provides a viable approach for synthesis of 2D organic topological materials, paving the way to explore many-body quantum states of topological FBs.

Figure 1

(a) and (b) Large-scale topographic STM images ($I_t=200\mathrm{pA}$, $V_b=-0.5\mathrm{V}$). The orientation of HOF is determined whose lattice vector is aligned $\sim 10º$ away from the $\mathrm{Au}[11\overline{2}]$ direction. (c) Close-up STM image showing a trigonal lattice with a lattice constant of $14.6\pm 0.2\AA$, averaged from line profiles. The dashed hexagon marks the unit cell of Au lattice showing the close-packed $[1\overline{1}0]$ direction which has a 20° angle with the THPB HOF lattice vectors. (d) Schematic lattice model indicating three H bonds in between THPB. (e) The relationship between the BZ of Au(111) surface and of HOF. (f) and (g) LEED patterns of clean and HOF-covered Au(111) surface taken at the energies of 100 and 25 eV, respectively. Their reciprocal lattices are marked with white dashed hexagons.

Figure 2

(a) The photoemission intensity plot of $E_B\text{−}{k}_x$ cut along the $K_{\mathrm{Au}}\text{−}\mathrm{\Gamma }\text{−}{K}_{\mathrm{Au}}$ direction at $k_y=0$ (left) and the integrated DOS from ARPES (right), taken from the bare Au(111) surface. $K_{\mathrm{Au}}$ is the $K$ point of Au(111) surface BZ. (b) The ARPES spectra (left), the second-derivative plot (middle), and the integrated DOS from the ARPES showing a peak at the FB energy of $-2.62\mathrm{eV}$ (right), taken along $\mathrm{\Gamma }\text{−}{K}_{\mathrm{Au}}$ direction from a 0.5 ML THPB film.

Figure 3

(a) The CEC measured at $-2.67\mathrm{eV}$ and 12 K. The states of Au $sp$ bands are clearly visible near the BZ boundary (half circle). The yellow dashed lines indicate three line cuts taken for ARPES measurements in (b)–(d). (b) High-resolution ARPES (left) and second-derivative (right) plots measured at 12 K from cut 1 along the $\mathrm{\Gamma }\text{−}{K}_{\mathrm{HOF}}$ direction as marked in (a). (c) Same as (b) for cut 2 along $\mathrm{\Gamma }\text{−}{K}_{\mathrm{Au}}$. (d) Same as (b) for cut 3 along $M_{\mathrm{HOF}}\text{−}{\mathrm{\Gamma }}_{\mathrm{HOF}}\text{−}{M}_{\mathrm{HOF}}$. $K_{\mathrm{HOF}}$, ${\mathrm{\Gamma }}_{\mathrm{HOF}}$, and $M_{\mathrm{HOF}}$ are special $k$ points in the BZ of THPB HOF. The dashed black lines are the DFT LDA Wannier bands superimposed on the experimental spectra. (e) The EDC of (d). The blue and black dotted lines denote the peak positions obtained by Gaussian fitting, representing bands 1, 2, and 3. The FB (band 1) locates at $-2.57\mathrm{eV}$.

Figure 4

(a) The optimized lattice structure overlaid with partial charge density derived from the top three valence bands belonging to the breathing-kagome lattice formed by CBRs of THPB. The brown or orange, red, and pink balls represent C, O, and H atoms, respectively. The charge density is plotted using an isosurface of $0.002\mathrm{eV}/{\AA }^3$. (b) The LDA band structure (blue dashed lines) with a gap corrected by HSE functional (black solid lines). (c) Illustration of an electronic breathing-kagome lattice formed by different hopping strength of $t_{\mathrm{H}}$ via H bonds versus $t_{\mathrm{C}}$ via covalent bonds [see also (a)], as if there were breathing bonds of different lengths. (d) The fit of the top three DFT valence bands (blue solid lines) by the TB breathing-kagome lattice model (red dotted lines) and Wannier bases (cyan dotted lines). (e) Topographic STM image and (f) differential conductance ($dI/dV$) mapping taken simultaneously at $+600\mathrm{meV}$, using $V_B=-200\mathrm{mV}$, $I_T=300\mathrm{pA}$, and a bias modulation of 5 mV.