Tuning two-dimensional band structure of Cu(111) surface-state electrons that interplay with artificial supramolecular architectures

We report on the modulation of two-dimensional (2D) bands of Cu(111) surface-state electrons by three isostructural supramolecular honeycomb architectures with different periodicity or constituent molecules. Using Fourier-transformed scanning tunneling spectroscopy and model calculations, we resolved the 2D band structures and found that the intrinsic surface-state band is split into discrete bands. The band characteristics including band gap, band bottom, and bandwidth are controlled by the network unit cell size and the nature of the molecule-surface interaction. In particular, Dirac cones emerge where the second and third bands meet at the $K$ points of the Brillouin zone of the supramolecular lattice.

Figure 1

(a)–(c) STM topographic images (0.5 nA; 1.0 V) showing three isostructural supramolecular honeycomb networks. Insets: chemical structure of the molecule used to assemble the structures. (d) Structural model of the networks. (e) Effective potential seen by a surface state electron as calculated by DFT. (f) dI/dV spectra recorded at the center of four different pores in S1 (top), S2 (middle), and S3 (bottom) structures.

Figure 2

(a)–(c) LDOS maps of S1 (25 nm × 25 nm), S2 (60 nm × 60 nm), and S3 (25 nm × 25 nm) acquired at the defined energies. (d), (e) FT-LDOS maps of S1 (10 nm${}^{-1}$ × 10 nm${}^{-1}$) and S2 (7 nm${}^{-1}$ × 7 nm${}^{-1}$) at nine incremental energies.

Figure 3

FT-LDOS calculations for (a) a 2D electron gas, (b) the S1 network, and (c) the S2 network. All plots are along the ΓK direction.

Figure 4

(a)–(c) Power spectral functions of 2DEG of S1, S2 (the supramolecular lattice spots are subtracted for clarity), and clean Cu(111) from top to bottom. Black dotted lines, simulated first band; red dotted lines, dispersion of Cu(111) surface state. (d) Experimental (black curve) and simulated (DFT-estimated potential) TDOS of S1 (top), S2(middle), and S3(bottom). (e), (f) Experimental (left) and simulated (right) unit-cell-averaged LDOS maps of S2 (8 nm × 8 nm) and S3 (5 nm × 5 nm) at the given energies. The inserted model is a guide for the eye.

Figure 5

(a)–(c) Calculated (DFT-estimated potential) band gaps as a function of the unit cell size ($L$) of 14 supramolecular networks. Different values of $L$ correspond to different numbers (n) of benzene rings in the arms of the network. (d) Calculated band gaps and (e) Dirac point energy and carrier velocity of 14 supramolecular networks. The black (red) squares denote the weak (strong) potential. The inset in the upper panel shows the magnified view of the red circle in S3. The dashed line in the low panel indicates the result obtained from $k·p$ theory.