Interface-driven formation of a two-dimensional dodecagonal fullerene quasicrystal

Abstract

Since their discovery, quasicrystals have attracted continuous research interest due to their unique structural and physical properties. Recently, it was demonstrated that dodecagonal quasicrystals could be used as bandgap materials in next-generation photonic devices. However, a full understanding of the formation mechanism of quasicrystals is necessary to control their physical properties. Here we report the formation of a two-dimensional dodecagonal fullerene quasicrystal on a Pt₃Ti(111) surface, which can be described in terms of a square-triangle tiling. Employing density functional theory calculations, we identify the complex adsorption energy landscape of the Pt-terminated Pt₃Ti surface that is responsible for the quasicrystal formation. We demonstrate the presence of quasicrystal-specific phason strain, which provides the degree of freedom required to accommodate the quasicrystalline structure on the periodic substrate. Our results reveal detailed insight into an interface-driven formation mechanism and open the way to the creation of tailored fullerene quasicrystals with specific physical properties.

Figure 1. Analysis of a self-assembled monolayer of fullerenes on 2Pt–Pt₃Ti(111).

(a) Low-temperature UHV-STM image of a fullerene monolayer deposited on a Pt₃Ti(111) single crystal terminated by two layers of Pt (2Pt–Pt₃Ti(111)) showing two differently oriented hexagonal (Hex1, Hex2) domains and one QC domain. Within the latter domain, two dodecagons with their inner hexagons rotated by ∼30° are marked. The indicated orientation of the substrate is determined directly from the atomically resolved 2Pt–Pt₃Ti(111) surface (scale bar, 5 nm; U_set=−2.03 V, I_set=0.47 nA, 77 K). (b,c) FFT of the STM image and LEED pattern (energy: 19.5 eV), respectively, showing the spots of the two hexagonal domains (red and green circles) and the quasicrystalline domain with 12-fold symmetry (yellow circles).

Figure 2. Dodecagonal square-triangle tiling measured by STM.

(a) High-resolution UHV-STM image of C₆₀ on 2Pt–Pt₃Ti(111) (scale bar, 3 nm; U_set=−2.03 V, I_set=0.47 nA, 77 K). The HOMO of fullerenes facing the surface with a hexagon is imaged under these conditions and the characteristic dip in the middle of the HOMO is clearly resolved. One dodecagon and the local structures reproduced in c,d are indicated in white. (b) Square–triangle tiling extracted from a, with colour-coded decomposition into different types of approximants, see text. (c–e) Three types of local vertex configurations around one fullerene (marked green) (scale bar, 1 nm): (c) (3².4.3.4), (d) (3³.4²), (e) (3⁶). (f) FFT of the STM image with 12-fold symmetry.

Figure 3. Adsorption configuration of fullerenes on 2Pt–Pt₃Ti(111).

(a) High-resolution UHV STM image of C₆₀ on 2Pt–Pt₃Ti(111) (scale bar, 1 nm; U_set=+2.22 V, I_set=2.9 nA, 77 K, slightly low pass filtered). The three-lobe structure of the unoccupied molecular orbitals of fullerenes facing the surface with a hexagon is clearly visible. (b) Schematic diagram indicating nine positions in the (1 × 1) 2Pt–Pt₃Ti(111) surface unit cell considered for the adsorption of fullerenes in DFT calculations using a (3 × 3) supercell (Supplementary Fig. 5). (c–f) Schematic top view of a fullerene adsorbed on 2Pt–Pt₃Ti(111) in bridge1, bridge2, top_Ti and bridge3 positions, respectively.

Figure 4. Proposed adsorption model of fullerenes on 2Pt–Pt₃Ti(111).

(a) High-resolution UHV STM image of C₆₀ on 2Pt–Pt₃Ti(111) (scale bar, 2 nm; U_set=+2.22 V, I_set=2.9 nA, 77 K, slightly low pass filtered). (b) Schematic diagram showing the local 3².4.3.4 structure assuming adsorption only on bridge1 positions of an ideal 2Pt–Pt₃Ti(111) surface.