A surface, located between a vacuum and a crystal substrate, forms a unique two-dimensional (2-D) lattice. By depositing atoms on the surfaces, adsorbate overlayers grow commensurately or incommensurately with respect to the substrate 2-D lattice, depending on a balance between adsorbate-adsorbate and adsorbate-substrate interactions. Such a degree of freedom, being specific to the surface system, results in formation of exotic long-range ordered phases, so-called surface superstructures or Moirè patterns. The unique environment has recently developed new research fields, such as twistronics, and has provided a space to examine interface materials that cannot be explored in a pure 2-D system. One of the notable findings is a long-range ordered layer of copper boride (Cu-Boride) that was grown incommensurately on the (111) surface of a fcc copper crystal. This was unexpected since it has been known that the bulk boron hardly forms compounds with the Group-11 elements. Structural analysis by diffraction unveiled that the 2-D copper boride on Cu(111) was composed of an alternating array of atomic boron and copper chains. This has indicated an intriguing relationship between the 2-D and 1-D atomic structures at the surface. Since the (110) surface of a fcc copper crystal is the well-known 1-D template in surface science, one can expect formation of a unique 1-D system at the B/Cu(110) surface.

In the present research, we experimentally examined a Cu(110) surface after boron deposition and discovered a new ordered phase, 3x’1’ by low-energy electron diffraction[1]. In the following observation by scanning tunneling microscope, we found that the 3x’1’-B/Cu(110) surface has a 1-D atomic structure of Cu-Boride [1,2]. As shown in an STM image of the 3x’1’ phase (Fig. 1(a)), the 1-D structures grow along the [110] axis, separated by trenches. The 1.1-nm trench interval corresponded to 3a_[001], where a_[001] is a size of the Cu(110) unit cell along the [001] axis. This indicates the origin of the three-fold periodicity of the 3x’1’-B phase. The 1-D structure is composed of two types of unit lengths along the 1-D direction, one commensurate and the other incommensurate with respect to the substrate lattice. A Fourier transform spectrum shows apparent signals that are ascribed to the two wavenumber units, a and b, along the 1-D direction. In the regular crystal, the number of a rank is mathematically equal to the number of dimensions of the structure due to its translational symmetry. When the rank is higher than the dimension of the structure, the structure is called quasi-periodic. The two vectors, given in Fig.1(b), cannot be described by one another. The existence, thus, verifies the quasi-periodicity of the 1-D system. Namely, we can designate that the B/Cu(110) surface as an array of quasi-periodic chains[2]. Such a long-range 1-D quasi-periodic surface structure has been modeled as a 1-D quasi-crystal and the structural parameters, obtained experimentally, satisfied formation conditions predicted by the theory [2]. This system provides an actual interface material to examine 1-D quasicrystals.

Fig. 1. Quasi-periodic 1-D structure in the B/Cu(110) system. (a) A scanning tunneling microscopy image (20 × 20 nm², tunneling current : 100 pA, Bias : 1.5 V.). (b) The 2-D power spectrum obtained by fast Fourier transform with line profiles crossing the origin in [001] and [110] direction.

References

• [1] Y. Tsujikawa, X. Zhang, M. Horio, T. Wada, M. Miyamoto, T. Sumi, F. Komori, T. Kondo, and I. Matsuda, Surf. Sci. 732, 122282 (2023).
• [2] Y. Tsujikawa, X. Zhang, K. Yamaguchi, M. Haze, T. Nakashima, A. Varadwaj, Y. Sato, M. Horio, Y. Hasegawa, F. Komori, M. Oshikawa, M. Kotsugi, Y. Ando, T. Kondo, and I. Matsuda, Nano Letters 24, 1160 (2024).

Authors

• Y. Tsujikawa and I. Matsuda