Nanoscale Turing patterns in a bismuth monolayer

Ordered patterns can arise out of randomness during morphogenesis. An explanation for this puzzle was put forward by Turing, who explained the emergence of stational patterns by invoking the interplay between an activator and an inhibitor with different diffusion rates [1]. Turing's theory of diffusion-reaction has proven to be highly influential across many disciplines. For example, the pigment patterns on seashells, stripes on tropical fish, and the purely chemical system of chlorite-iodide-malonic acid have been studied as Turing patterns. The typical length scale for biological pigment-based patterns ranges from millimeters to centimeters, and that for the purely chemical system is of the order of sub-millimeters. However, Turing patterns below micrometers are extremely rare in nature and have not been examined in detail.
Here we show that atomic monolayer bismuth grown on the surface of NbSe$_2$ by molecular beam epitaxy (MBE) provides another opportunity in "hard" condensed matter [2,3]. We report evidence of a Turing pattern with a period of five atoms (approximately 2nm) that appears in a strained atomic bismuth monolayer assembling on the surface of NbSe$_2$ subject to interatomic interactions and respective kinetics. We found stripe patterns and domain walls with Y-shaped junctions that bear a striking resemblance to what has been experimentally observed. This is the first demonstration of a Turing pattern at the atomic scale in hard condensed matter physics.

[1] A. Turing, Phil. Trans. R. Soc. Lond. B, 237, 37 (1952).
[2] A. Fang, C. Adamo, S. Jia, R. J. Cava, S.-C. Wu, C. Felser, A. Kapitulnik, Sci. Adv. 4, eaaq0330 (2018).
[3] Y. Fuseya, H. Katsuno, K. Behnia, A. Kapitulnik, Nature Physics (2021).