Nanometric Turing Patterns: Morphogenesis of a Bismuth Monolayer

Abstract

Turing's reaction-diffusion theory of morphogenesis has been very successful in understanding macroscopic patterns within complex objects ranging from biological systems to sand dunes. However, this mechanism was never tested against patterns that emerge at the atomic scale, where the basic ingredients are subject to constraints imposed by quantum mechanics. Here we report evidence of a Turing pattern that appears in a strained atomic bismuth monolayer assembling on the surface of NbSe${}_2$ subject to interatomic interactions and respective kinetics. The narrow range of microscopic parameters reflected in numerical analysis that observe stripe patterns and domain walls with Y-shaped junctions is a direct consequence of the quantum-mechanically allowed bond-lengths and bond-angles. This is therefore the first demonstration of a dynamically formed Turing pattern at the atomic scale.

6 pages, 4 figures

References in corpus (2)

• Transport Properties and Diamagnetism of Dirac Electrons in Bismuth
• Finding merit in dividing neighbors

Cited by in corpus (11)

• Turing pattern theory on homogeneous and heterogeneous higher-order temporal network system
• Turing patterns on discrete topologies: from networks to higher-order structures
• Quantum Turing bifurcation: Transition from quantum amplitude death to quantum oscillation death
• Physical interactions promote Turing patterns
• Turing instability in quantum activator-inhibitor systems
• Spiking at the edge
• Growth of self-integrated atomic quantum wires and junctions of a Mott semiconductor
• Weakly nonlinear analysis of Turing pattern dynamics on curved surfaces
• High-field immiscibility of electrons belonging to adjacent twinned bismuth crystals
• Physical interactions enable energy-efficient Turing patterns
• Turing patterns on polymerized membranes: a coarse-grained lattice modelling with internal degree of freedom for polymer direction