Synthesis of two-dimensional Tl(x)Bi(1-x) compounds and Archimedean encoding of their atomic structure.

Crystalline atomic layers on solid surfaces are composed of a single building block, unit cell, that is copied and stacked together to form the entire two-dimensional crystal structure. However, it appears that this is not an unique possibility. We report here on synthesis and characterization of the one-atomic-layer-thick Tl(x)Bi(1-x) compounds which display quite a different arrangement. It represents a quasi-periodic tiling structures that are built by a set of tiling elements as building blocks. Though the layer is lacking strict periodicity, it shows up as an ideally-packed tiling of basic elements without any skips or halting. The two-dimensional Tl(x)Bi(1-x) compounds were formed by depositing Bi onto the Tl-covered Si(111) surface where Bi atoms substitute appropriate amount of Tl atoms. Atomic structure of each tiling element as well as arrangement of Tl(x)Bi(1-x) compounds were established in a detail. Electronic properties and spin texture of the selected compounds having periodic structures were characterized. The shown example demonstrates possibility for the formation of the exotic low-dimensional materials via unusual growth mechanisms.