Atomically precise inorganic helices with a programmable irrational twist

Helicity in atomic scale structures often arises from the precise ordering of cooperative intra- and inter-molecular bonding interactions. The exclusivity of these interactions to natural, organic, or molecular systems has limited the demonstration and understanding of helical motifs in densely packed solid-state lattices. Herein, we report that the ordering of Ga atoms in GaSeI, a representative crystal from an exfoliable class of atomically precise III-VI-VII 1D van der Waals (vdW) crystals, manifests the elusive Boerdijk-Coxeter (B-C) helix motif. B-C helicity is a rare non-repeating geometric pattern arising from the distinct face-sharing order of well-defined tetrahedra with adjacent vertices defined by an irrational rotational or twist angle, previously thought to only exist in macro- to molecular-scale structures but not at the atomic scale. Using InSeI and GaSeI as models, we show that the structural degree of freedom in a 1D vdW lattice generally allows for the systematic twisting of a tetrahelical lattice defined by a periodic 41 screw axis in InSeI to its infinitely extending B-C helix counterpart in GaSeI. Helical coordinate analysis of GaSeI reveals that the Ga atoms forming the [GaSe3I]∞ repeating motif display B-C helicity whereas Se and I atoms order as concentric tetrahelices that form B-C helix variants with systematically expanded helical radii. This discovery of ideal B-C helicity in optically active vdW lattices exfoliable down to single helix chains presents a distinctive materials platform towards understanding aperiodic helicity and chirality in low-dimensional solids, enabling new opportunities in designing well-defined solid state materials for quantum transport and long-range chirality-driven phenomena.