Helicity in solids often arises from the precise ordering of cooperative intra- and intermolecular interactions unique to natural, organic or molecular systems. This exclusivity limited the realization of helicity and its ensuing properties in dense inorganic solids. Here we report that Ga atoms in GaSeI, a representative III–VI–VII one-dimensional (1D) van der Waals crystal, manifest the rare Boerdijk–Coxeter helix motif. This motif is a non-repeating geometric pattern characterized by 1D face-sharing tetrahedra whose adjacent vertices are rotated by an irrational angle. Using InSeI and GaSeI, we show that the modularity of 1D van der Waals lattices accommodates the systematic twisting of a periodic tetrahelix with a 41 screw axis in InSeI to an infinitely extending Boerdijk–Coxeter helix in GaSeI. GaSeI crystals are non-centrosymmetric, optically active and exfoliable to a single chain. These results present a materials platform towards understanding the origin and physical manifestation of aperiodic helicity in low-dimensional solids.
Conducting polymers are mixed ionic–electronic conductors that are emerging candidates for neuromorphic computing, bioelectronics and thermoelectrics. However, fundamental aspects of their many-body correlated electron–ion transport physics remain poorly understood. Here we show that in p-type organic electrochemical transistors it is possible to remove all of the electrons from the valence band and even access deeper bands without degradation. By adding a second, field-effect gate electrode, additional electrons or holes can be injected at set doping states. Under conditions where the counterions are unable to equilibrate in response to field-induced changes in the electronic carrier density, we observe surprising, non-equilibrium transport signatures that provide unique insights into the interaction-driven formation of a frozen, soft Coulomb gap in the density of states. Our work identifies new strategies for substantially enhancing the transport properties of conducting polymers by exploiting non-equilibrium states in the coupled system of electronic charges and counterions.