Emergent stable rotation angle and electronic reconstruction in curvature-imprinted PTCDA bilayers.

Curved organic bilayers provide a natural platform for coupling geometric degrees of freedom to electronic properties. However, the fate of the interlayer rotation angle after curvature imprinting remains unclear. Here we study curvature-imprinted bilayer PTCDA nanotubes and show that, once the carbon nanotube template is removed, the system relaxes to a finite and stable interlayer rotation angle rather than returning to a perfectly aligned configuration. We develop a geometric-electronic free-energy model that incorporates curvature-induced strain, lattice mismatch, and curvature-enabled polarisation coupling. The competition between these contributions leads to a non-zero equilibrium rotation angle, typically in the range 2∘-4∘, with an associated energy minimum of 15-30 meV. This energy scale implies dynamical stability on short time scales and robustness under low-temperature conditions. Tight-binding calculations, parametrised by the local curved geometry, support this spontaneous angle selection and reveal its electronic consequences. The stable rotation angle produces pronounced band broadening and systematic shifts of van Hove singularities (vHSs) by∼0.2 eV, an energy scale that exceeds both room-temperature thermal broadening and typical disorder-induced linewidths. These results identify curvature-imprinted PTCDA bilayers as a molecular realisation of a moiré superlattice in which the twist angle arises from internal energetic competition rather than external mechanical control. The predicted stability and associated vHS shifts are directly accessible via low-temperature scanning tunnelling spectroscopy, offering a controllable route toward geometry-driven band engineering in organic molecular films.