Helical waves for self-consistent first principles calculations of chiral one-dimensional nanomaterials

Chiral nanomaterials - particularly, one-dimensional (1D) structures – offer unparalleled opportunities for impacting the design of novel quantum, photonic and electromagnetic devices due to their unique (and sometimes anomalous) transport, optical, electric, and magnetic properties. We describe our efforts in formulating and implementing a self-consistent first principles simulations framework to enable the discovery and characterization of novel forms of such materials. Since conventional first principles methods, based on plane-waves e.g., are unable to suitably accommodate the helical potentials commonly associated with these structures, our methodology consists of expressing the equations of Kohn-Sham Density Functional Theory using Helical Bloch states and discretizing the resulting equations using specialized Laplacian eigenfunctions called Helical waves. Embedded within the equations of Kohn-Sham theory is the problem of electrostatics, which we tackle using a mixed spectral-finite difference formulation in our framework. We demonstrate our method using numerous examples of chiral 1D nanomaterials with intrinsic or applied twist, and describe the utility of our technique to study topological phases and/or correlated electronic states that may emerge in such systems.