Moiré-induced band-gap opening in one-dimensional superlattices of carbon nanotubes on hexagonal boron nitride

Recently, two-dimensional (2D) moiré superlattices have been extensively studied, and many interesting physical phenomena have been observed. However, their one-dimensional (1D) counterpart - 1D moiré superlattices - have been rarely explored yet. Here, we performed theoretical calculations of low-energy bands of 1D moiré superlattices of single-walled carbon nanotubes (CNTs) on hexagonal boron nitride (hBN) using a newly developed low-energy effective continuum model for 1D superlattices. We observed moiré-induced opening of small band gaps ranging from a few meV to a few tens of meV, which depends sensitively on the CNT chirality. The observed band-gap opening can be well understood by considering the coupling of electronic states between CNTs and the hBN using the effective continuum model. The results have been confirmed by the density functional theory calculations.