Moiré patterns in van der Waals heterostructures

Using scanning tunneling microscopy, we report the observation of moir\'e patterns (MPs) on van der Waals heterostructures comprised of various 2D allotropes of bismuth and antimony grown on highly ordered pyrolytic graphite and ${\mathrm{MoS}}_{2}$. The spatial periods of the MPs range from $\ensuremath{\lambda}\ensuremath{\sim}1$ to $\ensuremath{\sim}10$ nm. For all the reported cases ($\ensuremath{\alpha}$-bismuthene, $\ensuremath{\alpha}$-antimonene, $\ensuremath{\beta}$-antimonene, and monolayer bismuthene), we model the observations using a simple superposition model (SSM). Where possible, the results obtained from the SSM are compared to analytical prediction. MPs emerging from mixed symmetry stacking (hexagonal on rectangular) are explained without requiring commensuration of the layers.