Cascaded compression of size distribution of nanopores in monolayer graphene

Monolayer graphene with nanometre-scale pores, atomically thin thickness and remarkable mechanical properties provides wide-ranging opportunities for applications in ion and molecular separations¹, energy storage² and electronics³. Because the performance of these applications relies heavily on the size of the nanopores, it is desirable to design and engineer with precision a suitable nanopore size with narrow size distributions. However, conventional top-down processes often yield log-normal distributions with long tails, particularly at the sub-nanometre scale⁴. Moreover, the size distribution and density of the nanopores are often intrinsically intercorrelated, leading to a trade-off between the two that substantially limits their applications^5-9. Here we report a cascaded compression approach to narrowing the size distribution of nanopores with left skewness and ultrasmall tail deviation, while keeping the density of nanopores increasing at each compression cycle. The formation of nanopores is split into many small steps, in each of which the size distribution of all the existing nanopores is compressed by a combination of shrinkage and expansion and, at the same time as expansion, a new batch of nanopores is created, leading to increased nanopore density by each cycle. As a result, high-density nanopores in monolayer graphene with a left-skewed, short-tail size distribution are obtained that show ultrafast and ångström-size-tunable selective transport of ions and molecules, breaking the limitation of the conventional log-normal size distribution^9,10. This method allows for independent control of several metrics of the generated nanopores, including the density, mean diameter, standard deviation and skewness of the size distribution, which will lead to the next leap in nanotechnology.