Atomic-defect engineering in thin membranes provides opportunities for ionic and molecular filtration and analysis. While molecular-dynamics (MD) calculations have been used to model conductance through atomic vacancies, corresponding experiments are lacking. We create sub-nanometer vacancies in suspended single-layer molybdenum disulfide (MoS) via Ga ion irradiation, producing membranes containing ∼300 to 1200 pores with average and maximum diameters of ∼0.5 and ∼1 nm, respectively. Vacancies exhibit missing Mo and S atoms, as shown by aberration-corrected scanning transmission electron microscopy (AC-STEM). The longitudinal acoustic band and defect-related photoluminescence were observed in Raman and photoluminescence spectroscopy, respectively. As the irradiation dose is increased, the median vacancy area remains roughly constant, while the number of vacancies (pores) increases. Ionic current versus voltage is nonlinear and conductance is comparable to that of ∼1 nm diameter single MoS pores, proving that the smaller pores in the distribution display negligible conductance. Consistently, MD simulations show that pores with diameters <0.6 nm are almost impermeable to ionic flow. Atomic pore structure and geometry, studied by AC-STEM, are critical in the sub-nanometer regime in which the pores are not circular and the diameter is not well-defined. This study lays the foundation for future experiments to probe transport in large distributions of angstrom-size pores.

Manipulation and structural modifications of two-dimensional (2D) materials for nanoelectronic and nanofluidic applications remain obstacles to their industrial-scale implementation. Here, we demonstrate how a 30 kV focused ion beam (FIB) can be utilized to Received: ((will be filled in by the editorial staff)) Revised: ((will be filled in by the editorial staff))

We provide an overview of atom-scale apertures in solid-state membranes, from “pores” and “tubes” to “channels”, with characteristic sizes comparable to the sizes of ions and water molecules. In this regime of ∼1 nm diameter pores, water molecules and ions are strongly geometrically confined: the size of water molecules (∼0.3 nm) and the size of “hydrated” ions in water (∼0.7–1 nm) are similar to the pore diameters, physically limiting the ion flow through the hole. The pore sizes are comparable to the classical Debye screening length governing the spatial range of electrostatic interaction, ∼0.3 to 1 nm for 1 to 0.1 M KCl. In such small structures, charges can be unscreened, leading to new effects. We discuss experiments on ∼1 nm diameter nanopores, with a focus on carbon nanotube pores and ion transport studies. Finally, we present an outlook for artificial “size zero” pores in the regime of small diameters and small thicknesses. Beyond mimicking protein channels in nature, solid-state pores may offer additional possibilities where sensing and control are performed at the pore, such as in electrically and optically addressable solid-state materials.

Gas flows are often analyzed with the theoretical descriptions formulated over a century ago and constantly challenged by the emerging architectures of narrow channels, slits, and apertures. Here, we report atomic-scale defects in two-dimensional (2D) materials as apertures for gas flows at the ultimate quasi-0D atomic limit. We establish that pristine monolayer tungsten disulfide (WS2) membranes act as atomically thin barriers to gas transport. Atomic vacancies from missing tungsten (W) sites are made in freestanding (WS2) monolayers by focused ion beam irradiation and characterized using aberration-corrected transmission electron microscopy. WS2 monolayers with atomic apertures are mechanically sturdy and showed fast helium flow. We propose a simple yet robust method for confirming the formation of atomic apertures over large areas using gas flows, an essential step for pursuing their prospective applications in various domains including molecular separation, single quantum emitters, sensing and monitoring of gases at ultralow concentrations.