Nanometre-scale pores and capillaries have long been studied because of their importance in many natural phenomena and their use in numerous applications. A more recent development is the ability to fabricate artificial capillaries with nanometre dimensions, which has enabled new research on molecular transport and led to the emergence of nanofluidics. But surface roughness in particular makes it challenging to produce capillaries with precisely controlled dimensions at this spatial scale. Here we report the fabrication of narrow and smooth capillaries through van der Waals assembly, with atomically flat sheets at the top and bottom separated by spacers made of two-dimensional crystals with a precisely controlled number of layers. We use graphene and its multilayers as archetypal two-dimensional materials to demonstrate this technology, which produces structures that can be viewed as if individual atomic planes had been removed from a bulk crystal to leave behind flat voids of a height chosen with atomic-scale precision. Water transport through the channels, ranging in height from one to several dozen atomic planes, is characterized by unexpectedly fast flow (up to 1 metre per second) that we attribute to high capillary pressures (about 1,000 bar) and large slip lengths. For channels that accommodate only a few layers of water, the flow exhibits a marked enhancement that we associate with an increased structural order in nanoconfined water. Our work opens up an avenue to making capillaries and cavities with sizes tunable to ångström precision, and with permeation properties further controlled through a wide choice of atomically flat materials available for channel walls.

Biological membranes allow permeation of water molecules but can reject even smallest ions. Behind these exquisite separation properties are protein channels with angstrom-scale constrictions (e.g., aquaporins). Despite recent progress in creating nanoscale pores and capillaries, they still remain distinctly larger than protein channels. We report capillaries made by effectively extracting one atomic plane from bulk crystals, which leaves a two-dimensional slit of a few Å in height. Water moves through these capillaries with little resistance whereas no permeation could be detected even for such small ions as Na + and Cl -. Only protons can diffuse through monolayer water inside the capillaries. The observations improve our understanding of molecular transport at the atomic scale and suggest further ways to replicate the impressive machinery of living cells.It has long been an aspirational goal to create artificial structures and devices with separation properties similar to those of biological membranes 1-5 . The latter utilize a number of separation mechanisms but it is believed that angstrom-scale constrictions within protein channels 6,7 play a key role in steric (size) exclusion of ions with the smallest hydration diameters D H  7 Å, typically present in biofluids and seawater 8,9 . Such constrictions are particularly difficult to replicate artificially because of the lack of fabrication tools capable to operate with such precision and, also, because the surface roughness of materials is typically much larger than the required angstrom scale 1 . Nonetheless, several artificial systems with nanometer and sub-nanometer dimensions were recently demonstrated, including narrow carbon and boron-nitride nanotubes 5,10,11 , graphene oxide laminates 12,13 and atomic-scale pores in graphene and MoS 2 monolayers 3,4,14 . The resulting devices exhibited high selectivity with respect to certain groups of ions (for example, they blocked large ions but allowed small ones 12,13 or rejected anions but allowed cations and vice versa 2,3,5 ). Most recently, van der Waals assembly of two-dimensional (2D) crystals 15 was used to make slit-like channels of several Å in height 16,17 . They were atomically smooth and chemically inert and exhibited little ( 10 -4 C cm -2 ) surface charge 17 . The channels allowed fast water permeation 16 and blocked large ions with a complete cutoff for diameters larger than 10 Å (ref. 17 ). Small ions (for example, those in seawater with D H of 7 Å) still permeated through those channels with little hindrance, showing that an angstrom-scale confinement comparable to that in aquaporins 6,7 is essential for steric exclusion of small-diameter ions. In this report, we describe 2D channels with the height h of about 3.4 Å (ref. 18), which are twice smaller than any hydrated ion (smallest ions are K + and Clwith D H  6.6 Å) 8,19 but sufficiently large to allow water inside (effective size of water molecules is 2.8 Å). The achieved confinement matches the size of protein constrictions in biological ...

The field of nanofluidics has shown considerable progress over the past decade thanks to key instrumental advances, leading to the discovery of a number of exotic transport phenomena for fluids and ions under extreme confinement. Recently, van der Waals assembly of 2D materials 1 allowed fabrication of artificial channels with ångström-scale precision 2 . This ultimate confinement to the true molecular scale revealed unforeseen behaviour for both mass 2 and ionic 3 transport. In this work, we explore pressure-driven streaming in such molecular-size slits and report a new electro-hydrodynamic effect under coupled pressure and electric force. It takes the form of a transistor-like response of the pressure induced ionic streaming: an applied bias of a fraction of a volt results in an enhancement of the streaming mobility by up to 20 times. The gating effect is observed with both graphite and boron nitride channels but exhibits marked materialdependent features. Our observations are rationalized by a theoretical framework for the flow dynamics, including the frictional interaction of water, ions and the confining surfaces as a key ingredient. The material dependence of the voltage modulation can be traced back to a contrasting molecular friction on graphene and boron nitride. The highly nonlinear transport under molecular-scale confinement offers new routes to actively control molecular and ion transport and design elementary building blocks for artificial ionic machinery, such as ion pumps. Furthermore, it provides a versatile platform to explore electro-mechanical couplings potentially at play in recently discovered mechanosensitive ionic channels 4 .