Graphene is the most famous of the two-dimensional solids, and with good reason. We’ve all seen graphite in pencils, and it’s strange to think that this same substance, plus some household adhesive tape, led to a Nobel. (You probably wouldn’t want to try that experiment with actual pencils – the graphite is often blended with other materials. And even if you have a chunk of good-quality graphite, the single-atom-thick sheets, which is what you end up with after you do the adhesive-tape peel a few times, become basically invisible without a handy electron microscope). Graphene has very interesting properties, starting with it being much stronger than steel, and these are directly related to it being a completely bonded flat sheet of carbon atoms. It’s like some sort of mathematical ideal, a Platonic substance that showed up down here in the cave instead of just being a shadow on the wall. The shift from the bulk phase to the individual layers is a huge one, and has huge implications in optics, electronics, and materials science in general.
There are, by now, a number of other two-dimensional substances that have joined the ranks. Sticking with the pure elements, you have phosphorene, which can be produced by running the tape trick on flaky black phosphorus. (Similarly, arsenene has been predicted to exist, but I don’t think it’s been isolated yet). Borophene has been prepared on a metal substrate, but is overall much less well characterized. Then there’s germanene, which also (so far) has to be painstakingly grown on a surface, silacene (shown at right – it’s not flat like its graphene cousin, but rather is gently rippled), and stanene, which has been reported a couple of times but whose existence would benefit from some further shoring up. Almost all of this work is from 2010 on, and most of it is only from about 2014 or so: the field of two-dimensional materials is very new indeed, and it’s definitely still in the land-rush look-over-here phase.
Moving to single-layer compounds with more than one element in them opens the wild frontier up even wider. There have long been crystals known that have a “layer cake” structure, such as molybdenite, which has molybdenum and sulfur single-element layers. It has a similar slippery, scaly feel like graphite in the bulk phase, due to those sulfur layers sliding past each other, and is similarly used as an industrial lubricant. You can get this down to a two-dimensional layer of molybdenum sulfide, which is a material that’s showing up in the literature these days with great regularity. And it’s just the best-known example of a whole slew of metal-sulfur (or metal-selenium) 2D materials, the exploration of which is a very lively field (palladium selenide, anyone?). Two-dimensional boron nitride is also a hot topic, since its properties would seem to make it ideal for many nanotech applications (better, in fact, than graphene, could it only be produced in quantity). 2D thallium oxide has just been calculated to be stable and may even be available through exfoliation (tape or otherwise), and the list most certainly goes on.
Why stop there, though? Last year, a three-way graphenelike compound of silicon, boron, and nitrogen was predicted to exist, and no doubt there are people whacking away right now trying to prepare it. And even now, people are taking these 2D compounds and stacking them on top of each other, looking for unusual electronic properties and more. There are, beyond doubt, a huge number of artificial materials, which could be produced by the techniques now emerging – for instance, start with a layer of molybdenum sulfide, and then layer a completely different metal sulfide on top of that. Rinse and repeat – you could end up with a Dobosh-tort solid with two (or more, why not) metals along with sulfur, all present as single-atom layers piled on top of each other. The magnetic, optical, electrical, thermal, and mechanical properties of such things are anyone’s guess; I’m not sure if current modeling is up to calculating them after a certain point.
But as it stands, there’s a lot of chemistry (and physics) to be done. Once you get past the naturally occurring 2D-layer materials (graphite, black phosphorus, molybdenum sulfide), you’re faced with some rather large synthetic difficulties. Just because some allotrope or compound is predicted to be stable enough to exist doesn’t mean that you have a route to it, of course. Vapor deposition and other semiconductor-industry techniques can be a way in (although not a universal one), but there are surely chemical tricks to laying these things down that we haven’t learned yet, since it’s only (relatively) recently that we’ve had the tools to see what’s going on. Flatness, it turns out, looms large.