I hate being a nay-sayer, but the NYT article is making quite a spectacle about this whole thing. What the group has truly done is demonstrate a novel method for placing a single phosphorus atom within silicon and proceeded to measure the semiconducting properties of the resultant device with quite good precision. Because the doping is the result of a single atom, they can resolve more than just "on" and "off", and in fact can read three states from it, so it gets its quantum computing title.

As a materials scientist, I'm worried that they don't show any long-term data and all their results appear (from my not-so-thorough reading of the originating Nature Nanotechnology report) to be based on a single device. How repeatable is this result and how consistent are the signals across multiple devices? How far will the phosphorus atom diffuse over the lifetime of the device? Or even over the first few hours of its operation at room temperature? How closely can these devices be placed to each other on the silicon chip without getting cross-interference or depriving the dopant of its discrete quantum states? The dopants in a normal device aren't too terribly close to each other. And finally, how big must the surrounding structure be?

Don't get me wrong, this is excellent science and well deserving of its publication in such a prestigious journal, but the spectacle that the NYT is creating around this and the dreams of such a tiny device is a bit premature.

Graphene is most certainly not .34 nm thick. What you are quoting is the equilibrium spacing between one graphene sheet and the next in crystalline graphite. The true "thickness" of graphene is hard to gauge, actually. If you take the standard model of quantum mechanics, the carbon atoms within graphene are point particles, and therefore have no thickness. It is reasonable, then, to measure the extent of the electron clouds from the carbon. Since the electron clouds are statistical formulations, they theoretically extend to infinity. However, because I'm a materials scientist and not some fancy physicist with a deep, quantitative understanding of electron orbital theory, I would say a good guess is to say that the radius of the electron cloud around a particular atom is about equal to half the bond length between one carbon and the next. In this case, about 0.071 nm.

So if I were pressed to give an answer as to the thickness of a graphene sheet, not that it would generally matter in any context I'd think of, I'd call it 0.142 nm thick.

Your question can be answered in two ways. First, in the materials science community, it's common to denote a material or chunk of material that has a very high aspect ratio, for instance very large in one or two dimensions and small in size on the order of the atomic scale in the remaining directions as effectively one- and two-dimensional. In fact, quantum dots are thought of in materials science as generally zero-dimensional, even though they most certainly have more than one atom (and even if they comprised a single atom, the electron cloud extends in three dimensions). So, as far as the materials science and electron microscopy fields are concerned, this is two-dimensional.

Second, you tend to get your paper published in fancier journals and grab more headlines by having sensational things such as 2D (in this case) or quantum or some such buzzword in your title these days.

The more I read about this story, the more I think "This sounds an awful lot like grad school."

TEM Comments
This experiment was actually quite a bit harder to carry out than you think. (I imagine, as I wasn't involved in this study but do similar work.) Doing these experiments is like traveling to the moon in that the principles are relatively simple, but it's the details that are hard. While operation of the TEM is relatively easy, preparation of samples is extremely tedious even when the sample is relatively robust and isotropic and it doesn't matter where you need to look on the sample. Constructing a TEM specimen with the intention of looking at a tiny little feature of some larger piece of material is extremely difficult, taking hours or days, if even possible. It's even more difficult to prepare a specimen and have the right equipment set up to control and observe dynamic processes, such as lithium discharge from a single nanofiber. And viewing dynamics in a complicated system, like a battery, which contains at a very minimum three active components, anode, cathode, and electrolyte, is another order of magnitude harder. Plus you have to find a way to make the thing less than 20 nanometers thick and get it into a microscope at high vacuum without breaking or contaminating it, which is nontrivial. There's also the cost of the equipment, which is between $500,000 and $10 million for the microscope itself and another couple hundred thousand dollars for the specialized probes required to do this experiment. I do this for a living myself, as do many people across the world who are either pursuing or already have PhDs in microscopy and analysis, and if it were easy, it'd've already been done and we'd be out of the job.

Battery comments
We understand pretty much exactly why batteries wear out. Though the anodes in "real" batteries are usually some form of graphite, which expands less than 10% versus the SnOx in the video (~250%), there is still jostling of all the little powders that form the battery upon charging and discharging that eventually lead to the individual particles separating from the electrodes as a whole and essentially becoming dead micro-paperweights within the battery cell. It's just very hard to image them dynamically in a realistic operation because air and water vapor tend to destroy the materials nearly instantly.

This is some just really old news. Papers have been published on this and the other myriad sources of lithium battery degradation over the last several decades. In fact, this sort of coarsening, irreversibility, and poisoning are common in all such "nano" and even "micro" systems in which thermodynamics and kinetics are pitted against each other. For instance, at a three day international workshop on automotive lithium batteries half a decade ago, about a third of the talks were on various degradation mechanisms in these systems. On the other hand, this might be something completely knew that no one in the materials science or electrochemistry fields have heard of, but, being one of those people, and seeing the utter lack of detail in the news article and not being able to find the originating scientific publication, I doubt it. It looks like one of many articles on the subject that someone happened to pick up and submit. And yes, I'm a materials scientist and I study nano-scale materials, including battery electrodes.