This story is both scientifically interesting and hilarious in some places; you should continue reading it. I’ve divided it into several parts, as it is fairly long. It involves science, scientific politics, and gracious insults. Most importantly, it discusses how my lab at Brown University has shown strong evidence for the existence of Cooper pairs in insulators. In case some readers are backlogged on their scientific jargon (do they have RSS feeds for that?), I’ll describe what I mean.

A (very) Brief History of Superconductivity:

Superconductivity is mostly associated with (and named for) materials that have zero electrical resistance. If I had a superconducting power line, that would mean that I lose zero energy transmitting electricity wherever I want it to go. In case things get confusing in the technological future and the buzz words get out of control, a word of advice: never buy a superconducting heater. Superconducting materials have other interesting properties; they don’t allow magnetic field lines to pass through them (unless you’re a type II above H), and there’s a gap in the density of states. The first phenomenon allows for levitation demos, which are fun, and maglev trains—also fun. The second property is responsible for some tech gadgets like SQUIDs, which are the most accurate magnetometers possible (not just available). For a long time, superconductivity was a mystery, and still is in many ways. It was discovered in 1911 (which was right after Einstein’s famous theory of special relativity) by H. K. Onnes or a series of his fired graduate students. The story:

Heike Kamerlingh Onnes had some graduate students. He asked his students to measure the resistance of mercury down to liquid helium temperatures. Each time a graduate student came to Onnes’ office to tell him that the resistance of mercury suddenly dropped to zero at 4.2K, that student was fired. Finally, after going through a half-dozen idiotic graduate students, Onnes went down to his lab and measured the resistance of mercury himself. He found that the resistance suddenly dropped to zero at 4.2K. He won a Nobel prize for his work in 1913. (1911 paper + image ref)

No one could explain the phenomenon. More superconducting materials were found, including lead (T=7K) and niobium nitride (T=16K). Finally in 1957, Bardeen, Cooper, and Schrieffer presented a plausible theory (BCS theory) involving what are now known as Cooper pairs—two electrons that pair through the vibrations of the crystal lattice at low temperatures. (Remember electrons usually hate each other…via Coulomb forces.) For some reason BCS theory doesn’t work for the more recently discovered high-temperature superconductors (1986+); there are a lot of people working on that problem (see Woodstock of Physics). However, BCS theory works very well for many materials, and for others it forms a pretty good starting point. For our purposes here, Cooper pairs can be thought of as the “heralds” of superconductivity. As far as BCS is concerned, if they’re there, it’s superconducting, if they’re not, it’s not superconducting. As a technical note, phase coherence among the Cooper pairs is also required.

In 2007, my lab observed Cooper pairs in insulating thin films (ref). This result indicates that superconductivity can exist in insulators. In case that doesn’t strike a harsh chord, remember the etymology of the word ’superconductor’: zero electrical resistance. We seem to have found a contradiction. How is it possible that an insulator can be ’superconducting’? To convince you of our results, I’ll describe our experiments.

Thin Film Experiments on Nano-honeycomb Substrates:

Geometry
In my lab we measure the resistance of very thin films at really low (sub Kelvin) temperatures. We also make our films on substrates that have holes in them, so that the films we make look like sheets of honeycomb (see picture to the right). This geometry restricts the motion of electrons (or Cooper pairs). Imagine a bulk piece of superconducting material with Cooper pairs happily swimming around in 3-dimensions. Now slowly shave the material down to a nearly 2-dimensional sheet, then poke holes all over it. Given this scenario, you might understand how unhappy the Cooper pairs are in our films. We look at electric transport in this reduced geometry because it provides a way to test the limits of superconductivity. It is in the limit of weak superconductivity that we hope to learn in detail how the phenomenon comes about.

Superconductor-Insulator Transition: unholey vs. holey
Although I described the structure of our films by ’shaving’ away slices of a 3-dimensional block and then poking holes in it, we actually make our films in the opposite direction: by evaporating metal atoms onto the honeycomb substrates. We can make films so thin that they no longer superconduct. In these extremely thin films (~ 4 or 5 atoms thick), the resistance actually increases as the temperature is lowered, and it is presumed that the resistance is infinite at zero temperature. As more material is slowly added we watch the curve change. At a very specific thickness, the material will begin to superconduct as the temperature decreases. This process is shown in the figure to the left (Y. Liu et. al.) in a uniform bismuth film on a smooth substrate (no holes) and is known as the Superconductor-Insulator Transition (SIT).
(note: in this field, the words ‘insulator’ and ’superconductor’ always refer to the zero-temperature resistance value. While this is a useful classification, it can be confusing. For example, a true insulator has an infinite resistance–we never measure infinite resistances, but we can see that in some films the resistance tends toward infinity as the temperature goes to zero. We call this film an insulator.)

In our holey films the superconductor-insulator transition looks a little bit different, and is shown in the graph below the first. You could make the statement that the shape of our transition is different from the one on a smooth substrate in two dimensions because poking holes in two dimensions makes something of a a 1d-2d hybrid geometry. Or for those with less malleable imaginations: 2d with some additional restrictions.

At the transition’s edge
So far, we have made very weak superconductors. The films that do superconduct only just superconduct. Since we are already on the line between a superconductor and an insulator, we want to take a closer look and try to figure out why the insulator decides to become a superconductor at some thickness (or vice-versa). The answer might be found by studying the films very close to the transition thickness, and it turns out that there are many interesting things to be looked at. We will talk about one of them here: magnetoresistance oscillations.

The effect of magnetic field on holey films
Say we make a film of a certain thickness in the graph above (“a.” for example). We know that it has holes in it, so the currents that run through the film have to go around the holes. If we turn on a very small magnetic field perpendicular to the film, the magnetic field lines will penetrate the film at a right angle and also go straight through the holes. We note that the field lines bend the trajectories of the electrons. If the film is not superconducting, the field lines bend the electron trajectories uniformly throughout the film. However, in superconducting films, some of the electrons will end up circling around the holes (for reasons discussed below). I’d also like to introduce the idea of magnetic flux: each hole now contains some amount of magnetic flux, which is described by B*A when the field is perpendicular to a material’s surface; here, B is the magnetic field and A is the area of the hole. We could just as easily draw a circle somewhere in the film and calculate the amount of magnetic flux through that arbitrary circle.

If we repeat the analysis presented above with film c. instead of film a., a few things change. The obvious change is that the film in question is now a superconductor (at low temperatures). If it is also a type I superconductor (as many are), or a type II superconductor below H, the Meissner effect applies and magnetic field lines are no longer allowed to penetrate the film itself. (We will only discuss this case for our superconducting films.) In fact, the superconductor will set up currents that exactly cancel any magnetic flux that was planning on penetrating the film, and the resulting situation is that all of the magnetic field lines go through the holes in the film. Now each hole contains some magnetic flux, and if you were to arbitrarily draw a circle in the film, you would find that the magnetic flux in your circle is zero (as long as you do not encircle any holes). Now it is clear that the electrons in the film are deflected only around the holes, since this is where the field lines are sequestered. Some of them could even end up circling around the holes.

In superconductors* it turns out that magnetic flux, like charge, is quantized and only comes in packets of a certain size. (Despite statistics, no American family actually has 2.5 children.) This means that the holes in a superconducting film require certain amounts of magnetic flux. One, two, three, four… packets of flux, but not one and a half. However, we can vary the applied magnetic field continuously—meaning that I can turn on the magnetic field to a value that would provide 1.5 packets of magnetic flux per hole or whatever non-integer value I like… Something must give in order to satisfy the physical law of flux quantization. Luckily, we have neglected the electrons in this flux calculation thus far. As stated above, some of the electrons will circle around the holes; in a superconductor, this means that some electrons will circle around the holes in pairs. In other words, some Cooper pairs will circle around the holes. Electrons carry electric charge, and moving electric charge gives an electric current (by definition). Finally, electric current moving around a circle generates some magnetic flux. This is the mechanism by which the current in the film compensates for non-integer values of magnetic flux in the holes. If my magnet is trying to put a non-integer value of magnetic flux through a hole, Cooper pairs will circle around the hole in a number that exactly cancels the excess flux (or perhaps compensates for the missing flux needed to get to the next integer).

We must now ask ourselves how we expect to see the compensation process described above, and what that might tell us about the status of our films in their transition from insulators to superconductors.

Experimental aside: probing mechanisms
The problem with modern experimental physics seems to be in translation between the ‘physical’ and the ‘observable.’ It is most convenient (and some people may argue more ‘real’) to speak about physics microscopically. i.e. ‘The electrons go around the holes,’ or ‘The proton splits into 3 quarks,’ etc. However, the microscopic happenings of a material are rarely what is being observed. Rather, scientists use macroscopic probes into the microscopic world. Our probe for the thin film experiments is the macroscopic resistance of the film. As another example, the probe for detecting a muon decay is often a scintillator that emits photons when bombarded by a muon or an electron; the photons can then be amplified and detected. The trick to a good macroscopic probe is in finding one that will reveal a property that could only be caused by one particular microscopic action. Or at least, you’d like to be able to argue away all other possible microscopic scenarios that could result in your macroscopic observation.

Resistance in a changing magnetic field: a probe for Cooper pairs
Using the resistance of the film as our probe, let us try to infer what the microscopic happenings in the film do in a changing magnetic field. We’ll discuss three different stages toward the development of superconductivity (three different films): the strongly insulating (labeled a. in the figure), weakly insulating (b.), and superconducting (c.). The strongly insulating film is the thinnest, and the superconducting film the thickest.

In film a. the material is strongly insulating. We expect that when we turn on the magnetic field, the field lines will be allowed to penetrate both the holes and the film, and therefore we do not expect that flux quantization will be important here. Now, every time an electron attempts to move it just gets shoved back to its previous position because of scattering (collisions) due to the magnetic field lines. As the field is increased further, the density of field lines will increase, and the number of electron collisions/deflections will also increase. In the end, we only see the materials magnetoresistive properties, and learn nothing else by using our special geometry.

Onto the thickest film, and a more interesting case, film c. Since film c. superconducts at low temperatures, we will guess that flux quantization will butt in as we get closer to the superconducting state (at low temperatures), let’s try to figure out what the resistance might look like as the magnetic field is increased from zero.

We hold the temperature at some constant value that is close to the transition temperature (but above it). In zero field, we know that the resistance is some low value. When we turn on a small field, the ‘pro-superconducting’ part of the film starts to shove that magnetic flux into the holes by creating currents that circle around the holes. These electrons then tend to get in the way of the electrons that are just trying to get from one side of the film to the other—the resistance goes up. It reaches a maximum when the field I apply to the film is equivalent to trying to put 1/2 of a flux quantum in each hole. Then the supercurrents have to work their tails off trying to keep the flux out of the film, while they are also required to keep an integer amount of flux in each hole. The ‘traversing’ electrons have the most difficult time getting through the film in this situation (imagine this going on with people in a crowded train station. the electrons are people, some of them trying to travel and some of them working. I don’t know what would represent the magnetic flux. Maybe this analogy is better suited for the Harry Potter train station, but even there it’s a bit of a stretch…).

Contrarily, the traversing electrons have the easiest time getting through the film when the flux quantization rule for the holes is already satisfied by the amount of magnetic field applied by the user (me), i.e. I apply the equivalent of one flux quantum per hole. In this situation, the electrons working to make the supercurrents have much less to do and the traversing electrons have much less to run into. Graphically, this process results in magnetoresistance oscillations, shown in the graph below (the x-axis represents the applied magnetic field, and the y-axis represents the resistance of the film).

But I’ve pulled a fast one on you. The data shown above, which requires Cooper pairs and flux quantization to explain (which, in turn, require superconductivity), are not data from film c. The data shown above were taken on film b.—an insulating film. Thus, by these arguments, we have shown the presence of Cooper pairs in insulators.

Various terms have been used to describe this state, both theoretically and experimentally. “Bosonic insulator” is one, “superinsulator” is another. Though “superinsulator” is certainly a better buzzword, I think that it is somewhat misleading. The term “superconductor” is descriptive, however “superinsulators” are not necessarily excellent insulators. The state that we are discussing is that in which insulating behavior is facilitated by Cooper pairs.

Part II of this two-part series will further discuss Cooper pairs in insulators and will introduce other groups’ research on the topic. It will also include the gracious insults alluded to above; it is always interesting when science overlaps with anything involving interactions between people. In Part I, I hope that I have stimulated some interest in the topic of “superinsulators” without overwhelming the reader. I would also be happy to hear comments/criticisms/complaints.

Footnote:
*I say “in superconductors” specifically because that is the only application of this rule. Flux quantization comes about by requiring the superconducting wave function to be single-valued. This is good news because if I claimed flux quantization were true for any regular materials it wouldn’t make sense. You could have a slab of wood with magnetic field lines going through it and I would be telling you, “you can’t draw a circle that small because of flux quantization” when you can clearly draw whatever size circle you please. Anyway, I hope I’ve convinced you that flux quantization only makes sense in superconductors.