this video.

The idea of the uncanny valley definitely applies to food. I ignored the entire “moving” line because it radically diverges from the “still” line with respect to food. Here you go:

the uncanny valley of food

I just wanted to let everyone have a roundup of my favorite new “music videos.” These are certainly not official music videos and are often more videos with music soundtracks but I hope you enjoy…

Bathtub IV by Keith Loutit with Clementine by Megan Washington

Bathtub IV from Keith Loutit on Vimeo.

Come on Up To the House by the incomparable Tom Waits done by the fantastical body painter Anders Lovgren (forgive the lack of umalts)

Her Morning Elegance by Oren Lavie done by Violette Valeriey

oren lavie – her morning elegance from violette valeriey on Vimeo.

Lisztomania by Phoenix but not the real version… the “Brat Pack” version by avoidantconsumer (and really John Hughes RIP)

Lisztomania by Phoenix but not the real version… the Brooklyn version (the real version is pretty much junk and where do you get rooves like this!?) by thepinkbismuth (both versions and Phoenix’s song are what early summer 2009 felt like, condensed and dancified.)

Anyone else have any recent favorites? Maybe you will see more post here… but lets not kid ourselves.

First you have to be in Rhode Island or it’s immediate vicinity because you need coffee syrup (it might be available elsewhere but I can’t vouch for it but it just happens to be half the ingredients for the state drink… coffeemilk) which is pictured to the left. Then it is cream and cheap vodka.

2 oz vodka
1 oz coffee syrup
light cream

Done!

UPDATE: If you search for “coffee syrup” you don’t get this but if you search for “eclipse syrup” you do… bravo

So now the point of this is that Mankiw’s blog now has a great tie in done by the publisher of his textbook. The publisher went through his blog and made a “blog map” tying blog posts to specific citations in the textbook. Its pretty cool considering that the idea behind Mankiw’s blog is to keep students of Economics up to date with contemporary examples. Now I have no idea what the back end is like on the “blog map” but you can imagine how this could be seamlessly integrated in a very semantic way. For example tags on blog posts could auto update to the relevant citations on the map, certain phrases could trigger citation/tagging automatically, and on the textbook end you could imagine that sections be tagged in an electronic form as they are added in new additions thus updating citations throughout the blog map even with older posts. The awesome part is that you can really see the value added to the textbook. By linking it to the blog you basically get continuous additions by Mankiw making the value of his authorship continual rather than finite.

Time to look back, if just for a moment. ‘08 is probably a year that many want to leave far, far behind, but at least there was some decent music. For the 4th year running, here’s some albums I liked that you may want to check out.

Following college it has been increasingly difficult to present a solid list of compelling albums. With the slim trickle of new music reaching my ears when compared to the bountiful days of WBOR and Bowdoin College, I have a much smaller list of music to choose from. I know a lot of my friends find themselves in a similar situation. So- hopefully this provides a few new items for you. Here it is: my non-hipster approved list, starting, as usual, with number 10.

(10) Fleet Foxes- s/t (June 2008)
Alright, Ryan. Fine. I like it. I listened to it a bunch over the Holidays and it was good. My parents even remarked “this is great Christmas music!”. You win, you always do. Goulet.

(9) Cut Copy- In Ghost Colours (April 2008)
Disco’s back, baby! Or is it 80s pop-synth-electronica? Whatever it is, it’s fun. Though- I sometimes get odd looks if I crank this album while driving around town in my Miata with the top down. Can’t quite explain that one.

(8) Airborne Toxic Event – s/t (August 2008)
Maybe they don’t have the most developed sound- in fact, you might even liken it to that poppy-happy crap that swills out of most of the major labels. Then again, its catchy and I like it. I can’t fault that all too much. Perhaps my tastes are drifting more toward the mainstream at this point. Being further from the vast wealth of new music that is college radio, my exposure to new work has fallen off– though KEXP provides a steady stream of awesome indie music. Airborne Toxic Event has expanded their EP from 2007 quite nicely with a well-rounded album that offers fast paced songs like “Wishing Well” and more gallant, “epic” sounding songs like “Sometime Around Midnight”. All together the album hits a number of points, albeit with slightly emo lyrics, and provides an enjoyable listening experience.

(7) TV on the Radio- Dear Science (September 2008)
TV on the Radio (TOTR?) sound like a refined, professional version of The Mathematicians- especially in “Dancing Choose”. I cannot complain about such a resemblance. The more palatable sound perhaps means I would be able to get more than a small group of close friends to listen to the group- such has not been the case with The Mathematicians. I applaud those who see the genius in Dewey Decimal and Pete Pythgoras, and perhaps an album like Dear Science can be the gateway drug to more cultish favorites.

(6) Cold War Kids- Loyalty to Loyalty (September 2008)
Some records are “headphone albums” or “scream-out-loud-in-the-car albums”. Loyalty to Loyalty is most definitely a vinyl album. It is best enjoyed on a nice set of turntables with giant speakers attached, encouraging you to sit close by and drink in the intricacies of the music. CWK is still on my list of must-sees- I missed one show in Boston (for which I even had tickets!), but I won’t let such a tragedy happen again.

(5) Vampire Weekend- s/t (January 2008)
Again, more mainstream-ish. They seem to be getting popular awfully quick. I hope a second album follows that is just as good. I may have burned out on this one simply because I listened to it so often over the summer; that’s a sign of a great album in my book, though. I like cohesive albums, and this seems to lack the strong theme(s) that many of the other compilations on this list have, but each song is so strong on its own that I can let such a foible pass.

(4) Bon Iver – For Emma, Forever Ago (February 2008)
I want to be relaxing in a leather chair in front of a fireplace, looking outside at the falling snow, with a glass of scotch in my hand as I listen to this album. It is supremely relaxing, and evokes a distinct calm winter night vibe that is simply perfect. Okay- fine- their name is “Good Winter” but still… you could call them Bob’s Oyster Sandwich Team, and I’d still get the same feeling. I missed their show in Boston this year, which came at a perfect time to reflect on cold evenings, but I am not sure if I missed much- this really seems like an album for at home in the living room.

(3) Ra Ra Riot – The Rhumb Line (August 2008)
Somehow, an album for which I cannot particularly remember specific songs has made it to #3 this year. I am a loss of what to say. However, as I thought about the album in comparison to each of the others on the list, it kept climbing. There is just something about it that really works. It’s not pop crap, its not erudite indie drivel, and its certainly not emo crooning. Its just a great album. FWIW- they are the highest ranked “band I have not seen live” from any year (discounting last year because, as I mentioned in that email, the non- #1 albums really weren’t that great in the grand scheme of things).

(2) Amanda Palmer – Who Killed Amanda Palmer? (September 2008)
Some people call her narcissistic for her obsessions with talking about herself. I find it entertaining that Amanda Palmer details so many things in her life to her audience- it makes her one of the most accessible artists I have encountered. Whether it is watching her sing Rhianna’s Umbrella on some street in Belfast with a broken foot, or auctioning off band gear as a intermission at her concerts, or writing her own twitter updates, she connects with the crowd. The songs on Who Killed Amanda Palmer work toward this goal of sharing by being deeply personal. The rhythms are pretty catchy, and her powerful voice shines through as always. I was also impressed with the input of Ben Folds in producing and arranging the album. Well done! To top it all off, the opening track on this album rocks, and a killer opening track will always win me over. PS- the Dresden Dolls album this year, No Virginia, is quite good too- I just did not want to flood the list with Palmer entries (and the opening track of the Dolls album is rather weak).

(1) The Hold Steady – Stay Positive (July 2008)
When I first heard the Stay Posi’ songs at the Paradise last spring, the band clearly had not practiced them much in front of a crowd- I was worried. After hearing the full album, though, I was totally sold. It’s damn good. Really damn good. THS’s sound has matured from earlier iterations. Not the “that cheese smells terrible” sort of matured, but the “Craig Finn can carry a tune!” matured. If Craig can continue this upward trajectory, he may even win Jessi over one day. The Hold Steady managed to impress me while playing at the Orpheum in Boston- possibly the most horrid venue in the world for such a band- it was clearly designed for midgets with binoculars and highly sensitive hearing. Oh- and if it is still up, check out this video. Muppets doing THS. woot.

Now, the massive post scriptum, my historical top 10s, starting with 2005.

2005
10. The 88 – Over and Over
9. Absolute Music volume 47, Swedish edition
8. The Mathematicians – Level One
7. Maggie, Pearce and EJ – Morgon, Mittag, Nacht
6. Death Cab for Cutie – Plans
5. Roman Candles – Bang! Bang! Bang!
4. Why? – Elephant Eyelash
3. Broken Social Scene – s/t
2. The Decemberists – Picaresque
1. Clap Your Hands Say Yeah! – s/t

2006
10. Beirut – Gulag Orkestar
9. Killers – Sam’s Town
8. Yeah Yeah Yeahs – Show Your Bones
7. Wolf Parade – Apologies to the Queen Mary
6. Architecture in Helsinki – In Case We Die
5. Electric President – s/t
4. Dresden Dolls – Yes, Virginia
3. The Decemberists – Crane Wife
2. The Mathematicians – Level Two
1. The Hold Steady – Boys and Girls in America

2007
10. Feist – The Reminder
9. Radiohead – In Rainbows
8. Spoon – Ga Ga Ga Ga
7. Modest Mouse – We Were Dead Before the Ship Even Sank
6. Beirut – Flying Club Cup
5. The New Pornographers – Challengers
4. Tally Hall – Marvin’s Marvelous Mechanical Museum
3. Pela – Anytown Graffiti
2. Okkervil River – The Stage Names
1. The National – Boxer

2) Actually sign up for any of those products

3) Invite people over who need to reinstall N > 2 computers

4) Have absolutely nothing else to do

Merry day after Christmas. Cheers.

PS: The classic “NORAD tracks Santa” can be seen here: NORAD Santa Tracker (note that Iran is on the bad list… but the ISS was over Iran when Santa hit up that crew)

This has been a pretty fun little experiment for me, and I’ve come up with configurations anywhere from relative modesty to incredible setups which would cost tens if not hunders of thousands of dollars and include substantial modifications to wiring and home configuration (network closet anyone?)

Maybe some of you have some ideas. Cheers.

So, of course, people need to know how to do parallel simulations with this code. In all major package managers 4.0.2 hasn’t made it through any appropriate channels, so people have to build it themselves. Unlike most major scientific packages, building Gromacs is absurdly simple. Things are quite beautiful actually.

Anyway, my point isn’t to extol the virtues of Gromacs but rather to suggest that if something doesn’t work, do the initial work to figure out the problem and exhaust at least the most obvious problems with the software before throwing your hands up in the air. Problem with MPI? Test it first! Anyone working with MPI should at the very least be able to look up how to write a basic MPI application.

An example:

#include "stdio.h"
#include "mpi.h"

int
main(argc, argv)
int   argc;
char  *argv[];
{
  int  rank, size, length;

  char name[MPI_MAX_PROCESSOR_NAME];

  MPI_Init(&argc, &argv);
  MPI_Comm_rank(MPI_COMM_WORLD, &rank);
  MPI_Comm_size(MPI_COMM_WORLD, &size);
  MPI_Get_processor_name(name, &length);

  printf ("process %d of %d on %s\n", rank, size, name);

  MPI_Finalize();

  return 0;
}

If you’re on a modern Debian or Ubuntu build with OpenMPI installed (pretty much the standard MPI implementation you should be using), then build.

$ mpicc.openmpi -o hello hello.c
$ mpirun.openmpi -np 4 hello
process 1 of 4 on enskog
process 2 of 4 on enskog
process 3 of 4 on enskog
process 0 of 4 on enskog

I do love my MPI. And Gromacs does dynamic load balancing now … so freaking fast.

Cheers.

• Flying random airlines localized to a specific country is usually a very bad idea
• … Especially when those airlines are localized to a country where strikes are often completely random in nature.
• Never, ever, when traveling internationally, book multiple trips on the same day.

Now some specifics:

I arrive, after a really fantastic trip in Italy, to the major Rome international airport (FCO). My flight was to London on Alitalia, where I was to pick up a seperate set of flights back to Indianapolis. The UK government paid for my trip to and from London whereas my trip to Italy was for personal business, so these two trips were booked separately.

Accordingly to Alitalia, my flight was “confirmed” and my ticket was “valid”. Ha! Well it turns out that Alitalia was randomly striking at the time, but only sort of striking, as some pilots would show up to fly the planes and others would not. This seemed to be completely par for the course there, which didn’t make much sense to me. Turns out people had been waiting there for a flight to London for over 3 days. None of their flights had left due to this strike. And of course all other flights to London were way overbooked because Alitalia hadn’t had a flight there in nearly a week. But, of course, according to the airline, the tickets were still “valid”, they just didn’t have pilots to fly the planes.

As the time came where it became obvious that I wasn’t going to make my connections in London, I started to freak out a bit, since it seemed no one was going anywhere from Rome and I was never going to be able to get home. I forfeited my flights from London to Indianapolis and was stuck in Rome because of this crappy airline. So, I had to wake up my parents at 2 am on the west coast to book me new flights back to Indianapolis through Frankfurt and DC. What was a nearly free 2 week stay in Europe had just become much more expensive.

Obviously I couldn’t show up for my flights in London, so those tickets were just flat gone. Would Alitalia at the very least give me my money back? Of course not, they claimed my tickets were still “valid”. Good lord. Screw you people.

When I arrived in Rome and told the people I was staying with that I was flying out on Alitalia, they openly laughed at me and said “good luck getting home”. Ugh.

Never fly Alitalia.

Cheers.

Oh yeah, and there’s that pesky thing called work that I have to do too. Stupid conferences. At least I’m an invited speaker: get the N-star treatment.

Cheers.

Cheers.

UPDATE: Verdict: lame. See comment #1.

More to the point, I put up some pictures. You can check them out here.

Cheers.

For all its size, one of the areas where I have been left completely unsatisfied is in support for threads. Yes, of course POSIX threads are there and I’ve had some success implementing them in some of my older, now completely obsolete C code which I never want to look at again. It’s baffling to me that there is nothing in the STL which develops some nice thread classes. I know there are at least 2 (if not more) very experienced C++ programmers who read vdov.net, and I’m looking for advice. Have you looked at some developed thread classes and if so what have you thought? Recommendations? I would really rather not have to write my own thread classes from scratch (especially since accessing the C pthread library would be a nightmare here), as this is both utterly useless for my research and, well, I’d probably screw it up with near-fledgling knowledge of the language.

Cheers.

A man approached me while I stood in line at the Subway on the University of Chicago campus. He said, looking at my shirt, “Really? You think so?” I stared at him blankly. He continued “Are you from the area (central Ohio)?” Realizing he was talking about my t-shirt, I said “Yes”. The man replied “Well, welcome to intellectual heaven!” and walked away smiling. Still standing in line, I started to stew about this brief exchange:

Subway is intellectual heaven!? Is being from central Ohio or wearing a central Ohio t-shirt a sufficient qualification for admittance into intellectual heaven? Very unlikely.

Was I just welcomed by an (the) intellectual god? If yes, then I met an (the) intellectual god, a “sandwich artist,” and “ate fresh” in intellectual heaven after what must have been my untimely intellectual death.

What caused my intellectual death? I’d guess being constantly bombarded with advertisements and repeated t-rauma from my choice of t-shirts.

But wait! Where is intellectual hell? How can I be trying to answer such deep questions while reading mind-numbing advertisements for Doritos (taking snacking to a higher level), Mountain Dew (the new dew is up to you), Subway (eat fresh live green)? Am I really in intellectual hell?

[Update]: Is my hatred of advertisements legal in Canada?

This was a nice storm: decent MCS and individual supercell formation leading to a squall line. Loving thunderstorms and the study of weather as I do (thanks Meyers!), I was pretty busy taking pictures/watching/looking at weather data when I saw a swirling cloud of debris headed straight for the back of the house. I figured it couldn’t be that big of a deal so I just sat there and watched. Then the 100 mph winds hit the house and I hit the deck (and subsequently an interior room). While the damage to our house was moderate (shingles, aluminum siding and gutters missing, thrown AC unit, etc.), some other people right down the street didn’t fare so well.

Pictures of the storm and of some of the damage are available here.

Cheers.

Other notable events: crazy single engine Cessna ride to the island, touring the Leper colony after having hiked down (and subsequently hiked up) the tallest sea cliffs in the world. If you recognize those, it’s because Jurassic Park 2 & 3 were filmed there. And of course the cover of my first boy band album.

Congrats Mica & Jason! It was amazing, I was so happy to be there!

Cheers.

Cheers.

PS: The Colfax avenue bus is quite an experience.

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.