Horst Störmer, Dan Tsui & Bob Laughlin - 1998 Nobel Laureates in Physics at MIT Symposium 10/8/1999

[MUSIC PLAYING]

KASTNER: Experiments were done up the street. And if you walk across through Building 9 into Building 13, you can find the offices where Bob Laughlin yelled at me and his thesis advisor, John Joannopoulos, for many years. We really feel as though this is a family affair. And we're really delighted that Bob and Dan and Horst all agreed to come and speak today.

I want to express thanks on behalf of the Physics Department to Dave Litster, the Vice President for research and Dean for research for helping to support this. And for the Francis Bitter Magnet Lab. Bob Griffin also helped support it.

And I especially want to mention the David Harris lecture fund. David Harris was a student at MIT. And before his death, he discussed with his family a memorial that he would like. And he wanted a memorial which would be a living memorial as opposed to hardware or bricks and mortar. And so his family endowed a fund which provides resources for us to bring distinguished lectures to the physics department each year.

And this year we're especially delighted that that's being used to help support this symposium. So now, I'd like to call upon Dave Litster, who would like to say a few words. Dave.

LITSTER: Thank you, Marc. It says here another welcome. I'm not sure you need another welcome. But I think the reason I was asked to do this is to indicate that this lecture series is an important part of the intellectual life of the Institute as a whole and that what's happening this afternoon is also important to the rest of the Institute and not just the Physics Department.

So I welcome you. I was thinking about this prize a little bit. And the thing that-- the idea that popped into my head is that, very often, those of us who do basic science, experimental basic science, especially owe an enormous debt of gratitude to technology. But we seldom acknowledge it publicly. But it's very important.

And this Nobel Prize would never have happened without some very important pieces of technology. Sometimes, the basic scientists have to develop the technology themselves. And here, I see there were three important technological ingredients. The first was these very special materials with very high electron mobility. And those were developed by Horst and Dan together with Art Gossard at Bell Laboratories. Without those, the experiments could not have been done.

Secondly, the experiments required very high magnetic fields. And those happened to be available at the Francis Bitter Laboratory and no place else in the country. And so the experiments were done here. I think Peter Wolff will be telling us more later this evening for those who were there about it.

And the third bit of technology is something that people refer to as wet technology. It was the unusual brain of Bob Laughlin who happens to be able to think about things in a way different from most of us and, therefore, was able to explain this. So I think it's going to be an interesting afternoon. In fact, it's going to be a real intellectual treat. And I will sit down so that Bob Griffin can proceed and we can get it started. Thank you.

GRIFFIN: Well, thank you, Marc and Dave. I'm here because I'm Director, presently, the Director of the Francis Bitter Magnet Laboratory. And as many of you know, being Director of the Magnet Lab has been like being captain of a-- the last few years, at least-- being captain of a ship sailing on a really pretty rough sea. Some people-- one of my colleagues described us like being captain of the Titanic even.

But we've had some very good experiences, nevertheless during the last few years. And many of those were associated with visits from Horst Stormer and Dan Tsui. I mean, we're very closely connected, of course, with the experimental aspects of the fractional quantum Hall effect.

As Dave Litster just mentioned, the fractional quantum Hall effect was actually discovered at the Francis Bitter National Magnet Laboratory at that time. And it was actually approximately 18 years ago today, yesterday rather. I don't know if you realize that, October 7, 1981. And we're converging to the opinion that the experiment may have been done in cell four of the Magnet Lab. Maybe Horst and Dan can comment on that later on.

But we owe Horst and Dan a very great thank you, a very big thank you. They have been an enormous help to the lab. And I think everybody at the lab, particularly myself, really appreciates what they have done for the lab. And perhaps more than whatever we did for them.

And so I would like to express the gratitude of the laboratory and its members to both of those individuals for all of the nice interactions we've had. And also to add our congratulations to everyone here on the award of the 1998 Nobel Prize.

KASTNER: Thanks, Bob. So now I'm going to call on Ray Ashoori, who was post-doc with Horst Stormer at Bell Labs before he came to the MIT faculty to introduce Horst.

ASHOORI: Well, it's a pleasure and an honor for me to introduce Horst. Horst has been at Bell Labs since completing his PhD at the University of Stuttgart in 1977. And he started at Bell as a post-doc and a year later became a regular member of technical staff. And following sort of a meteoric rise, three or four years later became a department head, head of the famous semiconductor physics department which is where the transistor was invented.

And he became, after that, director of physics research in 1991. He's now a professor at Columbia. And he still holds an adjunct director position at Bell.

By the mid-1980s, when I was in grad school, Horst was already quite famous. In fact, I remember one of the older students in my lab having boasted, I saw Horst Stormer. And a lot of other adjectives came along with that. But you can imagine how thrilled I was when he chose me as a post-doc back in 1990.

So the first thing I noticed coming into the lab was just an amazing amount of inventiveness and a little bit of outrageousness that I think led Horst to do a lot of great things. The first or second day in the lab, he asked me, can you solder? I said, sure, I can solder. I thought it was just soldering wires together.

What he meant was, can you sit up on this table on top of a stool and solder a couple of wires-- solder, under a microscope, on the end of a long probe that we used, a low temperature probe, and solder little microscopic wires on this sort of flimsy set up. And the idea was-- we had an idea-- he had an idea for a very novel experiment.

And I was a little bit reticent about sitting up on the stool. So he showed me first that it could, indeed, be done. So it's this kind of spirit that made it just a tremendous amount of fun to be there.

Way back when he was a post-doc, he invented a technique for growing ultra pure semiconductor materials called modulation doping. And this discovery-- or this invention was one of the key items, I think, in finally giving rise to the discovery of fractional quantum Hall effect that he and Dan Tsui did here, as you've all heard.

And this kind of structure, actually-- it has had some technological relevance, in that, if you have a cell phone, you've got transistors made out of this kind of ultra pure material that Horst invented. And some of these ideas that he's had, in retrospect they seem so simple and maybe even obvious. But of course, before you make the discovery, before you have the idea, it's not at all obvious. And Horst is known, I think, for just seeing with amazing clarity what needs to be done.

Here's another sort of outrageous thing that he did. He invented a technique called cleaved edged overgrowth, which you take a wafer that you grow. It's very thin wafer. You cleave it inside of a machine that's used for growing these wafers. And you actually grow on this thin edge of a wafer. OK.

This allows you to make, it turns out, perfect one-dimensional structures. And the technique itself is difficult enough, but on top of this, when I came to his lab he's actually doing lithography on this half-millimeter edge. So imagine doing lithography-- the kind that's normally done on big semiconductor wafers-- on a very tiny edge.

And I was just amazed at the outrageousness of this quest. He actually made it work. And he has done beautiful 1D experiments-- experiments on one-dimensional wires since.

I also-- here, I'm blessed with being near Peter Wolff who was Director of the Magnet Lab at the time Horst and Dan made the discovery. And I just love listening to his stories about Horst and Dan during that time and how they-- when they discovered the fractional quantum Hall effect.

First of all, they're working inside of a very noisy big magnet where there's giant currents running through the spinner magnet, water rushing through it, making the whole system vibrate. This bore is about two centimeters wide.

Now, imagine you have room temperature outside this bore. Inside the bore, you want it to be 50 millikelvin. So you somehow have to develop a refrigerator that cools your samples down to 50 millikelvin. Horst and Dan did it, and that, of course, is what got them the prize.

So you can see how this kind of inventiveness is just critical to this kind of discovery. Here's another story about the first day on the job with Horst. He has tremendous energy. And you see this in the way he walks, because you just can't keep up with him.

So what I would notice is that he walks so fast that I would-- I couldn't walk as fast. So I'd end up running a few steps, then walking a few steps, and running a few steps. And this is how we progressed to lunch every day during my two years of Bell Labs.

After Horst became director, and that was after my first year at Bell, after a year, he would still come down to the lab, and he would do things like help me change the pump oil. You know, what a completely mundane job for Nobel Prize-winning director.

He's getting up because he's getting sick of this. But you could see you could see in him that there was a real love of just being in the lab. All right. Let me end with this.

Horst has received every physics award imaginable, the Buckley Prize, the Nobel Prize, the Franklin Medal, he's in the National Academy of Sciences. He's a truly, I think, extraordinary and rare person. And it's just a thrill to have them here just for the day. Here's Horst.

[APPLAUSE]

STORMER: Is this on? Is this on?

SPEAKER: Yeah.

STORMER: Ray, you haven't gotten any briefer. But thanks very much. I'm-- it's just too much honor. Thanks. Thanks very-- I must say-- you hear more and more of these things, and you start wondering about yourself. But, all I can say, I'm a very lucky guy that has worked with tremendous people, and not just collaborators but also then in the form of post-docs, and Ray is one of those.

And there are several others around. And they give me all this credit. And it's just not true. It's these guys that did it. And that Ray says help changing pump oil was very easy. It's the only thing I can do.

[LAUGHTER]

It's a pleasure to be back at what was, for many years, our part-time home, not far down here. Sort of a place you really wouldn't want to call home when you walk into it. It's a loud and noisy environment. But Dan Tsui and I came there for many years doing our experiments, eating cold pizza and drinking warm Coke, looking at data on chart recorder coming out, and singing together with our grad students funny songs from Monty Python.

It was a really good time for a few years that-- well, actually, it must be about a decade that we came up here. So it's a pleasure to be back at MIT. It doesn't mean that I haven't been back in the meantime visiting old friends, and many of them are in the audience. There's actually too many to go through one by one. If I do it, I know I'm going to forget one of them, so I better don't.

So we have three hours. I'm not sure the audience how long you're going to hold out for three hours. But I have the advantage of having the first hour, and Bob has the last hour. [LAUGHS] So let's see what we're going to do.

That's my first-- can I take this off? No. Almost not. You can imagine we're doing a lot of these recently. Actually, the two of us, Bob and I, have been on a tour through Scandinavia. And we started feeling very much like these gentlemen. It's just a good one that--

[LAUGHTER]

And it hasn't it hasn't stopped much since then. I'm looking very much forward to Wednesday, next week. I hope that some of the burden is going to be taken off from us. But I'm afraid it's not going to be condensed metaphysics, so it still will be rough going.

In fact, when I told Bob that-- I did this when we went to Stockholm, and I had only the pieces with me. I told Bob that I would be doing this. And he said, yeah, and I knew it who's going to be Pavarotti.

[LAUGHTER]

I told him, of course, the best. So I'm actually-- along in this vein, I thought, this is, of course, all this it's a great honor and it is a wonderful, wonderful week, and we had a very good time. And how good a time we had is perhaps shown in this one.

You come in in the morning, and you are sleepy and not shaved and washed, because you get off the plane. And so they want you to take a photograph in front of the King. This is the King. Yeah.

I remember, I swear, Lou told a Viagra joke.

No. I tell you why we're laughing. And you know why we're laughing. The Viagra jokes were old by then.

So they get you in front of the camera. And what all photographers do is-- you're never close enough, right? Photographers always do that. And because they have one hand on the camera they do it like this.

So they wanted us to stand closer together. And, you know, Bob and I say, I can't. He's, after all, in the middle there, and it's not so easy to get-- so Bob started out complaining. He said, what do you want? And I started laughing.

So the two of us just blurted out. And you see this is Louis Ignarro, one of the physiology prize winners. And he looks around. He's just totally flabbergasted at how poorly-- how badly physicists can behave in front of the kings. Well, of course, I mean, it was that one that ended up in the newspaper the next day.

My fellow countrymen have had good fun with me. Because, in fact, there was always this-- it raises sort of the question, is he German, or is he not? Can we can we count him as one of ours or not?

And this question actually goes on, and particularly because my umlaut-- I have an umlaut in my name, and I dropped it when I came to this country. Because a good friend of mine, Michael Schluter, who is no more-- but he told me drop you umlaut. Because A, the typewriter doesn't have it. They don't know what to do with it.

And then the smart guys put an E afterwards. So half of them drop the umlaut. The other half puts an E after the O. Then you have appear twice in the alphabet, and it's not next to each other. So I dropped my umlaut. But, now, of course, they have found the umlaut again. And you wouldn't believe, in the last APS meeting, I was in twice, once with and once without umlaut.

But this is what, actually, somebody from [INAUDIBLE] sent me the next day in the mail from Germany. This was-- this is sort of the equivalent of the, I don't know, daily news probably. This was the front page of it.

And when I got this in the mail, my first reaction is to fly home and kill my mother. Because that's me--

[LAUGHTER]

--as a five-year-old playing Indians and Cowboys. In Germany, then, of course, no concept of the whole thing. But I thought my mother had given him that picture. But indeed, they had shot it off the wall, because it's hanging together with my little brother who's here that they cut out. It's hanging on the wall in my life my parents' living room.

In Germany-- this is, here, referring to the picture our Nobel laureate. And then it says under here, already as a boy, he built a toy train with a rocket propulsion, which is actually-- which is true. What it doesn't say there.

So in very small letters here-- and, by the way, it blew up in his hand and ripped off his thumb, which is also true. It was a long time ago. I have no problem with this anymore. But it certainly doesn't show me as a very good experimentalist. So it was a little bit off.

Well, enough of the jokes. Let me try to talk a bit about the fractional quantum Hall effect and see how far I get in. And Dan said that however I get, he takes the second half.

So I want to talk about fractional charges and fractional quantum numbers. And I want to give you sort of an impression what this whole thing about. The way I judge the audience is actually that most of you actually know everything about it, and I might as well sit down. But, after all, you paid my ticket up here. So why don't I deliver.

I don't think I have to say much to this audience about condensed metaphysics. But I think-- let me just, perhaps, pick up at one point along this thought. And that is one of the big problems nowadays in condense metaphysics is electron-electron correlations, meaning that electrons are strongly interacting, of course, because they are charged.

And taking into account the correlation, the motion between electrons as it's forced upon them by the other electrons around them is a very difficult problem. Most of through our life, we get away with very crude approximations. Number one, forget it. Just don't take it into account. Twiddle a little bit around with the math and with that dispersion relation, and you're done.

But, in some cases, electron-electron interaction is everything. For example, in superconductivity, it's everything, mediated by phonons there. And what I want to show is another case where electron-electron interaction is everything.

And it's only electrons this time around, electrons in 2D that really show very strange behavior, indeed. In fact, the strange behavior that it shows-- and it's just the pool of two-dimension electrons, nothing else, in a magnetic field.

You get fractional charges out, which was, of course, a big surprise. The new electron quantum liquids, fractional quantum numbers, flux-- magnetic flux can be attached to electrons. At least, it looks as if it were attached to electrons. New particles are popping up that can sometimes be fermions and bosons, depending on what magnetic fields you have.

Huge magnetic fields, as big as the ones that you get next door-- or got next door, and you still get a good fraction of them next door-- can apparently disappear, 10 Tesla, or something like that, a million times the Earth's magnetic field, disappears. And the carriers that you have seem to be moving along as if there were no magnetic field. There's a mass popping up, which has nothing to do with the mass of the electron. And they may even superconduct in some sense. Let me see whether I get to this, give you a bit of an impression.

We're working on two-dimensional electron systems. And you can create two-dimensional electron system, and three-dimensional worlds are always at an interface between-- can you see-- always at an interface between two things. So you could do it on the surface of helium, and it is being done on the surface of helium, on the surface of anything. Typically, things are dirty. This is no comment about your floor. It's just dirty, in the sense microscopically, that there are dangling bonds where the electrons get stuck.

So it turns out, actually, the best way to make a two-dimensional electron system is that the interface between two things, between two semiconductors inside a semiconductor. The technique to do this was actually developed, invented, in the '70s by Al Cho at Bell Labs.

And it's a high vacuum evaporation technique. We basically evaporate two semiconductors on top of each other. And so this is a high vacuum chamber. And you evaporate gallium and arsenic, gives you one semiconductor. Gallium and aluminum and arsenic gives you another semiconductor. That's all you need to know.

And you grow it on the substrate, which provides a template so that the atoms go into the right place. Otherwise, it's just like ball bearings, in the sense, otherwise, it would be random. So you provided a nice underlying lattice for it to grow.

And, as you know, in order for semiconductors to conduct, you have to throw some dirt into it. You have to doping them. And, in this case, actually silicon becomes the doping. So silicon is the stuff that gives off an additional electron that then can move around in the material.

The way this looks is like this. This is about two-inch diameter. What is dark here-- disregard these things up there. They actually do have something to do with this what Ray brought up. And that is this cleave that you overgrow. This is not import.

It's just this part down here. This is the wafer. So they're shiny semiconductors, look like a silicon wafer, basically. And the reason that the black here is because the background was black. But this is a shiny surface of about 2-inch diameter, which then has been grown by MBE.

And the important aspect of this is that you have incredibly controlled in this E direction. You can grow these layers one layer after the other. So what you see here in the cross-section is four layers of gallium arsenide, four layers of aluminum arsenide, four layers of gallium arsenide. This is the black and white stripes.

You have a control. This was in one atomic layer. And this is-- so you form these layers that fluctuate by not more than one atomic layer, so about an angstrom. So this is the flattest surfaces that you can create with a control of, really, one layer. You know you can stop at five, or six, or seven layers. And this technique that was developed and invented in the 1970s we had then used in order to make very high mobility two-dimension electron system.

In three dimensions, there's sort of a catch-22 when you dope something. You throw in the silicon, which gives off the electron that then moves through the semiconductor. But your left with the charged the impurities of which the electron then, very often, bounces off.

So, yes, you introduce carriers. But you also introduce a scattering for it. In 3D, you hardly can get around it. In 2D, you can. Because in 2D, you can put the electrons in one layer and the dirt in the other layer. And therefore, they hardly see each other.

And this is the method to do it. It's called modulation doping, which is-- so the green is one semiconductor. The blue is the other semiconductor. You put the impurities into the green semiconductor, and they wander over into the blue semiconductor, because there they find lower energy.

This is a quantum well of about 100 angstrom thickness. And the electrons now can move in this plane. But they cannot move in this E direction because they are tightly confined.

In fact, they are so tightly confined that quantum mechanics plays an important role. They're confined that you see the first bound state and the second bound state, and they're separated by about, let's say, 10 millielectron volts. So quantum mechanics is an important aspect of this.

If you only have the lowest state occupied, and not the second one, the electron in the Z direction has no degree of freedom. It's just tight. It cannot do anything. But it can move in the x-y plane easily, in fact, very readily because it's such a nice plane, and then the impurities are away from it. So you get a very high mobility two-dimensional electron system in which the electron can run for very long distances before they scatter as anything.

The electron density is about 10 to the 11, which makes about an electron every 300 angstrom, something like this. Typically 10 to the 11. You can vary, but that's a typical density that you will find.

Mobility is nowadays as high as 10 million. In fact, last week-- no, it was the week before. Two weeks ago, we had a record of 23 million mobility, which is unheard of. I mean, I'll show you a little bit more about this.

You may not understand what mobility means. But it's a mean-free pass of about 100 microns. In fact, 20 million is about 200 microns. So the electron travels in this plane for about 200 microns without bouncing into anything.

And 200 microns is really big. It's about the thickness of your fingernail, which doesn't look so big. But on a microscopic scale, and on a little graphic scale what we can do nowadays, it is a huge mean-free pass. And it's these two-dimensional electron system, which then we can regard as a two-dimensional metal. They're basically nothing else but that with a very long mean-free pass. So it means that the lattice behind it hardly plays any role. It's like a two-dimension electron system just in free space.

Now, this technique was invented around 1978, something like this, by these four guys. And I show it to you for two reasons. The one is sort of a historical picture in terms of MBE machines. This is how MBE machines looked then.

In fact, what you did is this is a very high vacuum. These days, you still open it up, let all the air in, stuck your sample in, pumped it out over night. And the next morning, you get your growth. You don't do this anymore, much cleaner than that.

The people standing around here is Willy Wiegmann, Art Gossard, Ray Dingle, and this is me in an earlier incarnation, standing around the MBE machine for the photographer. And the important part-- the other important part why I'm showing to you is Art Gossard.

Art Gossard was the person that grew the sample on which we then discovered the fractional quantum Hall effect. And this was the first time mobilities went as high as 90,000. And that made it all possible. I mean, it brought it actually about.

So the sample is the most important ingredient to all of this. And Art Gossard and his assistant, Billy Wiegmann, they grew the sample. And it's really unfortunate that they didn't share with us in that prize. They shared with us in some previous prizes, but not in this one.

And I say it's unfortunate, because I think for us condensed metaphysicists, materials is just the most important aspect of our work. The people that have first hand on materials are the ones that very often are ahead in the science that they're doing because it's really the materials that get them to this initial step from where you then can start playing. So Art and MBE technology is a very important aspect of all of this.

So what you end up with then is a two-dimension electron system where by the separation of electrons from the doping impurities and then the suppression of scattering from those-- is there any kind of a pointer? No? All right.

You get very high mobilities. At very low temperatures, they get a very long mean-free pass. So it looks a bit like a billiard table in two dimensions. Electrons can only move into two--

Oh, there is one. Right. I should-- oh, this is this little guy there. Great. Thanks, Marc.

Let me show you how an MBE machine looks nowadays and the people that are running it. This is the crew nowadays that is making this 25 million-- 23 million mobility sample. Actually, the most important guy, Loren Pfeiffer, and his assistant Ken West. This is Kirk Baldwin, who's an assistant with me. And this is Amir Yacoby, who was a post-doc at the time.

So now, the MBE machine is about that thick. And you use much cleaner methods in order to get such high mobility. But again, these are the important guys to which we owe everything.

I'm very often being asked, why at Bell Labs? Why at fraction of charges? Is it ever going to be in the telephone system? And my only answer to this is this is only going to make our vacuum cleaners run only 1/3 speed, and that's about all. And it's a joke. So fractional charges will not have-- I don't see fractional charges having any kind of application, even in the long run.

But there's another aspect of all of this work, which has an application, and that's this one. Out of exactly the same material-- or exactly the same material in which we discovered, Dan and I discovered the fractional quantum Hall effect-- out of the same material, you can make field effect transistors.

It just looks like it. This is what is in every PC. It's a MOSFET. Never mind what it is. This thing just looks the same. But it's another material, and this specific technique of modulation doping creates mobilities that are much higher than here. And contact resistance are lower in all of this.

So these transistors, or transistors made out of this materials are the fastest and lowest noise transistors in the world still today. This is one built by Fujitsu, who actually was one of the first that made a microscopic transistor out of this. Never mind what the structure is. But this is the fastest, lowest noise transistor that you can get.

And it's in any of those around the world. Each one has one of those, radio telescopes. This is not a very big market. There's just about probably 100 or 200 around the world. So you cannot make money with that.

But you can make quite a lot of money with these things. So a lot of these high frequency 2 gigahertz telephones that-- cellular phones-- have in the front end, which is-- well, the microphone is a front-end maybe up there-- have one of these HEM transistors for very good performance. And the base stations have it in there.

So there's another part of this modulation doping, which is not basic science, but, really, technology. And I feel very fortunate that on one side this is modulation doping that we invented led to very basic science. And on the other side, it also led to an application.

And it's not so that the one came after the other. I think it's an important lesson. And we're not the first to teach this lesson, in a sense. Or the material is not the first to teach this lesson, that is that it's not always an invention, fundamental physics, and then there is application. Very often, these things go in parallel, and very often, actually, they go backwards, because the progress in technology is so important for us to do the next step in science too. OK.

Let's get a little bit closer to the fraction quantum Hall effect. If you have such a system, particularly if it's semiconductors, the easiest thing you can do apart from measuring its resistance is to measure the Hall resistance. All it is it's like a resistance measurement, but in addition, you put a magnetic field up.

So this is a two-dimension electron system. You run a current down it, and you put a magnetic field onto it. Then you measure two characteristic voltages, the one is along the current path. The other one is across the current path. The one is nothing else but the resistance, and the other one should be 0, as long as there's no magnetic field because the thing is symmetric.

But when you put a magnetic field on it, then you push the carriers to one side because of the Lorentz force. So you build up a voltage. Eventually, you'll build up a voltage from one side to the other. That's what you measure.

And these-- the voltage that you measure-- divided by the current, because it's proportional to it. So if you double the current, you get double the voltage. So you normalize it to the current. You get a resistance, of characteristic resistance, which is called the Hall resistance.

And as Edwin Hall has already figured out in the last century, I'll show this next the next few graph, Rxy, this resistance is proportional to E, to the magnetic field, and inversely proportional to the carrier density in the material. So it's a wonderful way of measuring carrier densities in material, particularly in semiconductors. Because, you see, the smaller end, the easier it is to measure. The smaller end, the bigger this number is. And typically, carrier concentrations are small in semiconductor as compared to metals.

So this is a wonderful way of measuring carrier concentration. And it's an industry standard. So this is the first thing you do.

And we've done this, of course, but Edwin Hall had done this already in the last century. This is why it's called Hall effect. He was a graduate student, by the way, at Johns Hopkins in 1879, when he discovered that in a very thin foil of gold.

He just did this experiment that I showed you. And this is the result here. In fact, there's another aspect to all of this, which I always enjoy, is for all of us that are writing papers that have to be 3 and 1/2 page and not any longer. It's interesting to read this introduction here. We have to fight with every word, take it word out, and make an acronym out of it, so that you save another five words. This starts out with, "Sometimes during the last university year, while I was reading Maxwell's Electricity and Magnetism--" I mean, by that time, you had already-- we're already over your page limit nowadays.

The other aspect is, just like it is expensive nowadays to publish color figures, it must have been expensive in those days to publish any kind of a figure. So his results are here only in form of a table. So I had to sit down and, for the first time, plot up Edwin Hall's data. And here is Edwin Hall's data now on a graph. He has plotted.

This is what we call nowadays the Hall resistance. It's actually a current through the gold leaf divided by the current through a magnetometer versus magnetic field in units of the Earth's magnetism. One does not know what these units are, but one knows that it's proportional to the magnetic field. So that's fine.

So this is magnetic field. This is Hall resistance. And you see, those are his data. It's a very nice straight line, just as we know. And, of course, since then, this experiment has been done in many ways by many people, and it's a perfectly nice straight line. And the slope of this line here gives you the carrier density of the material. The steeper it is, the less carriers are in it.

So this was a status until 1980 when Klaus von Klitzing came along and told us that this is not so at all. In fact, in two dimensions, it's not so at all. This is the original result, Klitzing, Pepper, and Dorda in 1980.

And it's plotted in a different way Edwin Hall would have plotted it. So I show you the way-- similar data. It's not the same data, but similar data locks if you plot it like Edwin Hall plotted it.

Magnetic field Hall resistance. This is the Hall resistance. I'll talk about the other one in a second.

So Edwin Hall would have told us this is a straight line. And so Klaus von Klitzing found-- of course, this is a very nice example. The steps were much weaker when he saw him. But there are lots of steps in there.

This is not all a straight line. These steps are in there. And not only are these steps very flat and sometimes very wide, but they are also quantized to units of H over E squared to an accuracy, nowadays, of a few parts and 10 to the 8. So a few parts in a billion, almost, a few 10 billionths accurately quantized to this ratio of natural constant.

This came as a big surprise. In fact, there are some inklings in the theoretical literature that sort of foresaw this in some sense, but not really pointed it out. You experimentalists should-- and it was obscure. But Klaus von Klitzing discovered this, actually, at the Magnet Lab in Grenoble, the sort of sister institution in Europe.

So this is not all a straight line. But it's plateaus and it's quantized. And I show you also what the resistance does as a function of magnetic field. That's the other property.

It looks like the derivative of this. So whenever this is flat, it's actually a deep minimum. And then when it makes a transition, you get a spike out of it. So the magnetic resistance looks like the derivative of the Hall resistance.

I show you this because, later I've sometimes show you these data, because they're sort of more dramatic than even the Hall resistance. But it's the same-- the origin is it has the same origin. Here comes my two view graphs explanation of the integer quantum Hall effect.

If you put a magnetic field on a two-dimensional electron gas, than the electrons classically perform rotary motion around the magnetic fields. So quantum mechanically, this is just a harmonic oscillator, so this is my quantum mechanical oscillator. And then there are bound states in there.

And there's only a certain number of bound-- well, there's an infinite number actually. But they are discrete, and there's nothing in between. So the electron can be in this state, in this state, or in this state, and nothing in between.

So in a three-dimensional electron gas, there is actually something in between. But in 2D, there's nothing in between. And therefore, there's only allowed states at this energy, at this energy, and this energy, and nothing in between. I forget the spin, or leave the spin out for most of my talk. It's just complicates matters here, but it's very easy to take into account.

The other aspect of this quantization is that the number of electrons you can fit into a squared per one of these Landau levels, as they are called, is only a ratio of a natural constant in proportion to the magnetic field. So you take-- if you take this wave function, it makes sort of a size out of it. You take a cookie cutter and just cut out, see how many fit in there. And you see that the number of electrons per level is just e times B over h.

And it's independent of the mass. It's independent of epsilon of the materials, independent of everything. It's eB, only proportional to the magnetic field. So the integral quantum Hall effect actually happens when I fill up an exact number of these states, of these Landau levels.

And you can see that very easily. You take the number of electrons per level, which is eB over h. Then if i, 1, 2, 3, 4 of these levels is filled, then it's just i times d. You put this into the equation that I showed you earlier that Edwin Hall derived already in the last century, and you get the result, h divided by ie squared. So it's really true.

There's a big but here. And this took ingenious people to figure out. Because what you assume in there is that the number of electrons, in a certain sense, is quantized, and that the system is ideal. You do it here. But it's never like this, the number of electrons is fixed once and for all. And you never have an exact number of Landau levels occupied except for singular points.

So all this says is that the long-- right, this is my Hall line here along the magnetic field line. There's a few discrete points. But when I go up, this resistance is exactly this number. But it doesn't say that there's any plateaus. I wouldn't even know where they are.

So this is a bit of a fake doing this way. But I cannot go much deeper into it. What it tells you is that this connection between the quantization of the Hall resistance and the two-dimensional system, the two-dimension electron system has something to do with filling up exact numbers of Landau levels.

And this big but here has to do with localization in two dimensions. There's actually an important aspect. If you had an ideal two-dimension system, you would not see the quantum effect. It requires dirt in order to see it.

I think it's this sort of totally counterintuitive. You need dirt. You need impurities. You need localization of electrons in order to see it.

In fact, the guy that figured it out is going to give a talk sometime today. This is the-- I will not go through this argument, of course. But the bottom line off of Bob's argument, one way at least of looking at it, is that Rxy, this-- you can actually regard it-- which is this number-- you can actually regard it as a ratio of flux, of magnetic flux, quantum to the electronic charge. So it's the ratio of flux quantum to electronic charge.

And therefore, you can look at this, the quantum Hall effect, if you turn this argument around, as being a measure of e. So that is a very accurate measurement of the electronic charge, which is then the flux quantum divided by whatever you measure. And then this is an integer. And the integer you always know whether it's 1, 2, 3, or 4. You cannot be that far off. So it is one way of looking at the integer quantum Hall effect that is a very accurate measurement of the electronic charge.

The other aspect that I always found perplexing is that you measure something to an accuracy of a few parts 10 to the 8 in a sample that looks as terrible as that one. This is about three millimeters wide, about 15 millimeter long.

This is indium here that is put on and diffused in order to make contact. The black part is actually the surface of the semiconductor, which is really shiny. These parts have been scratched away with an ultrasonic scratcher, really a very intrusive method. And those are gold wires running off here.

This is a sample that was made by Dan Tsui. I would have done a much nicer job, but I'm sure that my contacts wouldn't have worked. Dan's worked. And, in fact, that's the sample in which we discovered the fractional quantum Hall effect.

So in terms of the integral quantum Hall effect already, it is always so amazing that, independent of geometry, independent of how you put your contacts on, you measure something, a quantity to a few parts 10 to the 8. And, of course, this is the essence of a standard, that it does not depend on, in this case, on the geometry at all. You can even make a round sample with all the contacts on the edges. As long as you do that, you also measure it.

This is a picture that's probably going to bring some emotions up in some of the people that are sitting here in the audience, certainly, Larry, I would think. This is-- I don't know which cell it is, but Larry can tell us. Which cell is it, Larry? It was downstairs someplace, yeah, I think so.

This is 23 Tesla, I suppose. Picture that was shot much later, dilution refrigerator-- that's the fridge. This is the can for around it. This is the pumping system. A person is about as big as this pumping system.

And we went with samples through the Magnet Lab and did experiments in high magnetic fields, and later on then with a dilution refrigerator. This is about 10 years later, I would think, but still when the Francis Bitter National Magnet Lab was in-- up here. Well, it still is up here, only without the National.

Dan and I were coming up here for several years to do experiments. And we were typically getting up on Sunday morning, driving up here, having a long four-hour chat. Depending on who was driving, it was either three or four hours-- four or five, I should say, I think. We're not that fast.

And we had this brand new sample form Art Gossard. We were doing experiments down in whatever cell. I don't know which cell it was. We were working on silicon MOSFETs, actually.

Dan had invited me to come up with him. He was there already since quite a while doing experiments on silicon. And then with this new sample, we started working together on this modulation dopes systems.

So here's the result of October, 6, 1981. This is the Hall resistance. This is the magnetic field, just what Edwin Hall would have done. And it's a very nice straight line.

This is an offset here, so they get it still on the chart recorder paper. It's an old technology to take data. You take a pen and pull it over a piece of paper. And then you look at the trace. And that's what your data is like.