Anyone with less than a master’s degree visiting the Kavli Institute for Theoretical Physics immediately wants to disappear.
The place makes the nicest Hilton look like a truck stop hotel. It has that distinct expensive feel, but no amount of money will get you in. Folks here have paid for their stay with years of gnarly physics and math courses. Framed architectural drawings and geometric designs that would put a smile on the face of M.C. Escher occasionally punctuate the winding terra cotta hallways. And somewhere on the second floor, about the time you’ve gotten thoroughly lost, you’ll come across the office of Dr. Matthew P.A. Fisher, the newest member of the prestigious American Academy of Arts & Sciences.
He joins other members of the Academy past and present, including George Washington, Ben Franklin, Daniel Webster, Ralph Waldo Emerson, Albert Einstein, Winston Churchill, Bill Gates and Walter Cronkite. Not to mention other UCSB appointees, Joe Polchinski and David Gross, also of the Institute for Theoretical Physics.
Fisher’s parents are from Britain. He has a B.S. from Cornell, a Ph.D. from the University of Illinois and worked for several years at the IBM labs in Yorktown Heights, New York. When he speaks, his accent is a strange combination of all these places, with a touch of “excited physicist” mixed in.
His ocean-view office has two desks in opposite corners, on which sit three computers. Across the room from these is a large chalkboard filled with ugly integrals sandwiched between two bookshelves replete with physics references and bound notes. It seems that sitting down and working in this office are mutually exclusive activities.
It’s a nice room in a nice building. But as Fisher explains, it’s not so much an office as it is a ballroom.
Welcome to the Dance
“Imagine there’s this dance hall that you’re not allowed into, but you know that everyone inside is having a great time. You know that inside there’s a beautifully elaborate dance going on. It’s all choreographed and the dancers are whirling around and switching partners,” Fisher says. “Now imagine that it’s your job to try and figure out what that dance is without going into the dance hall.”
Imagine now that the dancers are not people but electrons and you have the puzzle of a career. Electrical current, for instance, is merely the movement of electrons from one place to another. Picturing the way electrons interact with one another is a difficult problem. For simplicity’s sake physicists for many years have used something called “Fermi Liquid Theory” to describe electrical circuits in which electrons simply don’t interact at all.
To use the analogy of people once again, imagine yourself walking between classes late on a Friday afternoon. As you walk, you probably take into account uneven pavement, sidewalk edges or ditches that block your path, but the campus is big enough and sparsely populated enough that you generally don’t have to worry about bumping into other people as you move from one place to another.
In the same way, using Fermi liquid models scientists can determine the movement of electrons through a circuit, taking into account obstructions, electrical resistance and wiring flaws. Most of the time these models work well enough. But there are times when Fermi Liquid Theory can’t describe what’s going on. There are times when the theory becomes a poor way of understanding the world.
That’s because there are times when electrons dance.
Semiconductors, Carbon Nanotubes, and High Temperature Superconductors (Oh, my!)
Before you can understand how electrons dance, you must first understand what a dance hall is from an electron’s perspective. Fisher is particularly interested in three kinds of materials: carbon nanotubes, semiconductors (under special circumstances) and high-temperature superconductors.
CARBON NANOTUBES
Carbon atoms are extremely versatile. They make up all sorts of things from high-priced jewelry to your skin. By themselves, without any other types of atoms, carbon atoms can form four different materials. Diamonds are a form of carbon in which carbon atoms are bound together into a giant lattice. In fact, a perfect diamond is actually a single carbon molecule. Another form of carbon is the buckminsterfullerene molecule, fondly referred to by physicists as the “bucky ball,” in which over sixty carbon atoms form a molecule shaped like a soccer ball. A more common form of carbon is graphite in which carbon atoms are arranged into stacked sheet-like molecules. Your pencil lead is made out of graphite and when you write with it, these sheets of carbon are laid out onto the page.
In recent years, materials researchers have found that they can effectively take the ends of a sheet-like graphite molecule and join them to make a tube. These tubelike molecules are called carbon nanotubes and they actually form molecular wires that conduct electricity. Tiny wires like this don’t leave electrons any room to get around each other. In a wire this small, electrons have to interact. They have to dance.
SEMICONDUCTORS AND THE QUANTUM HALL EFFECT
Semiconductors are lattices of atoms with four spare electrons. When the atoms bond, they share these electrons. Each atom bonds with four neighbors at right angles with one another. Most commonly, the atoms used in semiconductors are silicon atoms. Together the silicon atoms form a big grid. Because all of the electrons in the grid are tied up by stable bonds, it doesn’t conduct electricity. To this end, atoms like arsenic or boron are mixed in with the silicon – a process known as doping.
Arsenic has five free electrons and boron has only three. When arsenic bonds with its neighboring silicon molecules, it has an electron left over. So a semiconductor doped with arsenic has extra electrons floating around within the grid. These can move about relatively freely. Since electrons can now move through the material, it can be said to conduct electricity, but not very well. It is a semiconductor. Because this type of semiconductor has extra electrons, it has an overall negative charge and is referred to as an n-type semiconductor.
A semiconductor doped with an atom like boron, which has only three electrons, finds itself in the opposite situation. It needs extra electrons to form a complete grid. It has an overall positive charge and is referred to as a p-type semiconductor. Left to its own devices, a p-type semiconductor will inhale additional electrons. Thus, it also conducts electricity and is a semiconductor.
An n-type and a p-type semiconductor placed side by side are in a happy state of affairs. The extra electrons flow from the n-type semiconductor into the p-type semiconductor. As long as there is a battery attached to the circuit to keep supplying new electrons, the process continues. If, however, the battery is flipped around it can exert a bigger pull on the electrons than the junction between the two semiconductors. So electrons are no longer allowed to flow between the two semiconductors.
This sort of one-way valve allowing current to flow in one direction but not the other is called a diode. Sandwiches of three semiconductors (i.e. p-n-p or n-p-n) are called transistors. Initially they don’t allow current to flow in either direction. However, when a small current is applied to the center of the sandwich from an external source, it supplies the center semiconductor with the charge that it wants and allows current from the circuit to flow through the transistor. So a transistor is basically an on-off switch for current. The on and off positions of these switches can be used to represent the ones and zeros your computer uses to do math.
At the junction between two semiconductors, there are always electrons roaming about. When these are exposed to a magnetic field, they begin to interact wildly. Their strange dance is known as the Quantum Hall effect.
HIGH-TEMPERATURE SUPERCONDUCTORS
A superconductor is a material that conducts electricity with no resistance. Resistance is the sum of the processes that impede an electron’s progress through a circuit. Traditionally, superconductors are created by taking a material and chilling it close to “absolute zero” – the lowest possible temperature. The temperature of an object is merely the average kinetic energy of the molecules that make it up. Simply put, the molecules of an object at absolute zero do not move at all. In a regular conductor like a wire, the positively charged nuclei of atoms are bouncing around with high kinetic energies. Because of this, electrons stand a much better chance of slamming into one of them. In a superconductor near absolute zero, this ceases to be a problem. Superconductors are highly desirable in engineering. Imagine, for instance, if power lines could carry electricity to your house without losing any current. The amount of money saved worldwide would be unfathomable. However, cooling a material to near absolute zero takes so much energy that it currently isn’t worth the trouble.
In 1986, a new class of superconductors was created which only need to be chilled to half of absolute zero. Though still too inefficient for many industrial applications, these new superconductors, dubbed high-temperature superconductors, may be the first step toward the kind of ultra-efficient materials that electrical engineers dream about. There’s only one problem. No one knows how they work.
But one thing is clear. Fermi Fluid Theory isn’t going to describe the process.
“It’s a completely new dance that we just don’t understand,” Fisher says.
Big Thoughts Concerning the Very, Very Small
The Quantum Hall effect was discovered in 1983. By 1984 there was math to describe it. Robert Laughlin, a physicist at Stanford University, made a lucky guess about the kind of dance that electrons in semiconductors were doing and walked away with a Nobel Prize. A few of the experiments that proved his theory were designed by Fisher and his friends, who were then a graduate students in Illinois. Fisher has stayed with the field ever since.
An example of the kind of theory he is working with can be explained by describing what happens to electrons interacting in a carbon nanotube. You may recall from high school physics that opposite charges attract and like charges repel one another. The electrons in a carbon nanotube repel each other and, left to their own devices, they space out evenly along the tube, putting as much space as possible between themselves and their neighbors. When you run a current through the nanotube a new electron is introduced and when it moves down the pipe it starts a sort of compression wave along the tube.
A good example of a compression wave is a slinky. When you stretch a slinky out and hit the end of it, the rings bunch up and the pattern of bunched up and spaced out rings makes its way down the slinky until all the rings are spaced out again. You can think of each ring in the slinky as an electron in the nanotube. When the new electron is introduced, it causes the one nearest to it to move, which causes the next one to move and so on. The pattern changes.
The place where the pattern of the spacing changes is called the “domain wall.” It’s just as easy to imagine introducing a new electron in the middle of the tube. In this case, compression waves would extend in each direction. A domain wall would exist in each direction. Fisher and his colleagues have found that it is easier to keep track of the motion of the domain walls than it is to keep track of every individual electron.
Since half the effects of the new electron’s charge are exerted in one direction down the nanotube and the other half are exerted down the other, it is also possible to say that half the electron’s charge is present at each domain wall. Since scientists are keeping track of a moving point with an electrical charge, they find it convenient to think of these points as actual particles.
Though these are not real particles and little more than placeholders, they serve great purpose in describing the dances of electrons. These placeholders have earned the name Laughlin quasiparticles.
In the case of the Quantum Hall effect, electrons are interacting in two dimensions instead of one. They circle one another like dancers and the point around which they spin is called a vortex. The vortex is analogous to the domain wall in the carbon nanotube. In this case the quasiparticles have one-third the charge of an electron. Electrons can also orbit the vortex in one direction or another, and scientists refer to the directions as positive and negative.
Fisher and his colleagues have developed laws of interaction for these quasiparticles that have to do in part with whether they are positive or negative.
For several years now, Fisher and his colleagues have been attempting to develop similar laws of interaction for high temperature semiconductors. So far their theories have not stood up to experiments.
“If they had, we would have gone to Stockholm for the Nobel Prize,” Fisher says.
But high temperature semiconductors are a much more complex problem. Some physicists think the puzzle is chaotic and altogether unsolvable.
“It could be that the devil is in the details,” Fisher says, “But I’m an optimist. I think there’s something new and exotic going on.”
The holy grail of all this research would be to understand completely how electrons interact with one another – a discovery that would apply not merely to circuits and computers but to everything we see and touch as well as to life and consciousness itself.
“There are less neurons in your head than transistors in a computer chip but there are wonders going on in there,” Fisher says.
