“Superconductivity”

a tale of mystery, intrigue, suspense, and scandal.

For your enlightenment and entertainment,ELMSS presents…

Selected Big Ideas of Physics

Conservation Conservation Newton’s Lawsof Energy of Momentum

Ef = Ei Pf = Pi inertia F = ma action/reaction

"The only reason for time is so that everything doesn't happen at once.“ – A. Einstein

1905, Einstein, relativity: The laws of physics are the same for all non-accelerated observers, and the speed of light in free space is a constant.

If you believe these and conservation of momentum, then

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Newton’s 2nd law becomes F = m(dv/dt)+v(dm/dt).

Also, if you believe in conservation of energy, then E = mc2.

“Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. THAT'S relativity.” – A. Einstein.

Let’s think about conductors and insulators. Resistivity is a measure of how well or poorly a material conducts electricity.*

copper 1.7x10-8 ·m

graphite 1x10-5 ·m

silicon 1 ·m

rubber 1x10+15 ·m

That’s a factor of about 100,000,000,000,000,000,000,000 difference between a good conductor and a good insulator!

* Resistance = · (length of conductor) / (cross sectional area of conductor), hence the units of .

Metals

What is your mental picture of a metal? Solid, made of atoms, has electrons that can move?

+ + +

+

+

+ +

+ + ++

-

-

-

---

- - -

-

-

The metal atoms are positioned in a regular, symmetric array. They are heavy and don’t move around. They lower their energy by donating one (as shown) or more electrons to the metal as a whole. The lightweight electrons are free to move around and conduct electricity.

How do metals conduct?

Electrons carry the charge.

When you apply a voltage, an electron feels a force.

According to Newton, the force accelerates the electron.

As long as the voltage is applied, the electrons in a metal should go faster and faster.

They don’t. In fact, they seem to move about as fast as a tired snail. Why?

Something must be impeding their progress. Something must be holding them back.

Here’s the “classical” picture of the mechanism for the resistance of a metal:

+ + +

+

+

+ +

+ + ++

-

Voltage electron “drift” velocity

The voltage accelerates the electron, but only until the electron collides with a + ion. Then the electron’s velocity is randomized and the acceleration process begins again.

Predictions made by this theory are typically off by a factor or 10 or so, but it was the best we could do before quantum mechanics.

"Anyone who has never made a mistake has never tried anything new.“– A. Einstein

Quantum mechanics, developed in the 1920’s and 1930’s, fixes this discrepancy. Instead of starting with Newton’s laws, we start with a QM equation, which in its simplest form, looks something like this:

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When we solve this equation for an electron moving in the periodic potential of the metal ions, we notice two remarkable facts:

This is really just a “funny” way of writing conservation of energy!

electrons moving in a metal do not act like particles; rather they act like waves, and…

because electrons are waves, they travel freely through the metal without interacting with the metal ions.

If electrons don’t collide with metal ions, what do they collide with (after all, metals do have resistivity)?

Answer: they collide with impurities, or with metal ions which happen to be vibrating and in the “wrong” place when the electron wave passes by.

Periodic vibrations of atoms in solids are called “phonons.”* Think of plucking a guitar string. The resulting wave travels along the string. Now think of reaching in and plucking an atom with nanotweezers. The forces between atoms pull the plucked atom back into position, setting up a wave of atomic vibrations which travels through the material.

*Phonons: think “phonograph” or “telephone.” Phonons are atomic vibrational waves that travel back and forth through solids. Think of them as sound waves in solids.

blah de blah blah…

When is he goingto get to the point?

Better be soon!

"Do not worry about your problems with mathematics, I assure you mine are far

greater.“—A Einstein

Two last items before we get to superconductors…

First, imagine a perfect conductor. What would happen if you tried to bring a magnet close to it? What would happen if you tried to remove the magnet?

Faraday’s Law: a changing magnetic field produces a voltage in a conductor.

Lenz’s law: an induced voltage gives rise to a current in the conductor whose magnetic field opposes the original change in field.*

*Conservation of energy again!

Second, how does a refrigerator work?

The compressor (B) compresses a gas (ammonia?). The gas temperature increases.

The hot gas passes through coils at the back of the fridge and gives up heat to the room air. The gas turns into liquid at high pressure (purple).

The gas passes through an expansion valve (C), vaporizes, and becomes very cold (-27 F).

The cold gas absorbs heat from the fridge contents (A) and the gas pressure forces the gas back into the compressor.

Lather, rinse, repeat…Picture “borrowed” from http://www.howstuffworks.com.You should go there often.

In 1908 a Dutch physicist, Kamerlingh Ohnes, learned how to liquify helium (using a fancy “refrigerator”). Liquid helium has a temperature of 4.2 K. If you pump on it and reduce the vapor pressure, you can get down to around 1.5 K.

Hoo haa it’s Christmas time!

What shall we play with first?

Hint: quantum theory to explain metallic conductivity has not been invented yet.

"If we knew what it was we were doing, it would not be called research, would it?“—

A. Einstein

Resistance versus temperature for mercury metal, H. K. Ohnes, 1911 (Nobel Prize, 1913).

We have a problem. No theory explains this. What to do with this mystery?

Measure properties, think, think some more, wait until someone does find a theory?

Is the resistance in a superconductor really zero?

How do you measure something that is zero?

You can make a loop of a superconductor, inject a current in it, and measure over time the magnetic field due to the current.

This was done, and after monitoring the current for a number of years and observing no change, the scientists shut the experiment down.

We can’t say from experiment that the resistance is zero, but we can say it is far smaller than any capability of ours to measure (the theory says it really is zero).

What can you do with superconductors?

Make wires that carry current with no energy loss.

Make very powerful magnets?

Make incredibly sensitive magnetic field detectors.

Levitate trains?

?????

"It is the supreme art of the teacher to awaken joy in creative expression and knowledge.“—A. Einstein

The mechanism of superconductivity remained a mystery from 1911 until 1957.

Key observations:

The Meissner effect (1933).

The “best” metals do not seem to be superconductors. Among superconducting metals, better metals make poorer superconductors, and vice versa. What makes a metal a good conductor?

The isotope effect. A lighter isotope of mercury becomes superconducting at a higher temperature (i.e., more readily) than a heavier isotope.

The Meissner Effect

Cool a superconductor while it is in a magnetic field.

Below Tc there can be no resistance so there can be no voltage inside the superconductor.

From Faraday’s law the magnetic field inside cannot change.Classical physics says the magnetic field inside must remain constant However, we actually observe that the field lines from the external field are “expelled” from the superconductor. How?

A supercurrent (screening current) is induced on the surface in a direction such that it cancels the external field.

But this costs energy, and if it costs too much energy, the superconductor becomes normal .

A superconductor like this, called a Type I superconductor, is limited in its current-carrying capability because it can tolerate only very small magnetic fields.

The Meissner effect is the litmus test for superconductivity.

A Type II superconductor acts like a Type I superconductor in small magnetic fields. In large magnetic fields, it “sacrifices” part of itself so that the rest can remain superconducting.

Type II superconductors can carry enormous currents and make incredibly powerful superconducting electromagnets.

Where’s The Beef?

This is all descriptive so far. Phenomenological. Empirical equations and empirical parameters. We’ve got to find a theory!

BCS theory, 1957. Won Nobel Prize for Bardeen, Cooper, and Schrieffer in 1971.

The key observation was the isotope effect, which puts us on the trail of phonons.

The Role of Phonons

Electrons attract protons. A region of increased + charge is produced.

Like a pluck on a guitar string, this disturbed region travels through the material.

Another electron elsewhere can absorb the momentum in the phonon. In “human” language, the electron is attracted to the region of increased + charge.

Two electrons can interact at a distance and attract (!) each other because they both “want” to go to the region of increased + charge.

If the attraction exceeds the electron-electron repulsion, a “bound pair” is formed. The pair is called a “Cooper pair.”

Key elements of BCS theory…

Electrons move in correlated pairs that do not lose energy by interacting with the lattice. These paired electrons are not necessarily close; on average they might be separated by 100’s or even 1000’s of atom spacings

The electrons in Cooper pairs have opposite spins and equal and opposite linear momenta. The Cooper pair thus has zero spin and zero momentum.

Electrons have a spin of ½ (QM again!) and strongly “dislike” each other (more than just - - repulsion).

Zero-spin particles “like” either so much they all try to crowd together in the same “state” (energy and momentum).

At T=0 all Cooper pairs are in the same energy state .

Cooper pairs can also be formed with net momentum. Electric current!

In the superconducting state, the Cooper pairs are constantly scattering each other, but the total momentum remains constant. Remember—the paired electrons have opposite momentum. If one gains momentum, the other loses momentum There is no net change in the current.

Because all Cooper pairs act together, a single lattice ion cannot scatter a single Cooper pair. Only thermal energy can break the pairing.

Ordinary metals are good conductors if the electron-lattice interaction is weak.

Superconductivity results from a strong interaction between electrons and lattice!

Meanwhile, Back at the Ranch…

Here are some superconducting materials and their transition temperatures (in degrees Kelvin):

Zn 0.85 Al 1.18 Sn 3.72 Hg 4.15Pb 7.19 Nb 9.25 Nb3Ge 23.2

Nb3Ge was discovered in 1973 and was long the record-holder for highest Tc. The holy grail of superconductivity researchers is a room-temperature superconductor (why?). Even a material superconducting at liquid nitrogen temperature (77K) would be amazing.

What’s the fuss about liquid nitrogen? Nitrogen is plentiful, easy to liquefy, and cheap as milk!

BCS theory beautifully explained all aspects of superconductors, but seemed to predict that 30 K (give or take a couple of degrees) was the highest possible temperature at which a material could be superconducting.

During the years I was involved in superconductivity research (1981-1985) all of us “knew” that we would never see the Meissner effect from a 77K superconductor.

What should funding agencies (NSF, industry) do? Close up superconductivity shops and put everybody to work somewhere else?

"It's not that I'm so smart , it's just that I stay with problems longer .“—A. Einstein

In 1986, Georg Bednorz and Alex Muller, working for IBM Zurich, announced that they had discovered a compound containing lanthanum, barium, copper, and oxygen that became superconducting at 35K. Their compound was a ceramic material more like your coffee cup than a metal.

Overnight anybody who knew superconductors or ceramics seemed to be cooking up new compounds in their ovens, and record high temperature superconductors seemed to be announced almost daily.

Paul Chu, of the University of Houston, made a stunning breakthrough when he announced the discovery of a material that became superconducting at 93K, well above liquid nitrogen temperature.

The suspense was palpable. A Nobel Prize was in the works. Who would be the winner?

In early 1987, Chu circulated a preprint of a paper describing superconductivity at 93K in a ceramic containing Yb, Ba, Cu, and O.

Intrigue!

When the paper appeared in print, every occurrence of Yb was replaced by Y.

It was just a typo, Chu explained…

Final draft of paper inside.

"As far as I'm concerned, I prefer silent vice to ostentatious virtue.“—A. Einstein

Bednorz and Muller won the 1987 Nobel Prize for their discovery.

The world record Tc for a superconductor is 138K, for a compound containing mercury, thallium, barium, calcium, copper, and oxygen.

No current theory can fully explain high-Tc superconductors. BCS theory is clearly a good starting point, and just as clearly not the final answer. There is another Nobel prize waiting for one of your students!

"If A equals success, then the formula is: A=X+Y+Z. X is work. Y is play. Z is keep your mouth shut.“—A. Einstein

Scandal?“May, 2002. Outside researchers have presented evidence to Bell Labs management of possible manipulation of data involving five separate papers published by its researchers in Science, Nature, and Applied Physics Letters over a 2-year period.”

“The papers describe a series of different device experiments, but physicists are voicing suspicions about the figures, portions of which seem almost identical even though the labels are different.”

“Particularly puzzling is the fact that one pair of graphs show the same pattern of "noise," which should be random. The groundbreaking papers include Bell Labs physicist Jan Hendrik Schön as lead author and his colleagues at Murray Hill and elsewhere as co-authors. Schön is the only researcher who co-authored all five papers in question.”

“Until this week, many physicists believed the impressive string of results was worthy of consideration for a Nobel Prize, although other groups have reported no success in reproducing Schön's most striking results.”

“Bell Labs spokesperson Saswato Das says that company officials take the concerns ‘very seriously’.”

“Within hours of hearing of them on 10 May, Das says that Lucent management decided to form an external review panel chaired by Stanford University physicist Malcolm Beasley.”

Source:   American Association for the Advancement of Science

Appendix

Visit http://superconductors.org to learn about the history and uses of superconductors, and to find out why scientists have been startled at the discovery of plastic superconductors and superconductors that are simultaneously ferromagnets.

On the next page are some more interesting quotes by Einstein (small type—not intended for Powerpoint display!

"As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.""Relativity teaches us the connection between the different descriptions of one and the same reality.""I sometimes ask myself how it came about that I was the one to develop the theory of relativity. The reason, I think, is that a normal adult never stops to think about problems of space and time. These are things which he has thought about as a child. But my intellectual development was retarded, as a result of which I began to wonder about space and time only when I had already grown up.""The secret to creativity is knowing how to hide your sources.""The important thing is not to stop questioning.""Only two things are infinite, the universe and human stupidity, and I'm not sure about the former.""Things should be made as simple as possible, but not any simpler.""Sometimes one pays most for the things one gets for nothing.""Common sense is the collection of prejudices acquired by age 18.""Strange is our Situation Here Upon Earth.""If you are out to describe the truth, leave elegance to the tailor.""I never think of the future. It comes soon enough.""Not everything that counts can be counted, and not everything that can be counted counts.""The faster you go, the shorter you are.""The wireless telegraph is not difficult to understand. The ordinary telegraph is like a very long cat. You pull the tail in New York, and it meows in Los Angeles. The wireless is the same, only without the cat."