# Superconductivity

```For your enlightenment and entertainment,
ELMSS presents…
“Superconductivity”
a tale of mystery, intrigue, suspense, and scandal.
Selected Big Ideas of Physics
Conservation
of Energy
Ef = Ei
Conservation
of Momentum
Pf = Pi
Newton’s Laws
inertia
F = ma
action/reaction
&quot;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
t
t0
1 v2 / c2
L L0 1  v 2 / c 2
m
m0
1 v2 / c2
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 &middot;m
 graphite
  1x10-5 &middot;m
 silicon
  1 &middot;m
 rubber
  1x10+15 &middot;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
units of .
=  &middot; (length of conductor) / (cross sectional area of conductor), hence the
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:
electron “drift” velocity
Voltage
-
+
+
+
+
+
+
+
+
+
+
+
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.
&quot;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
QM equation, which in its simplest form, looks something like this:

 2  2
j

 U
2
t
2m x
This is really just a “funny” way of
writing conservation of energy!
When we solve this equation for an electron moving in the periodic
potential of the metal ions, we notice two remarkable facts:
 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 going
to get to the point?
Better be soon!
&quot;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.
&quot;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?
 ?????
&quot;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
Electrons have a spin of &frac12; (QM again!) and strongly “dislike” each
other (more than just - - repulsion).
The electrons in Cooper pairs have opposite spins and equal and
opposite linear momenta. The Cooper pair thus has zero spin and
zero momentum.
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 4.15
Pb 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?
&quot;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?
Intrigue!
In early 1987, Chu circulated a preprint
of a paper describing superconductivity
at 93K in a ceramic containing Yb, Ba,
Cu, and O.
When the paper appeared in print,
every occurrence of Yb was replaced
by Y.
Final draft of paper inside.
It was just a typo, Chu explained…
&quot;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
&quot;If A equals success, then the formula is: A=X+Y+Z. X is work. Y is play. Z is
Scandal?
“May, 2002. Outside researchers have presented evidence to Bell
Labs management of possible manipulation of data involving five
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 &quot;noise,&quot; which should be random. The
groundbreaking papers include Bell Labs physicist Jan Hendrik Sch&ouml;n
as lead author and his colleagues at Murray Hill and elsewhere as coauthors. Sch&ouml;n 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 Sch&ouml;n'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!
&quot;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.&quot;
&quot;Relativity teaches us the connection between the different descriptions of one and the same
reality.&quot;
&quot;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.&quot;
&quot;The secret to creativity is knowing how to hide your sources.&quot;
&quot;The important thing is not to stop questioning.&quot;
&quot;Only two things are infinite, the universe and human stupidity, and I'm not sure about the
former.&quot;
&quot;Things should be made as simple as possible, but not any simpler.&quot;
&quot;Sometimes one pays most for the things one gets for nothing.&quot;
&quot;Common sense is the collection of prejudices acquired by age 18.&quot;
&quot;Strange is our Situation Here Upon Earth.&quot;
&quot;If you are out to describe the truth, leave elegance to the tailor.&quot;
&quot;I never think of the future. It comes soon enough.&quot;
&quot;Not everything that counts can be counted, and not everything that can be counted counts.&quot;
&quot;The faster you go, the shorter you are.&quot;
&quot;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.&quot;
```