Download What`s “SUPER” about SUPERCODUCTORS?

Crήstos
Panagòpoulos
• Matter is the substance of which all physical objects are composed.
• The density of matter is a measure of the composition of matter and the
compactness of the constituent entities in it.
• Dense matter physics is the study of the physical properties of material
substance compressed to high density.
• The density range begins with hundreds of grams per cubic centimeter
and extends to values ten to fifteen orders of magnitudes higher.
• Condensed matter physics is concerned with the "condensed"
phases that appear whenever the number of constituents in a
system is extremely large and the interactions between the
constituents are strong
“… at each new level of complexity, entirely new properties
appear, and the understanding of this behavior requires research
which I think is as fundamental in its nature as any other”
Philip W. Anderson 1972
Si-crystal
semiconductor
MgB2 superconductor
NaxCoO2
superconductor
2 atoms
3 atoms
1 atom
La2-xSrxCuO4
superconductor
4 atoms
DNA giant molecule
Many atoms
• One of the reasons for calling the field "condensed matter
physics" is that many of the concepts and techniques
developed for studying solids actually apply to fluid systems:
For instance, the conduction electrons in a conductor form a type
of quantum fluid with essentially the same properties as fluids
made up of atoms:
Under high pressures and low temperatures electrons may
condense into a quantum fluid:
• A quantum fluid can refer to a cluster of valence electrons (the
electrons located within the outermost energy level of an atom)
moving together after they undergo fermionic condensation
(fermions are particles with half-integer spin) 
• Quantum fluids exhibit the remarkable property of remaining liquid at
absolute zero temperature and zero pressure. This effect arises from their
large zero-point energy and the small inter-atomic forces, both of which
prevent the formation of a solid phase.
• A quantum fluid can also refer to a superfluid (made up of atoms).
• What exactly is a superfluid?
As the name suggests, a superfluid possesses fluid properties similar to those
possessed by ordinary liquids and gases, such as the lack of a definite shape and
the ability to flow in response to applied forces.
A superfluid phase is a phase of matter characterised by the complete absence of
viscosity - formed by fermionic particles (fermions are particles with half-integer
spin) at low temperatures.
•
It is the phase or state of matter in which it loses all its resistance to change its shape:
Resistance to changing the shape of an object is its intrinsic property. In liquids, this property is
manifested through its stickiness or internal resistance to flow.
•
But superfluid is totally devoid of viscosity.
• Superfluid has another bizarre property. It cannot be made to rotate like
water in a pot. - water if stirred with a stick in a container swirls round
imaginary axes.
• Superfluids do not show this property. When stirred, it will create lots of
vortices. Strangely though, the superfluid loses it superfluidity at those
vortices, whereas it retains its quality elsewhere.
•
Imagine that a (tightly sealed!) bucket of superfluid
rotates.
•
A vortex can form in the middle, with fluid moving around
in a circle, much like a water vortex in a draining bathtub.
•
The amazing difference is that, at a given distance from
the vortex center, only certain fluid velocities are
allowed! There is a minimum velocity, then twice that
minimum, then three times the minimum, etc. No inbetween values can occur, so the vortices are said to be
quantized.
•
Therefore, in contrast to the example of a glass of
water above, the rotation in superfluids is always
inhomogeneous. The fluid circulates around
quantized vortex lines.
•
The vortex lines are shown as yellow in the
figure, and the circulating flow around them is
indicated by arrows.
•
There is no vorticity outside of the lines
because the velocity near each line is larger than
further away. (curl v = 0, where v(r) is the velocity
field.)
•
The velocity around each vortex line is determined by
h/m, where h is the Planck's constant, and m the mass of
one atom.
•
The presence of the Planck's constant means that
quantized vorticity is a consequence of quantum
mechanics. h is very small, but so is m, so the ratio h/m is
quite macroscopic.
•
Therefore, superfluidity is a quantum phenomenon on a
macroscopic scale.
•
The number of vortex lines depends on the constant h/m.
There are approximately 1000 vortex lines in a container
of radius 1 cm that is rotating 1 round per minute.
Where could we find superfluidity?
• Helium - 3 atoms are fermions
 particles with half integer spin.
Helium
p
n
He - 3
p
1 millionth of a
centimetre
p
n
He - 4
n
p
• Helium - 4 atoms are bosons 
particles with integer spin.
Onnes
• As the temperature drops, so does the pressure and/or the
volume & the reverse.
• Hence, we can cool He gas in liquid or reduce its volume.
However, reducing its volume is equivalent to applying
pressure.
1911 (-269 C)
Onnes
1938
Kapitza and Allen discover superfluidity in
He-4
Superfluids flow without resistance
Normal fluid
Superfluid
For T > 2.4Κ (-271 C)
When it is heated up it
boils like water
For T < 2.4Κ
Perfect thermal conductor
For T < 2.4Κ – gravity ...
If the bottle containing helium
rotates for a while and then
stops, helium will continue to
rotate for ever – there is no
internal friction (for as long
as He is at T = -269 C or lower
• Helium-4 atoms are bosons  particles with integer spin.
• Superfluidity had been found in helium-4 at about 2 degrees kelvin, but
because helium-4 has integer spin, it can form a condensed phase
without the need for a pairing mechanism:
• Due to integer-spin, bosons obey Bose–Einstein statistics, one
consequence of which is the Bose–Einstein condensation of particles —
in such case a number of bosons can share the same quantum
state, and their superfluidity can be understood in terms of the Bose
statistics (which determines the statistical distribution of identical
indistinguishable bosons over the energy states in thermal equilibrium)
that they obey.
• Specifically, the superfluidity of helium-4 can be regarded as a
consequence of Bose-Einstein condensation - a phase of matter formed
by bosons cooled to temperatures very near to absolute zero where a large
fraction of the atoms collapse into the lowest quantum state, at which point
quantum effects become apparent on a macroscopic scale in an interacting
system ----- just like in Bose-Einstein condensates
• The primary difference between superfluid helium and a BoseEinstein condensate is that the former is condensed from a
liquid while the latter is condensed from a gas.
•
Fermions such as helium-3 follow Fermi-Dirac statistics and should not
actually be condensable in the lowest energy state.
•
For this reason superfluidity should not be possible in helium-3 which, like
helium-4, can be liquidised at a temperature of some degrees above
absolute zero.
•
But fermions can in fact be condensed, but in a more complicated manner.
This was proposed in the BCS theory for superconductivity in metals,
formulated by John Bardeen, Leon Cooper and Robert Schrieffer (Nobel
Prize in Physics 1972).
•
The theory is based on the fact that electrons are fermions (they consist of
one particle only, an odd number) and therefore follow Fermi-Dirac statistics
just as helium-3 atoms do.
•
But electrons in greatly cooled metals can form pairs and then behave
as bosons.
• Because of the analogy with electrons and BCS it was expected that
He-3 would also become a superfluid.
• Although many research groups had worked with the problem for
years, particularly during the 1960s, none had succeeded and many
considered that it would never be possible to achieve superfluidity in
helium-3.
Early 1970s
Lee
Osheroff
Richardson
• In 1972 Leggett reported new states where all
of the pairs' spins line up spontaneously, like a
row of bar magnets.
1938 Pyotr L. Kapitsa discovered the superfluidity of liquid Helium 4
Nobel Prize in 1978
1941-47 Lev Landau formulated the theory of quantum Bose
liquid - 4He superfluid liquid. 1956-58 he further formulated the
theory of quantum Fermi liquid.
Nobel Prize in 1962
Early 1970s David M. Lee, Douglas D. Osheroff,
and Robert C. Richardson discovered the
superfluidity of liquid Helium 3.
Nobel Prize in 1996
Anthony Leggett first formulated the theory of superfluidity in liquid 3He in
1965.
Nobel Prize in 2003
In fact, the phenomenon of superconductivity, in which the electrons condense into a
new fluid phase in which they can flow without dissipation, is analogous to the
superfluid phase
(Just as atoms can move without viscosity in a superfluid - the atoms formed up into
pairs, electrons can flow without resistance in a superconductor).
Now let us see how one cools an experiment:
To obtain cooling say from 300K to 255K the most effective method would be to cause a
gas, contained in a cylinder equipped with a movable piston, to undergo an adiabatic (in
which no heat enters or leaves the system), almost reversible expansion. Since work is
done at the expense of the internal energy of the gas, the temperature drops. This method
has two disadvantages:
1. It requires pistons moving in cylinders and therefore presents problems of lubrication,
vibration and noise
2. As the gas gets colder, the temperature drop for a given pressure drop is smaller.
It is therefore important we avoid these problems. A good process is one in which a fluid
(gas or liquid) at high pressure seeps through a tiny opening or series of openings,
adiabatically and reversibly, into a region of lower pressure. This called a throttling
process and the temperature change accompanying a throttling process is known as the
Joule-Thompson effect.
If a liquid about to vaporise undergoes a throttling process a cooling effect accompanied
by partial vaporisation always occurs.
Kapitza's Helium Liquefier (1934)
This was the first successful large scale liquefier to use an expansion engine. It was the
prototype from which commercial helium liquefiers were later developed.
Early continuously operating liquefiers used the Joule-Thomson effect, i.e. the cooling when
compressed gas is expanded through a nozzle. Since helium is a nearly ideal gas the effect is
small and the method is inefficient. But cooling by adiabatic expansion is a strong effect for all
gases, ideal and non-ideal.
Kapitza had to overcome the problem of lubricating the piston (grease would solidify at such
low temperatures). He used a loose fitting, grooved piston which the gas leaked past. The eddies
produced by the grooves limited the flow of gas and equalised the pressure around the piston so
that it ran true.
The efficiency of the finished liquefier was much higher than that of the Joule-Thomson
liquefiers.
The figure opposite indicates the flow circuit in which He-gas,
compressed to about 30 atm, is pre-cooled by liq N2, after which
the majority of the gas is expanded in the engine E and returns
through the heat exchangers C, B, and A.
The minor fraction of compressed gas (about 8 per cent) passes on
through exchangers to a Joule-Thompson expansion (a gas
undergoes a temperature change when it expands slowly through
a porous plug) valve 4.
Kapitza used an unlubricated engine with a clearance of about
0.05 mm between the piston and cylinder, the small gas loss past
the piston serving as a lubricant.
The part of the liquefier below the N2 vessel is surrounded by a
radiation shield thermally anchored to the liq N2 container, and
the whole assembly is suspended in a highly evacuated metal
vessel. This liquefier produced about 1.7 l/h at an overall
liquefication efficiency of 4 per cent.
Cooling to 0.3K
He(III) is obtained as a decay product of tritium and therefore is only available in
small quantities. The boiling point of 3He is 3.19K and the critical temperature 3.32K
at a critical pressure of 1.15 atm.
4He has a superfluid transition at 2.17K, 3He remains normal down to 2.6 mK. Below
1K the vapour pressure of 3He becomes more than two orders of magnitude greater
than that of 4He. A thermally shielded bath of liquid may be boiled under pressures of
0.001Torr or less which correspond to T<0.3K. As a result, 3He has become widely
used to provide an additional stage of cooling which encompasses the range from 0.25
to 1K.
The diagram shows two conventional schematic
cryostats in each of which there is a small 3He
chamber attached to the experimental space.
The pumping tube acts also as the condenser for
initially producing the liq 3He and therefore must be
in thermal contact with a pumped 4He bath along
part of its length.
This 4He bath may be either the main dewar as in
(a) or a separate chamber as in (b). This 1K cooling
stage can also be a copper plate cooled by a tube,
soldered or welded to it, carrying liquid 4He at a rate
controlled by a suitable flow impedance. The latter
can be a porous plug. There can also be a
condensing line, shown dotted in (a) which then
allows continuous circulation of the 3He.
3He/4He
The diagram on the right shows a typical dilution
fridge. 3He gas at a pressure 20-30Torr from the
backing side of the pumping system enters the
cryostat, is pre-cooled to 4.2K, and then
condenses in the 1K cooling stage (pumped 4He).
It then goes successively through a throttling
impedance, heat exchanger attached to the still,
other heat exchangers and into the mixing
chamber.
There phase separation occurs with the lighter
3He-rich phase forming the top layer and some
3He diffusing across the phase boundary where
adiabatic dilution causes cooling.
It then diffuses through the quasi-stationary liquid
4He, via the heat exchangers to the still.
This is electrically heated to a temperature of 0.6K
which evaporates the 3He preferentially as it has a
much higher vapour pressure than 4He and then
the 3He vapour goes to the pumping system
through a tube of graded diameter.
Why bother measure at low temperatures?
• In matter at temperatures close to absolute zero, the thermal,
electric, and magnetic properties undergo great change, and the
behaviour of matter may seem strange when compared with that at
room temperature.
• Thermal fluctuations are greatly reduced and effects of interactions
at the quantum-mechanical level can be observed. As the
temperature is lowered, order sets in (either in space or in motion),
and quantum-mechanical phenomena can be observed on a
macroscopic scale.
• Considerable attention has been addressed to the general problem of
ordering in disordered systems leading to studies of spin glasses,
localization, and lower dimensionality.
• Quantum statistics are investigated in atomic hydrogen and deuterium,
stabilized in states known as spin-polarized hydrogen (H↓) and spinpolarized deuterium (D↓).
• Many practical applications have emerged, including the use of
superconductivity for large magnets, ultra-fast electronics for computers,
and low-noise and high-sensitivity instrumentation. This type of
instrumentation has opened new areas of research in biophysics, and in
fundamental problems such as the search for magnetic monopoles,
gravity waves, and quarks.
• The development of low-temperature techniques has
revealed a wide range of other phenomena:
1. The behaviour of oriented nuclei is studied by observing the
distribution of gamma-ray emission of radioactive nuclei
oriented in a magnetic field.
2. Other areas of study include surfaces of liquid 3He and liquid
4He, 3He–4He mixtures, cryogenics, acoustic microscopy,
phonon spectroscopy, monolayer helium films, molecular
hydrogen, determination of the voltage standard, and phase
transitions.