Condensed Matter

Discussion

superconductivity

The resistivity of a conductor decreases with decreasing temperature. In the case of copper, the relationship between resistivity and temperature is approximately linear over a wide range of temperatures

The resistivity of copper deviates from a linear function at low temperature.

The resistivity of copper does not vanish at absolute zero. Instead, it levels off in what is known as the residual resistance. Copper has a residual resistance of 0.020 nΩ m.

Resistance has two causes

1. defects like…
   1. impurities
   2. grain boundaries
   3. stresses
2. lattice ion vibrations

The latter cause results in "ordinary resistance". The former results in residual resistance. To get rid of the residual resistance…

1. use ultra pure mercury (instead of pure gold or platinum) which is easy to distill, cooled to make a wire instead of drawn (stressed) through a die
2. cool it to reduce vibration

Heike Kamerlingh Onnes, Leiden, 1911
Surprise, surprise, surprise. At low temperatures, instead of zero residual resistance Kamerlingh Onnes discovered zero resistance; now know as superconductivity (originally called supraconductivity). Kamerlingh Onnes thought his equipment was experiencing a short circuit. Second paper of 1913 introduced the word "supraconductivity"

• "The resistance of pure mercury at helium temperatures." Comm. Leiden. 120b (28 April 1911).
• "The disappearance of the resistivity of mercury." Comm. Leiden. 122b (27 May 1911).
• "On the sudden change in the rate at which the resistance of mercury disappears," Comm. Leiden. 124c (25 November 1911).
• "The imitation of an ampere molecular current or a permanent magnet by means of a supraconductor." Comm. Leiden. 140b (Day Month 1914).

About half the elements are superconducting under the right conditions: low temperature, high pressure, amorphous phase, thin films. Elements that are good conductors are not superconductors. The element with the highest transition temperature is niobium 9.25 K. Rhodium is the superconductor with the lowest known transition temperature of 325 μK. Neither gold nor bismuth is superconducting, but Au₂Bi is at 1.8 K

• The material must be cooled below a characteristic temperature, known as its superconducting transition temperature or critical temperature (T_c).
• The magnetic field to which the material is exposed must be below a characteristic value known as the critical magnetic field (H_c).
• The current passing through a given cross-section of the material must be below a characteristic level known as the critical current density (J_c).

Persistent current: no decrease of induced current could be observed in the superconductive state for the duration of the experiment (1 hour)

It is uncanny to see the influence of these "permanent" currents on a magnetic needle. You can feel almost tangibly how the ring of electrons in the wire turns around, around, around — slowly and almost without friction.

Find a good quote from Onnes' Nobel speech

Magnetism destroys superconductivity
Type I vs. Type II superconductors,

Meissner Effect:

• complete flux expulsion (field forced out when temperature drops below critical)
• complete flux exclusion (field can't penetrate when turned on below critical temperature)

Demonstration of the Meissner Effect. Named after Walther Meissner (1882–1974) Germany. Superconductors are also superdiamagnetic. Superdiamagnetism: Fritz, Heinz London, Oxford explained the Meissner effect in terms of surface current, produced a magnetic field within the superconductor that opposed the field imposed from outside

BCS theory

BCS theory, Cooper pairs, two electrons with an attractive interaction always form a bound pair (in the presence of a filled Fermi sphere). Worked out of a cramped office on the 3½ floor in an annex of the Institute for Advanced Studies. They jokingly called it the "Institute for Retarded Studies".

• John Bardeen, Leon N. Cooper, J. Robert Schrieffer. "Microscopic Theory of Superconductivity." Physical Review. 108 (1957): 162–164.
• John Bardeen, Leon N. Cooper, J. Robert Schrieffer. "Theory of Superconductivity." Physical Review. 108 (1957): 1175–1204.

high temperature superconductors

three families of high-temperature, non-intermetallic superconductors

1. cuprates
2. bismuthades
3. fullerites

high temperature superconductivity
Bednorz, Müller. Zeitschrift fur Physik. Condensed Matter. April 1986.

Which is correct?

• Liquid helium is 500 times more expensive than liquid nitrogen.
• With liquid nitrogen 50 times cheaper than helium and thus the promise of commercial viability for the new materials. FERMILAB
  liquid nitrogen is 50 times less expensive than helium (10 cents a liter instead of $5 a liter). ORNL
• Michigan Technological University
  "Posted on the door are Rules, Usual Procedures, Price ($0.75/liter)…."
  "The price for liquid helium from August 1, 2000 will be $3.25/liquid liter."

In addition to the savings in cost resulting from the displacement of liquid helium by liquid nitrogen for cooling, it is now apparent that superconductivity applications with more inexpensive refrigerants — or eventually no refrigerant at all — are possible. The race for new superconductors with higher T_c continues. The current record (1997) is for a the mercury barium calcium copper oxide (HBCCO) compound which superconducts at about 134 K without pressure. Under hydrostatic pressure, this compound superconducts at 164 K, which is Freon temperature

organic superconductors

Doping C60 with alkali metals like potassium or rubidium leads to superconducting compounds with transition temperatures of 18–20 K and 20–30 K, respectively, 1991 may people, 20 hexagons and 12 pentagons like a football (soccer ball), 60 carbon atoms

magnesium diboride

superconducting technology

large scale vs. small scale

• magnetic resonance imaging (MRI)
  "Magnetic Resonance Imaging (MRI) is currently the most important market for low temperature superconductors. MRI enables physicians to obtain detailed images of the interior of the human body without surgery or exposure to ionizing radiation. MRI devices are now available only at major hospitals and specialized MRI centers. They are very bulky machines largely because of the amount of thermal insulation required to keep the liquid helium from evaporating. The amount of liquid helium to operate an MRI device costs about $30,000 per year. It has been estimated that the use of liquid nitrogen superconducting magnets could save $100,000 per year in overall operating costs for each MRI device. In addition, the initial cost of the machines would be far lower, and the physical size of the machines would be much smaller."
• microwave antennas
  "Communications - Superconductors could improve capacity, coverage and quality of service for personal communications devices, such as hand held communicators to generate and read e-mail."
• magnetic levitation (maglev)
  • maglev train
  • magnetic bearings
  • vibration isolation
• superconducting magnetic energy storage (SMES)
  "energy is stored within a magnet that is capable of releasing megawatts of power within a fraction of a cycle to replace a sudden loss in line power."
• fault current limiters
  "A current limiter is designed to react to and absorb unanticipated power disturbances in the utility grid, preventing loss of power to customers or damage to utility grid equipment."
  "They can limit the peak short-circuit current automatically by their transition from the superconducting to the normal state. This means high short-circuit capacity during normal operation and a limitation of the short-circuit currents in case of a fault."
• power transmission cables
  "Conduct electricity with little or no resistance and associated energy loss. Can transmit much larger amounts of electricity than conventional wires of the same size."
  "Superconducting cables can provide 2 to 5 times more power than conventional cables of the same size."
  Increased capacity without the need to purchase new land for utility right of way.
• electric motors
  large industrial and marine motors over 1,000 hp
  "Conventional motors are made primarily of iron, which makes them heavy and increases the frictional load seen by the motor bearings. All iron can be eliminated when constructing superconducting electrical machines with HTS windings. The removal of the iron teeth in the armature not only makes superconducting motors lighter (with lower inertia), it also leaves more room for armature copper, which lowers the electrical losses and also improves machine efficiency. These reductions in losses result in lower operating costs than conventional motors."
• Electric generators
  lighter, higher efficiency
• transformers
  "Improved energy efficiencies from smaller, lighter transformers. Reduced environmental concerns from elimination of fire and environmental hazards. Liquid nitrogen is safe, nonflammable, and environmentally friendly as it is simply the liquid form of the most abundant element on Earth. Using it as a dielectric and coolant instead of oil eliminates the dangers of explosion and contamination of the soil from leaks. An HTS transformer replaces the copper wire coils in a conventional transformer with lower loss HTS wire. Inexpensive and environmentally benign liquid nitrogen replaces the conventional oil as the electrical insulation (dielectric) and provides the necessary cooling for the HTS. More generated power can be utilized by consumers rather than lost in the environment as heat."
  "If all transformers in the United States equal to or greater than 100 MVA were replaced with HTS transformers, the lifetime energy savings from conventional transformer losses could account for 340 billion kWh or 10.2 billion dollars."

superfluidity

Pyotr Kapitsa, Soviet Union
Helium I vs. helium II. Helium II is a different phase than helium I
Helium liquefies under normal pressures at 4.2 K. From 4.2 K to 2.17 K it behaves like many other liquids, although it has an exceptionally low surface tension and is extremely transparent. Below 2.2 K it behaves quite differently.

• expands upon cooling
• will not boil
• will leak through even the finest pores
• will crawl up and out of its container
• has no viscosity
• is less dense than helium I (which is pretty low as it is)
• has a larger heat of vaporization than helium I (3 million times larger)
• has a lower surface tension than helium I (which is also quite low)
• has no entropy [this must be a misprint]

The mechanisms for this phase transition, and the details of the superfluidity in ⁴He and ³He, are very different. ⁴He has an even number of constituent particles (protons, electrons, and neutrons), which makes it a boson, meaning it is governed by Bose-Einstein statistics. At low temperatures, all the bosons in a sample will want to occupy the same quantum-mechanical ground state, forming a Bose-Einstein condensate. This condensate is responsible for the superfluid behavior of ⁴He below T_λ = 2.17 K.

In contrast, ³He is a fermion, since it has one less neutron than ⁴He. Fermions obey the Pauli exclusion principle, which says that in a sample of many identical fermions, no two can occupy the same quantum-mechanical state. Bose-Einstein condensation is ruled out for ³He, so another mechanism is needed to explain its superfluid behavior. That mechanism is provided by the Bardeen-Cooper-Schrieffer (BCS) theory.