The Physics
Opus in profectus

Condensed Matter

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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

Resistivity of copper from 0–900 kelvin showing nearly linear behavior

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

Resistivity of copper from 0–100 kelvin showing nonlinear behavior at low temperatures

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.

Resistivity of copper from 0–40 kelvin showing nonlinear behavior and a nonzero minimum value 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"

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

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:

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

Superconducting transition temperatures for selected elements
element Tc (K) element Tc (K)
aluminum 1.175   rhodium 0.00037
cadmium 0.517   tin 3.722
lead 7.196   titanium 0.39
mercury 4.154   tungsten 0.015
niobium 9.25   uranium 0.2
      zinc 0.85

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".

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?

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 Tc 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

Milestone superconducting transition temperatures
year Tc (K) material, comments
1911 4.154 Hg (superconductivity discovered)
Heike Kamerlingh Onnes
Universiteit Leiden
1913 7.196 Pb
Heike Kamerlingh Onnes
Universiteit Leiden
1932 9.25 Nb (pure element with highest critical temperature)
Walther Meissner, H. Franz, H. Westerhoff
Physikalisch-Technische Bundesanstalt
1932 11.5 NbC
Walther Meissner, H. Franz, H. Westerhoff
Physikalisch-Technische Bundesanstalt
1941 16.1 NbN
G. Aschermann, E. Friederich, E. Justi, and J. Kramer
Physikalisch-Technische Bundesanstalt
1953 17.1 V3Si
G.F. Hardy and J.K. Hulm
University of Chicago
1954 18.05 Nb3Sn
B.T. Matthias, T.H. Geballe, S. Geller, and E. Corenzwit
Bell Telephone Laboratories
1967 20.7 Nb3Al0.75Ge0.25
G. Arrhenius, E. Corenzwit, R. Fitzgerald, et al.
University of California, San Diego
1974 23.2 Nb3Ge (classical superconductor with highest critical temperature)
J.R. Gavaler, M.A. Janocko, and C.K. Jones
Westinghouse Research Laboratories
1986 30 La1.85Ba0.15CuO4 (high temperature superconductivity discovered)
Georg Bednorz and Alex Müller
IBM Zurich Research Laboratory
1987 93 YBa2Cu3O7 (liquid nitrogen barrier broken)
M.K. Wu, J.R. Ashburn, C.J. Torng, et al.
University of Alabama and University of Houston
1988 105 Bi2Sr2CaCu2O8
H. Maeda, Y. Tanaka, M. Fukutomi, and T. Asano
Tsukuba Magnet Laboratory
1988 120 Tl2Ba2Ca2Cu3O10
Z.Z. Sheng and A.M. Hermann
University of Arkansas
1993 133 HgBa2Ca2Cu3O8
A. Schilling, M. Cantoni, J.D. Guo, and H.R. Ott
Laboratorium für Festkörperphysik
1995 138 Hg0.8Tl0.2Ba2Ca2Cu3O8.33
P. Dai, B.C. Chakoumakos, G.F. Sun, et al.
University of Kansas, Lawrence
1994 164 HgBa2Ca2Cu3O8 (under 30 GPa pressure)
L. Gao, Y.Y. Xue, F. Chen, et al.
University of Houston
2015 203 H2S (under 90 GPa pressure)
A.P. Drozdov, M.I. Eremets, I.A. Troyan, et al.
Max-Planck-Institut für Chemie
2020 287.7 carbonaceous sulfur hydride (under 267 GPa pressure)
E. Snider, N. Dasenbrock-Gammon, R. McBride, et al.
University of Rochester

superconducting technology

large scale vs. small scale


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.

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 Tλ = 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.