Superconductivity

Heike Kamerlingh Onnes, in 1908 at Leiden, was the first to liquefy helium, reaching $T \approx 4{,}2$ K. In 1911, measuring the resistivity of mercury at those temperatures, he noticed that $\rho$ did not simply decrease: it plunged exactly to zero below $T_c = 4{,}15$ K. In 1913 he received the Nobel Prize.

Principle — Superconductivity

Below a critical temperature $T_c$ characteristic of the material, the resistivity of a superconductor is rigorously zero. A current set in motion in a superconducting loop keeps circulating for years without any energy loss.

Material	$T_c$
Hg (mercury)	4.15 K
Pb (lead)	7.2 K
Nb (niobium)	9.3 K
NbTi (alloy)	9.5 K
YBa$_2$Cu$_3$O$_7$ (YBCO)	93 K
HgBa$_2$Ca$_2$Cu$_3$O$_x$	135 K

Two features define the superconducting state:

• zero resistance (no energy loss under direct current);
• Meissner effect (1933): the superconductor completely expels the magnetic field from its interior (perfect diamagnetism). Hence the spectacular magnetic levitation of a magnet above a YBCO pellet cooled with liquid nitrogen.

Applications.

• Magnets for medical magnetic resonance imaging (MRI): NbTi coils immersed in liquid helium, fields $\sim 3$ T.
• LHC magnets at CERN: about 1200 NbTi dipoles at $1{,}9$ K, fields of $8{,}3$ T to bend protons at 7 TeV.
• Urban transport: the Shanghai Maglev and the Japanese L0 (record 603 km/h, 2015) exploit superconducting coils.
• Quantum computers (Google, IBM, Rigetti): the qubits are superconducting Josephson junctions at $\sim 20$ mK.

Historical context

The microscopic explanation of “classical” superconductivity arrived only in 1957 with BCS theory (Bardeen, Cooper, Schrieffer; Nobel Prize 1972): electrons pair up into Cooper pairs mediated by lattice vibrations, and these pairs obey bosonic rather than fermionic statistics, forming a condensate that flows without resistance. High-$T_c$ superconductivity, discovered in 1986 by Bednorz and Müller (Nobel Prize 1987) in cuprates, is not standard BCS: its microscopic mechanism is still a subject of research today (Simonyi 2012).

Links

Topics: Electric circuits Concepts: Ohm’s law

Related exercises: Problem — resistance of a light bulb · Problem — resistance and power of an ohmic conductor · Problem — voltage drop in a copper cable