Superconductor and critical magnetic field

Superconductor

A superconductor is a material whose electrical resistance drops abruptly to zero when it is cooled below a certain temperature called the critical (transition) temperature T_c. Examples: mercury (T_c = 4.2 K), lead (7.2 K), niobium (9.2 K), YBa₂Cu₃O₇ (about 92 K).

Critical magnetic field

A strong magnetic field destroys superconductivity. The minimum field that restores the normal (resistive) state at a given temperature is the critical field B_c(T). It varies with temperature as

B_c(T) = B_c(0) [1 − (T/T_c)²]

  Bc |
 Bc(0)|*
     |   *
     |      *       Normal state
     |  SC     *
     |  state       *
     |_____________________*__ T
                          Tc

B_c = B_c(0) at T = 0 and falls to zero at T = T_c. Below the curve the material is superconducting. Related to this, a current above the critical current I_c = 2πaB_c/μ0 (Silsbee's rule, wire of radius a) also destroys superconductivity.

Characteristics

1. Zero resistance: a current set up in a ring persists for years without a source.
2. Meissner effect: a superconductor expels magnetic flux from its interior (B = 0), i.e. perfect diamagnetism, χ = −1. This differs from a mere perfect conductor.
3. Critical temperature, field and current exist as limits.
4. Type I (pure metals): sharp transition at B_c. Type II (alloys, ceramics): mixed state between lower and upper critical fields B_c1 and B_c2; they stay superconducting to high fields.
5. Isotope effect: T_c ∝ 1/√M.
6. Heat capacity shows a jump at T_c; an energy gap appears.
7. Applications: powerful magnets (MRI, maglev), SQUIDs, lossless cables.