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Field expulsion; type I vs type II

Short answer

The Meissner effect expels magnetic flux: screening currents on the surface cancel the applied field inside, so B=0 and χ=−1. Type-I superconductors have a single low H_c, complete expulsion up to H_c, and a sharp transition. Type-II have two critical fields (H_c1, H_c2); a mixed vortex state extends to high H_c2, enabling large current densities.

How does a superconductor expel magnetic field? Differentiate between type I and type II superconductors.

How a superconductor expels the magnetic field

When a superconductor is cooled below TcT_c in a field H<HcH < H_c, it pushes all flux out of its interior. This is the Meissner effect, and it makes the material a perfect diamagnet.

  1. Below TcT_c electrons form Cooper pairs, which move without scattering.
  2. The applied field induces persistent screening currents on the surface, in a layer about the London penetration depth λL\lambda_L (10 to 100 nm) thick.
  3. These currents create a field that exactly cancels the applied field inside:
B=μ0(H+M)=0  ⇒  M=−H,χm=−1B = \mu_0(H + M) = 0 \;\Rightarrow\; M = -H, \quad \chi_m = -1
  1. Inside, the field decays as B(x)=B0e−x/λLB(x) = B_0 e^{-x/\lambda_L}, so it is essentially zero beyond a few λL\lambda_L.
     normal (T > Tc)          super (T < Tc)
     | | | | | |              \  \     /  /
     | |+---+| |               \  +---+  /
     | ||   || |    ---->       ) |   | (
     | |+---+| |               /  +---+  \
     | | | | | |              /  /     \  \

The expulsion happens whether the field is applied before or after cooling, so it is a property of the superconducting state, not just of zero resistance.

Type-I vs type-II superconductors

 -M                         -M
  |    /|                    |   /\
  |   / |                    |  /  \
  |  /  |                    | /    \_
  | /   |                    |/       \__
  |/    |____ H              +----|------|--- H
  0    Hc                    0   Hc1    Hc2
   Type-I                     Type-II
PointType-I (soft)Type-II (hard)
Critical fieldSingle HcH_cTwo: Hc1H_{c1} and Hc2H_{c2}
Meissner effectComplete up to HcH_cComplete only up to Hc1H_{c1}
TransitionSharp, normal at HcH_cGradual; mixed (vortex) state between Hc1H_{c1} and Hc2H_{c2}
Value of fieldLow, about 0.01 to 0.2 THc2H_{c2} very high, up to 20 to 100 T
Current capacityLow JcJ_cHigh JcJ_c (with flux pinning)
MagnetizationReversibleIrreversible, hysteresis
MaterialsPure metals: Pb, Hg, Sn, Al, InAlloys, compounds: NbTi, Nb3_3Sn, V3_3Ga, YBCO
UsesLimited (research, SQUID parts)Magnets for MRI, accelerators, maglev

✓ Answer checked by Claude Opus 5.5 (high effort)

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