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Critical current density, critical field, soft vs hard

Short answer

Critical current density J_c = 2H_c/r is the maximum current per area a superconductor can carry; critical field H_c varies as H_0[1−(T/T_c)^2]. Soft (type-I) have one low H_c, sharp transition, low current; hard (type-II) have two critical fields, a mixed state with flux pinning, high H_c2 and high J_c.

What is critical current density and critical magnetic field in superconductors? Differentiate between soft and hard superconductors.

Critical magnetic field

The critical magnetic field HcH_c is the minimum field that destroys superconductivity at a given temperature. It is largest at 0 K and becomes zero at TcT_c:

Hc(T)=H0[1−(TTc)2]H_c(T) = H_0\left[1 - \left(\frac{T}{T_c}\right)^2\right]

Critical current density

The critical current density JcJ_c is the maximum current density a superconductor can carry without losing superconductivity. The current's own magnetic field must stay below HcH_c. For a wire of radius rr (Silsbee's rule):

Ic=2πrHc,Jc=Icπr2=2HcrI_c = 2\pi r H_c, \qquad J_c = \frac{I_c}{\pi r^2} = \frac{2H_c}{r}

Soft vs hard superconductors

Soft superconductors are type-I; hard superconductors are type-II.

 -M                         -M
  |    /|                    |   /\
  |   / |                    |  /  \
  |  /  |                    | /    \_
  | /   |                    |/       \__
  |/    |____ H              +----|------|--- H
  0    Hc                    0   Hc1    Hc2
   Type-I                     Type-II
PointSoft (Type-I)Hard (Type-II)
Critical fieldsOne, HcH_cTwo, Hc1H_{c1} and Hc2H_{c2}
Field valueLow (below about 0.2 T)Hc2H_{c2} high (up to tens of T)
Meissner effectCompleteComplete only below Hc1H_{c1}
TransitionSharpGradual, through mixed (vortex) state
MagnetizationReversible, no hysteresisIrreversible, large hysteresis (flux pinning)
Critical currentSmallLarge
CompositionMostly pure metalsAlloys and compounds
ExamplesPb, Hg, Sn, AlNbTi, Nb3_3Sn, V3_3Ga, YBCO
UsesFew practicalMRI and accelerator magnets, cables

Hard superconductors are "hard" because flux vortices get pinned at defects, so they resist flux movement, show hysteresis like hard magnetic materials, and can carry large currents in strong fields.

✓ Answer checked by Claude Opus 5.5 (high effort)

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