Vortex Pinning in Type-II Superconductors

Applied Conditions

Applied field B / B_c2 0.40

Drive current J (a.u.) 2.0

Pinning strength (a.u.) 4.0

Temperature T / T_c 0.30

Vortex State

Vortices

Pinned

Drift velocity

0.0000

J / J_c

0.00

Transport state

—

How it works

In a type-II superconductor, magnetic field above H_c1 penetrates as discrete quantised flux tubes ("vortices"), each carrying one flux quantum Φ₀ = h/2e. They arrange into a triangular Abrikosov lattice with spacing:

a = sqrt( 2·Φ₀ / (√3·B) )

An applied transport current J exerts a Lorentz force per unit vortex length, f_L = J × Φ₀, pushing vortices sideways. Material defects (grain boundaries, dopant clusters — the grey dots below) create pinning potentials that resist this motion up to a critical force f_p. As long as f_L stays below the local f_p, vortices sit still: zero resistance, true superconductivity. This defines the critical current density:

J_c = f_p,max / Φ₀

Near J_c, thermal energy lets vortices hop between pinning sites even while formally "pinned" — Anderson–Kim flux creep:

v = v₀ · exp[ -(U₀/k_BT) · (1 - J/J_c) ]

Once J exceeds J_c everywhere, vortices depin and stream continuously ("flux flow"). A moving flux line induces a real electric field E = B·v along the current, so flux flow means dissipation and finite resistance — the practical reason engineered pinning (irradiation defects, nanoparticle inclusions) is what makes a wire useful at high current, not superconductivity alone.

B slider — sets vortex density via the lattice spacing above; more field, more vortices.
J slider — the driving Lorentz force; push it past the local pinning threshold to depin vortices.
Pinning strength — average defect strength, i.e. how large J_c is.
Temperature — controls thermally-activated flux creep below J_c, and how "soft" the transition to flux flow looks.

Vortex (flux line) Active pinning site Idle pinning site

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