Vortex Pinning: 2D Cross-Section of Flux Creep & Flow

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

This is a top-down 2D cross-section of the same physics as the 3D slab: magnetic field above H_c1 penetrates a type-II superconductor as discrete quantised flux tubes ("vortices"), each carrying one flux quantum Φ₀ = h/2e, arranged in 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 (rightward here). Grey dots are material defects that pin vortices up to a critical force f_p. Below f_p, vortices sit still: zero resistance. 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"), inducing a real electric field E = B·v along the current — resistive dissipation. This is why engineered pinning (irradiation defects, nanoparticle inclusions), not superconductivity alone, is what makes a wire carry high current losslessly.

B slider — vortex density via the lattice spacing above; more field, more vortices.
J slider — driving Lorentz force; push 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.
Drag on the canvas to pan; scroll/pinch to zoom.

Vortex (flux line) Active pinning site Idle pinning site

top-down view — current drives vortices →