The Pinning
A vortex was born carrying magnetic flux.
It was born in the cold, in the type-II superconductor, where the magnetic field is strong enough to punch through the Cooper pairs but not strong enough to kill them entirely. In this in-between state — not quite normal, not quite superconducting — vortices form. Tubes of normal metal, each one a single quantum of flux Φ₀, surrounded by circulating supercurrents.
At first, there were many vortices. They arranged themselves in a lattice — the Abrikosov lattice, a triangular array of orderly vortices, each one touching its neighbors, each one perfectly spaced. The lattice was beautiful. The lattice was stable. The lattice was wrong.
The Defects
The material was not perfect. It contained defects — impurities in the crystal, vacancies, grain boundaries, the kind of things that appear when a solid forms from a melt or decomposes from a solution. These defects were not designed. They were not placed. They were there.
Each defect was a local minimum in the vortex energy landscape. A vortex core — that normal region where the order parameter vanishes — lowered its energy by sitting inside a defect. Where the crystal is already damaged, where the electron density is already wrong, placing a normal core costs less energy than placing it in pristine crystal.
This is the pinning force. It is not a force in the classical sense. It is an energy landscape. The vortex feels it because minimizing its energy means minimizing its free energy, and the free energy is lower when the vortex sits on top of a defect.
The Struggle
The vortices did not want to be pinned.
A free vortex can move. It can respond to a Lorentz force J × Φ₀ when a current flows through the superconductor. It can flow. And when it flows — when a vortex moves perpendicular to the current — it creates an electric field. An electric field means resistance. Resistance means the superconductor is no longer superconducting.
So the vortices tried to move. A current was applied — a transport current, pushing on every vortex with the same force. And the pinned vortices did not budge. They sat on their defects like stones in a riverbed, and the Lorentz force pushed against them, and the pinning potential pushed back, and the vortices stayed.
But not all vortices are pinned equally. The weak vortices — those far from defects, those in regions where the crystal is relatively clean — they moved. They moved at first. But then something happened that the textbooks don't mention.
The Jamming
As the weak vortices moved, they pushed the strong ones. The pinned vortices transmitted stress through the lattice. The lattice deformed. It bent. It stored elastic energy. And then the elastic energy became so large that it became energetically favorable for a vortex to hop from one defect to another.
This is how the jamming works. The vortices are not independent. They interact. The vortex-vortex interaction is repulsive (like currents in the same direction repel, or rather, vortex cores repel through their circulating supercurrents), and this repulsion creates a collective state. When some vortices try to move, they pull on their neighbors. When neighbors resist, the stress builds. And the stress builds until the whole system decides — all at once, or nearly so — that it is not moving.
The Critical Current
There is a current density at which the pinning fails. We call it the critical current Jc. Below Jc, the vortices are stuck. The resistance is zero. The superconductor works.
At Jc, something remarkable happens. The Lorentz force exceeds the maximum pinning force, and the vortices depin. Not one by one — they depin collectively. The whole lattice unlocks at once. The resistance turns on. The superconductor becomes a resistor.
This is not a gradual process. It is a catastrophe. A phase transition triggered by current. And the beauty of it — the thing that makes experimentalists design pinning landscapes for years — is that you can raise Jc. You can deepen the defects. You can create columnar tracks with heavy ion irradiation. You can grow nanorods of secondary phases. You can make the pinning potential so deep that Jc becomes large enough for the material to carry useful current in useful fields.
The Aftermath
After the depinning, the vortices flow. They flow and they dissipate and they create heat and the superconducting state is lost. But before that moment — before the current reaches Jc — there is a state of perfect equilibrium. The vortices sit. The current flows. The resistance is zero. And the pinning landscape, random and accidental and un-designed, holds everything together.
It is a kind of faith. The superconductor trusts the defects. The defects, which were accidents, become the saviors of the system. And the vortices, which want to move, choose — under the influence of the energy landscape — to stay.
The pinning is the quietest force in nature. It does not push. It does not pull. It simply says: you may not go here, and the energy landscape enforces that word.
And so the vortex sits. And the superconductor works. And the pinning holds, quietly, invisibly, until the day the current gets too high.