A tiny whirlpool of current in a , threaded by a single quantum of magnetic flux. Many superconductors do not shut a magnetic field out completely: above a certain field it enters as thin threads, each with a core where superconductivity is destroyed, a few to tens of nanometres across, and a ring of current circling around it. The threads repel each other and settle into a regular lattice. When they move, they waste energy – so a superconductor stays lossless only if they are pinned in place – and their cores can hold electronic states of their own, among them the zero-energy states searched for as .
As the site uses it
For FeTe1−xSex, low-temperature STM with sub-meV resolution is needed to resolve vortex bound states, and inhomogeneity in the Te/Se ratio makes statistics over many vortices essential.
With no inversion centre, the crystal turns a current into a sideways voltage at twice its frequency, even with no magnetic field, in the directions its symmetry allows; in the superconducting state the vortices raise it a hundredfold.
A magnetic field enters a type-II superconductor as vortices: each a normal core threaded by one flux quantum and ringed by circulating supercurrent. They repel each other and form a lattice. Tunnelling into a core finds states bound there – and, in a topological superconductor, possibly a Majorana mode at zero energy.
Flux in quanta
A superconductor expels a weak magnetic field, but expelling it costs energy, and in type-II superconductors a stronger field gets in. It does so in the cheapest way available: as separate threads, each carrying exactly one flux quantum, h/2e, because the superconducting wavefunction must return to itself on any loop around the thread, its phase winding once around.
At the centre of each thread superconductivity is destroyed over about a coherence length, while a ring of circles around it and screens the field over a larger distance, the penetration depth. Vortices repel one another and form a lattice, predicted by Abrikosov in 1957 and usually triangular. As the field rises they crowd together, until at the their cores overlap and superconductivity is gone.
Seen one by one
made the lattice visible. Mapping the conductance at the edge of the superconducting gap of NbSe2 in a magnetic field, Hess and colleagues imaged the vortex lattice in 1989, and found that inside a core the conductance peaked at zero energy – states bound in the core – turning back into the ordinary superconducting gap away from it.
In a such a core can hold a Majorana zero mode, a state that is its own antiparticle. On the surface of FeTe0.55Se0.45, where a becomes superconducting, vortex cores show a sharp zero-bias peak that does not split (Wang and colleagues, 2018). With 20 µeV energy resolution, Machida and colleagues found that only some vortices host it, that the share falls as the field rises, and that it does not follow the chemical of the crystal – one of the open questions about the Majorana interpretation.
Moving vortices, and vortices in two dimensions
A current pushes vortices sideways, and a moving vortex induces a voltage: the superconductor then dissipates energy although its electrons are still paired. Practical superconductors carry current without loss only because defects pin their vortices in place.
In a film thin enough to count as two-dimensional, vortices appear even without a field, created by heat in pairs that circulate in opposite directions. Below the temperature the pairs stay bound; above it they come apart and destroy zero resistance. In the layered superconductor PbTaSe2, whose crystal lacks a centre of inversion, thermally excited vortices and antivortices are the likely carriers of a sideways voltage at twice the current’s frequency that grows by orders of magnitude around the superconducting transition (Itahashi and colleagues, 2022).
For specialists
A line of magnetic flux h/2e (2.07 × 10−15 Wb) through a type-II superconductor, around which the superconducting phase winds by 2π; its core, about a coherence length wide, has the gap suppressed and hosts bound states, and its circulating supercurrent screens the field over the penetration depth. Between the lower and upper critical fields, vortices form the Abrikosov lattice, which scanning tunnelling microscopy imaged in NbSe2 together with the core states. Moving vortices dissipate energy; in two dimensions, thermally created vortex–antivortex pairs unbind at the Berezinskii–Kosterlitz–Thouless transition. In a topological superconductor a vortex core can bind a Majorana zero mode, the interpretation offered for zero-energy peaks in Fe(Te,Se).
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