Illustrated Physics
physics, drawn
Concept

Superconductivity — where it appears

The state in which a material has exactly zero resistance and expels magnetic field from its interior, below a critical temperature. It is a thermodynamic phase rather than a limit of good conduction, its carriers are pairs of electrons, and the flux through a superconducting ring can only be a multiple of h/2e.

Named by 4 essays across one field — each of them below, with the objects they name alongside it.

The screening that survives to zero frequency. How far a magnetic field gets into copper against how fast it is changing, drawn beside the London depth of a superconductor with a carrier density of 6.0e+28 per cubic metre. The metal's curve falls as one over the square root of the frequency — measured on the drawn curve as -0.5000 against −½ — and it is a straight line on these axes with no bottom: at a hundred hertz the field reaches nine millimetres in, and at zero frequency it reaches all the way through, because a normal metal screens by dissipating and a steady field dissipates nothing. The superconductor's line is flat at 21.7 nanometres. The frequency does not appear in the expression for it, so there is nothing for it to depend on, and the screening is as complete at zero frequency as at any other. The two lines cross at 9.0e+12 hertz, in the far infrared, and above that the ordinary metal is actually the better screen — which is a useful corrective, because a superconductor's advantage is not that it screens harder but that it does not need the field to be changing. What the picture cannot show is where the flat line stops: above the energy gap the pairs break, the superconductor becomes an ordinary metal, and the flat line turns into a sloping one.

The field that is pushed out

A perfect conductor keeps whatever field was inside it when its resistance vanished. A superconductor expels the field either way, and the difference between remembering and expelling is the experiment that showed superconductivity is a state of matter rather than a very good conductor.

electromagnetism · Superconductivity The size of the quantum says what is carrying the current. What the flux quantum would be for each candidate carrier charge, in units of 10⁻¹⁵ webers, against the measured value drawn as a line. A single electron would give 4.1357, a pair 2.0678, a triple 1.3786. The measurement is 2.0678, which picks the pair and excludes the others by a factor of two — not by a few per cent, so no question of experimental accuracy arises. The whole of the argument is that the condensate's wavefunction must come back to itself round the ring, which makes the enclosed flux a multiple of h over the carrier's charge; measuring the multiple therefore measures the charge, without any charge ever being measured. That is how the pairing was established in 1961, four years after it was proposed and by an experiment that looks nothing like a measurement of a charge.

The two in the flux quantum

A superconducting ring cannot hold whatever flux is applied to it. It holds a whole number of quanta and drives a current to make up the difference, and the size of that quantum is Planck's constant divided by twice the electron's charge. The factor of two was measured in 1961, four years after somebody predicted that the carriers are pairs — by an experiment in which no charge is measured at all.

electromagnetism · Superconductivity The ring picks a whole number and pays for the difference. The kinetic energy of the screening current in a superconducting ring, against the flux applied from outside, in units of the flux quantum. Each parabola belongs to one winding number — the number of times the condensate's phase turns round the ring, which has to be an integer because the wavefunction has to come back to itself. The ring cannot hold an arbitrary flux, so it holds the nearest whole number of quanta and drives a current to make up the difference; the energy of that current goes as the square of the mismatch, which is what each parabola is. The lowest curve at each applied flux is the state the ring is in, and the winding number changes at exactly the half-integers — 0.50 and 1.50 and 2.50 here. So the measurable properties of the ring are periodic in the applied flux with a period of one quantum, which is 2.0678 × 10⁻¹⁵ webers and is about the flux the Earth's field puts through a square micrometre.

Two lengths, and which one is longer

A superconductor has a depth to which a field leaks in and a distance over which superconductivity itself can be built up. Which of the two is larger decides the sign of the energy of a boundary — and therefore whether the material keeps every field out or fills itself with a lattice of holes.

electromagnetism · Superconductivity A current with no voltage, and then a voltage that is a frequency. Current against mean voltage for a Josephson junction shunted by a resistance, in units of its critical current and of the critical current times the resistance. Up to the critical current the junction carries a supercurrent at exactly zero voltage, set by the difference of the two superconductors' phases. Above it a mean voltage appears, growing as R√(I² − Ic²) and approaching the ohmic line at large current; the curve is integrated from the junction equation and checked against that result at three currents. The voltage is not steady. It is a train of pulses, each the phase slipping by one turn, at a frequency of 483.6 GHz per millivolt: for a junction with Ic = 1 mA and R = 1 Ω, one unit of the voltage axis is 1 mV and 484 GHz.

The voltage that is a frequency

Two superconductors separated by a barrier a nanometre thick carry a current with no voltage at all, set by the difference of their quantum phases. Push harder and a voltage appears — and a voltage makes that phase difference run, so the current oscillates at 483.6 gigahertz for every millivolt. Shine microwaves on the junction and the voltage locks to exact multiples of the frequency divided by a ratio of fundamental constants, with nothing about the junction in it. That is why a volt is now counted in cycles.

electromagnetism · Superconductivity

Named alongside it

The objects these essays reach for when they reach for this one.

CondensateFlux quantumMacroscopic quantum stateOrder parameterPhase coherencePhase transitionSkin depthCirculationCooper pairCritical fieldFlux expulsionFlux freezing

All concepts