Josephson effect
In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them.
The effect is named after the British physicist Brian Josephson, who predicted in 1962 the mathematical relationships for the current and voltage across the weak link.
The Josephson effect has many practical applications because it exhibits a precise relationship between different physical measures, such as voltage and frequency, facilitating highly accurate measurements.
[clarification needed] These consist of two or more superconductors coupled by a weak link.
The weak link can be a thin insulating barrier (known as a superconductor–insulator–superconductor junction, or S-I-S), a short section of non-superconducting metal (S-N-S), or a physical constriction that weakens the superconductivity at the point of contact (S-c-S).
Josephson junctions have important applications in quantum-mechanical circuits, such as SQUIDs, superconducting qubits, and RSFQ digital electronics.
The NIST standard for one volt is achieved by an array of 20,208 Josephson junctions in series.
[3] The DC Josephson effect had been seen in experiments prior to 1962,[4] but had been attributed to "super-shorts" or breaches in the insulating barrier leading to the direct conduction of electrons between the superconductors.
He was then 23 years old and a second-year graduate student of Brian Pippard at the Mond Laboratory of the University of Cambridge.
Josephson studied the experiments by Ivar Giaever and Hans Meissner, and theoretical work by Robert Parmenter.
Pippard initially believed that the tunneling effect was possible but that it would be too small to be noticeable, but Josephson did not agree, especially after Anderson introduced him to a preprint of "Superconductive Tunneling" by Cohen, Falicov, and Phillips about the superconductor-barrier-normal metal system.
Anderson later remembered: We were all—Josephson, Pippard and myself, as well as various other people who also habitually sat at the Mond tea and participated in the discussions of the next few weeks—very much puzzled by the meaning of the fact that the current depends on the phase.
Josephson then submitted "Possible new effects in superconductive tunnelling" to Physics Letters in June 1962[1].
John Bardeen, by then already Nobel Prize winner, was initially publicly skeptical of Josephson's theory in 1962, but came to accept it after further experiments and theoretical clarifications.
In January 1963, Anderson and his Bell Labs colleague John Rowell submitted the first paper to Physical Review Letters to claim the experimental observation of Josephson's effect "Probable Observation of the Josephson Superconducting Tunneling Effect".
[7] These authors were awarded patents[8] on the effects that were never enforced, but never challenged.
[citation needed] Before Josephson's prediction, it was only known that single (i.e., non-paired) electrons can flow through an insulating barrier, by means of quantum tunneling.
Josephson was the first to predict the tunneling of superconducting Cooper pairs.
Other uses include: The Josephson effect can be calculated using the laws of quantum mechanics.
, which can be interpreted as the wave functions of Cooper pairs in the two superconductors.
To solve the above equation, first calculate the time derivative of the order parameter in superconductor A:
The critical current of the Josephson junction depends on the properties of the superconductors, and can also be affected by environmental factors like temperature and externally applied magnetic field.
This DC Josephson current is proportional to the sine of the Josephson phase (phase difference across the insulator, which stays constant over time), and may take values between
This means a Josephson junction can act as a perfect voltage-to-frequency converter.
[19] Rewrite the Josephson relations as: Now, apply the chain rule to calculate the time derivative of the current: Rearrange the above result in the form of the current–voltage characteristic of an inductor: This gives the expression for the kinetic inductance as a function of the Josephson Phase: Here,
Note that although the kinetic behavior of the Josephson junction is similar to that of an inductor, there is no associated magnetic field.
[20] The supercurrent flowing through the junction is related to the Josephson phase by the current-phase relation (CPR): The superconducting phase evolution equation is analogous to Faraday's law: Assume that at time
Therefore, the energy stored in a Josephson junction is a state function, which can be defined as: Here
Again, note that a non-linear magnetic coil inductor accumulates potential energy in its magnetic field when a current passes through it; However, in the case of Josephson junction, no magnetic field is created by a supercurrent — the stored energy comes from the kinetic energy of the charge carriers instead.
The Josephson penetration depth usually ranges from a few μm to several mm if the critical current density is very low.
