Josephson effect

The Josephson effect is a physical effect, which describes the tunnel current between two superconductors. It was theoretically predicted in 1962 by Brian D. Josephson and later verified in numerous experiments, first in 1962 by John Rowell at Bell Laboratories (some with Philip W. Anderson). Josephson was awarded the 1973 Nobel Prize in Physics.

Although the Josephson effect was first measured in superconductors, however, the term was generalized: One speaks of the Josephson effect, if two macroscopic wave functions are weakly coupled ( coupling via a tunnel barrier ).

Descriptive Description

The electric current in superconductors is not how it is in normal conductors the case, carried by individual electrons, but of electron pairs, the so-called Cooper pairs, as postulated by the BCS theory.

When two superconductors separated by a few nanometers thin, non - superconducting barrier, Cooper pairs can tunnel from one superconductor through the barrier to the other. Such a superconductor - normal metal - superconductor ( SNS) - or superconductor-insulator - superconductor ( SIS) design is called Josephson junction. Now, a power source connected to the Josephson junction and a low electrical current is passed through the contact, he continues to behave as a superconductor, without interruption, as the Cooper pair tunnels through the barrier.

Josephson equations

In a superconductor, all the Cooper pairs are in the same quantum state, so can be described by one and the same wave function describe (see BCS theory ). In a Josephson junction, the wave functions of the two superconductors are coupled through the thin, non- superconducting layer ( the magnitude of the coupling is essentially determined by the thickness of the layer determined ). The supercurrent ( carried by Cooper pairs flow) through this layer has the size

Wherein the phase difference of the superconducting wave function representing both sides of the barrier, and the critical current of the barrier.

The following applies:

Where Φ0 is the magnetic flux quantum. This equation is called. Because of the phase difference changing occurs a constantly changing supercurrent. Substituting the second Josephson equation into the first Josephson equation is obtained for the corresponding frequency ( Josephson frequency)

Using the values ​​of the constants obtained for the ( very low ) voltage of the frequency of 1 microvolts 483.597870 (11) MHz. Similar to the unit ohm through reduction of conventional Ohms (see von Klitzing constant) is defined by fixing the conventional Josephson constant, the unit of voltage: 1 V corresponds to 483 597.9 GHz and 1 mV corresponds to 483.5979 GHz.

It remains to mention that the current depends on external magnetic fields by a Josephson junction. In fact, is the first Josephson equation:

Here, the magnetic vector potential, and the integral is a line integral that extends from the first superconductor over the barrier to the second superconductor.

Characteristic of a Josephson junction (not hysteresischer case without magnetic field)

Comparisons: On a Josephson junction not only tunneling of Cooper pairs through the barrier takes place, total found at the Josephson junction, the following process takes place:

  • Tunneling of Cooper pairs through the barrier ( Josephson effect )
  • Tunneling of single electrons through the barrier
  • Break Cooper pairs and the resulting single-electron tunneling through the barrier ( high in comparison with the band gap voltage of the superconductor )
  • Ohmic conduction through the barrier at SNS contacts, not at SIS contacts
  • The two superconductors with the barrier between them behave like the plates of a parallel plate capacitor.

Since all these processes take place in parallel, applies

  • The measured voltage is the voltage of the Josephson effect; from it can be set via the second Josephson equation to calculate directly.
  • The current measured is the total current of all the processes taking place, that is substantially the sum of the current of the Cooper pairs and the current of the single-electron temporally smoothed by the capacitor effect of the contact.

DC Josephson effect is the voltage small, ie the energy of the Cooper pairs in the electric field towards negligible, results in the minimization of the free energy of the system that adjusts with the balance. That

No external voltage source, so that the Josephson current is compensated by tunneling of single electrons in the opposite direction, so that there is no voltage build up. Is a (low ) voltage is applied, the Josephson current, however, flows due to the electric field from the power source, so that is valid for the measured current substantially:

AC Josephson effect If the voltage is so large that the thermal effects are negligible, the Resistively and capacitively Shunted Junction ( RCSJ ) is usually model used to set up a differential equation for. Here, the total current is set as the sum of the Josephson current, ohmic current, current of a capacitor. Forced by a voltage source at a constant voltage by a phase of results

, Ie, the Josephson current is then an alternating current with angular frequency.

Technical realization of Josephson junctions

The barrier to separate the two superconductors may be only a few nanometers thick, so that quantum mechanical tunneling processes can take place. This can be realized in various ways:

  • Development of a SNS or SIS arrangement in thin film technology by sputtering or laser ablation
  • A thin tip of superconducting material that is pressed on a superconductor ( point contact / top contact) has, similarly, since tunneling effects occur at the sides of the tip (possibly such a large current is in the normal state once sent by the arrangement that the thinnest point the constriction oxidized by the heat and so a thin insulating oxide layer is formed )
  • A very narrow waist in a superconducting film ( the effects are the same as the top contact)
  • In strongly anisotropic high -temperature superconductors such as Bi2212 or LaO0.9F0.1FeAs pnictide superconductivity occurs only in planes between the planes are insulating layers. By patterning can therefore be produced from single crystals intrinsic Josephson junctions.

Applications

Josephson junctions are used as extremely fast switching elements and very accurate voltage stabilizers. They are also used in systems to measure extremely small magnetic fluxes ( SQUIDs ).

Josephson junctions are highly accurate frequency-to- voltage converter. When inverse Josephson effect one operates the Josephson junction with a voltage of the form

It can be shown, that Ic is then constant. This arrangement is used in verification offices as a very accurate frequency - to-voltage converter for the calibration of tension and then called Josephson normal or Josephson quantum standard.

Limitations

Since Josephson effects occur only in conjunction with superconductors, they must be cooled to very low temperatures, making the operation technically quite complex and under certain circumstances can be very costly. A frequently used material for the production of superconducting such contacts is niobium, which is superconducting at 9.2 Kelvin. Cooling this liquid helium temperatures (having a temperature of 4.2 Kelvin ) is used. Josephson junctions of high-temperature superconductor materials can also be cooled with liquid nitrogen temperature ( 77.4 degrees Kelvin ). Liquid nitrogen is much cheaper and easier to produce than liquid helium, however, the manufacturing process for Josephson junctions of high temperature superconductors is much more expensive.

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