1. What is the difference between usual tunneling and Josephson tunneling ?

Usual tunneling involves tunneling of electrons across an insulating barrier. This will take place even for non-superconductors such as for a Normal Metal-Insulator-Normal Metal junction. On the other hand, in Josephson tunneling pairs of electrons (Cooper pairs) tunnel across a barrier and require a superconductor (at a temperature below ) on either side of the barrier.

2. What is the difference between the critical current density of a superconducting wire and that for a Josephson junction ?

For a superconducting wire, the critical current density is the current density that is passed through it beyond which it develops a resistance and therefore a voltage develops across it. This is because the current through the superconductor generates a magnet field which, when it exceeds the critical magnetic field, makes the superconductor normal. On the other hand, in a Josephson junction, the critical current density beyond which there is voltage across the junction is called the Josephson critical current. At these currents, the superconductors themselves are still superconducting but Cooper pairs can not tunnel across the barrier.

3. If a 1 microvolt dc voltage is applied across a Josephson junction, find the frequency of the ac current that is developed.

483.6 MHz

4. Work out the algebra starting from Equation 21 to obtain Equation 22.

5. What is the effect of a large on the characteristics of a Josephson junction?

The implication of a large is that the time constant of the circuit, in the equivalent circuit of the Josephson junction, is large. This means that the time taken to charge the capacitor is large. Therefore if one starts out with no current in the circuit, the voltage will be zero and will remain zero even if we now pass a current which is less than the junction critical current. On increasing the current further, the voltage will abruptly jump and will now follow the linear curve . If we now decrease the current, even to zero, the voltage will be stuck to the value (discharge time of the capacitor is large) till the becomes zero. Therefore, there is hysteresis in the characteristics.

6. Calculate the value of the flux quantum.

Web (SI units)

7. Starting from equation 28, work out the details to obtain equation 32, i.e.,

By taking specific values for the argument in the above equation draw the corresponding curve.

(1)

8. What is the origin of the word ``interference'' used in the SQUID?

The dependence of the max current on the magnetic flux is similar to the Young's double slit interference pattern. The currents in the two arms of the loop can interfere constructively or destructively giving rise to maxima and minima as a function of the flux in the loop.

9. Look up on the internet and in other literature various applications of superconductors.