Josephson's Effect

abhaymv

Hello,
What exactly is the difference between ac Josephson Effect and DC Jsephson effect?When does each occur?What is the relevence of magnetic field here?In which cases are potentials applied?I tried to find the answer in the net,but couldn't find any satisfactory explanations.I have not begun to study quantum mechanics in detail.Can someone help me?Please explain in simple terms.

PS:Equations are not very important as far as I am concerned.I just want to get an idea about the phenomenon.

f95toli

This sounds a bit like homework. Your questions are quite general but the answers are easy to find.
Have you tried looking in a textbook? E.g. Tinkham or Waldram.

Btw. You don't really need QM at all in order to understand the answers to your questions, simple circuit models will do.

abhaymv

Its not homework.I didn't understand the lecture in my class.I have only bits of info.I think by what I understand,
Both phenomenon occur when two superconductors are seperated by an extremely thin insulator.
Also that electons penetrate the insulators in pairs called cooper pairs.

But I cannot understand the distinction between the processes.I tried a textbook,but it gives a vague answer in terms of quantum mechanics,in relation with something called a SQUID.

f95toli

The DC and AC Josephson "effects" are more or less just the name of the two Josephson equations, they are not really separate phenomena.
The DC Josephson effect (tehj 1st equation) tells you that the current through the junction depends on the phase difference across it, and the AC Josephson effect (the 2nd equation) relates the voltage across the junction depends to the time derivative of the phase.

Look at e.g the wiki for the Josephson effect.

abhaymv

Thank you.I didn't know that they related to the same phenomenon.

abhaymv

Just to be clear on this,
DC josephson effect:Occurs when there is no ptential difference,and cuttent varies between -I to I
AC Josephson effect:Occurs when the applied potential crosses a critical potential,V_c

I am still unclear about what occurs in between the time when a small potential is applied,and then it rises to V_c..

Please tell me where I am wrong.

Also,in the derivation of DC josephson tunnelling,

we see:
i(h/2π)(∂φ/∂t)=Eφ

But,when applied to electron probability density in semiconductor 1,this becomes:
i(h/2π)(∂φ₁/∂t)=(h/2π)Tφ₂
where T is the tunnelling frequency.

IS Eφ₁ equal to (h/2π)Tφ₂?
(We just studied the derivation,an explanation was not given..)

Also, in the derivation of AC josephson effect,there is an extra term -eVφ₁.
Where V is the potential.
Wy is the potential term subtracted?Doesn't the potential support the flow of electron pairs across the junction?

DrDu

An easy explanation can be found also in the "Feynman Lectures".

abhaymv

Thank you