Josephson current in normal metals

[QuantumLeak]

Hi all,
just a small question: why does a normal metal junction does not show a josephson like current when inserted in a squid setup? I guess it is something related to the coherence of the ground state...

 

[f95toli]

A Josephson current is -by definition- a current of Cooper pairs, which can not exist in normal metals (ignoring proximity effect for the moment).

Also, I am not sure I understand what kind of geometry you have in mind. A SQUID is -again by definition- a superconducting ring with one of more Josephson junctions, so where would you put the normal junction?

 

[wildwildebees]

Yes I agree with f95, the Josephson effect involves coupling of the wavefunctions of 2 superconductors on either side of a thin barrier (less than about 10 Angstroms). If a supercurrent is driven across the junction, the relative phase between the two wavefunctions adjusts itself, up until the point where the two wavefns are completely in phase, in which case you're at the maximum/'critical' current.

The DC SQUID setup is a way of taking advantage of this behaviour. But I can't see why using a normal-insulator-normal junction in a DC SQUID would be any different fundamentally than using one on its own - you might have to clarify why you think the SQUID part is important.

Perhaps you're asking why the wavefunctions of single electrons don't couple across a non-superconducting junction? In which case I'm not too sure! (In fact, perhaps they do couple, I don't know) You'd probably have to look at how Josephson derived his 1st equation for that.

 

[DrDu]

I guess the question is rather why we use an insulating gap and not a metallic gap in a josephson junction?
In case of the AC josephson effect, to observe this effect, there has to be a constant voltage difference between the two superconductors. A metal would not sustain such a voltage difference.

 

[ZapperZ]

Also, a metallic gap will simply create a short and the "regular" current transport will dominate rather than the tunneling current.

Just so we are clear, single-electrons DO tunnel across an insulating barrier. That is what one gets in SIN and NIN tunnel junctions. The physics of SIS tunnel junction has extra components in it, including the Josephson current that can exist at zero bias.

Zz.

 

[f95toli]

I guess the question is rather why we use an insulating gap and not a metallic gap in a josephson junction?
In case of the AC josephson effect, to observe this effect, there has to be a constant voltage difference between the two superconductors. A metal would not sustain such a voltage difference.

Although in many cases the barrier is somewhere between I and N, this would e.g. be true for all high-Tc junctions. Specifically, junctions are sometimes characterised by their transmissivity which is a parameter between 0 and 1. This is the so-called BTK model for junctions which works surprisingly well in most cases.

Also, you get the AC Josephson effect even in an SNS junction, you don't need a constant voltage difference (=voltage bias) which is fortunate since this is almost impossible with many junctions (because of their impedance, which is often just a few ohms). junctions are nearly always current biased in experiments(the exception being small Al junctions which can sometimes be voltage biased).


Moreover, one can make all sorts of funny junctions. SINIS junctions are quite popular at the moment, but one can also have S-Se-S (Se being a semiconductor), S-2DEG-S etc.

 

[DrDu]

Also, you get the AC Josephson effect even in an SNS junction, you don't need a constant voltage difference (=voltage bias) which is fortunate since this is almost impossible with many junctions (because of their impedance, which is often just a few ohms).

That's interesting and I don't quite understand it, but I know the experimental side very badly.
From what I remember from Steven Weinbergs book (QFT) the Lagrangian depends on $\partial_\mu \phi -e A_\mu$ which should be 0 in equilibrium. Hence $\partial/\partial t \Delta \phi =\Delta U$ i.e. a constant voltage induces an oscillating phase difference and this in turn an oscillating current. I don't see how you can get an oscillating current with no voltage difference (i.e. with a N conducting gap).

 

[f95toli]

There IS a voltage difference, the fact that the barrier is normal doesn't mean that it "shorts" the junction completely, there is still a finite resistance (although sometimes it is only of the order of one ohm) since the junction is driven by a constant current.

The usual circuit model for this is the RSJ model (or RCSJ if you include capacitance), you have a "Josephson element" which is governed by the Josephson equations in parallel with a resistor (and a capacitor in the RCSJ model).
If you solve the ODE when this is driven by an external AC current you will get Shapiro step (with locking) and all the other effects associated with the AC effect.

The main difference between SNS and SIS junctions experimentally, is that the former has a resistive branch from zero voltage, whereas the the latter just "jumps" to 2*Delta as soon as you apply a current larger than Ic (and in "proper" SIS tunnel junctions you also get various quasiparticle effects that are invisible or non-exisistent in SNS junctions).

I remember that back when I was a PhD student we had all sorts of problems communicating with our theory group. They would do all their calculation assuming voltage bias whereas all our experiments were done with current bias, the latter is quite tricky to model if you want to use microscopic theory and not the simple phenomenological model I outlined above.
Moreover, voltage bias and current bias sometimes give qualitatively different results, so the difference is not only practical.

 

[DrDu]

Very interesting. Never heard of Josephson steps. However, I found quite a nice lecture on that topic (in German though):
http://www.pit.physik.uni-tuebingen...hys-V_WS03-04/ExP-V(3)-Kap6-Supraleitung6.pdf