|
> Nanotech forum > Nanotech > Size of phase slips in superconducting nanowires
|
|
| Pages: 1 2 |
Size of phase slips in superconducting nanowires |
Alexey
Join Date:
Mon Apr 2 04:58:18 2007
Posts:78
Reputation:11
 |
Size of phase slips in superconducting nanowires |
| Thermally activated phase slips in nanowires have a size of about 2.2*ksi(T). This is calculated from the minimization of the free energy. What about quantum phase slips, which occur at T=0? Should their size be estimated from the minimization of action? Can they have a size much different that 2ksi(T=0)? |
| Created: Mon Apr 2 18:36:34 2007
|
|
Physya The Cat
Join Date:
Wed Apr 18 04:02:53 2007
Posts:19
Reputation:11
|
RE: Size of phase slips in superconducting nanowires |
you mean much longer...? - quaite possible
However, I don't think there is a good way to describe quantum fluctuations in thermodynamic sense, because there is no feel for the timescale. |
| Created: Wed Apr 18 04:14:03 2007
|
|
Alexey
Join Date:
Mon Apr 2 04:58:18 2007
Posts:78
Reputation:11
|
RE: Size of phase slips in superconducting nanowires |
| Fizja, your suggestion is interesting. But I think there is time scale. It is given by hbar/delta probably. So the action can be defined quite well. The size of the core is an important things since it tells what part of the wire gets normal. It seems, from what I learned from Sergei' Khlebnikov, that the core might be much longer that the coherence length. In fact it could be as big as ~100 nm. |
| Created: Wed Apr 18 04:39:21 2007
|
|
Physya The Cat
Join Date:
Wed Apr 18 04:02:53 2007
Posts:19
Reputation:11
|
RE: Size of phase slips in superconducting nanowires |
Well, the fact that you can get something that has dimensionality of time does not mean it correspond to a physical phenomena. Think about quantum phase transitions where time literally stands still.
Another timescale will be associated with the phonon frequencies participating in formation of the Cooper pairs... |
| Created: Wed Apr 18 06:28:01 2007
|
|
Alexey
Join Date:
Mon Apr 2 04:58:18 2007
Posts:78
Reputation:11
|
RE: Size of phase slips in superconducting nanowires |
yes, right, in a quantum transition the time scale diverges, because the energy difference between two phase goes to zero, right?
But what is your point? do you doubt that Action can be computed for a quantum phase slip?
|
| Created: Thu Apr 19 01:20:32 2007
|
|
Physya The Cat
Join Date:
Wed Apr 18 04:02:53 2007
Posts:19
Reputation:11
|
RE: Size of phase slips in superconducting nanowires |
The energy difference for two phases is zero for ANY phase transition at the transition point.
And yes, one can compute action (something like S/hbar~(kF*xi)^2, but I am not sure how will you estimate size. With all possible timescales, you can also have different lengthscales (of the same energy). |
| Created: Thu Apr 19 16:19:01 2007
|
|
Alexey
Join Date:
Mon Apr 2 04:58:18 2007
Posts:78
Reputation:11
|
RE: Size of phase slips in superconducting nanowires |
Cat,
I agree with all these statemtns-all continuous quantum transitions have their time scale diverge at the critical point. This happenns beacsue the energy differnece between two phases is zero at this point. All these pacts can be understood from the fact that tau=hbar/deltaE.
In the case of a quantum phase slip (QPS) the system makes a quantum transition from a state without QPS (E=0 in this sate) to a state with a normal core (QPS core). This second state has energy deltaF=A*L*Hc^2/8Pi. So I guees the time scale should be tau=hbar/deltaF, right? Since the energy conservation is violated here. The energy is increased during the phase slip be the amout deltaF. This violation can not last forever. It can only last for a time hbar/deltaF. Right?? |
| Created: Sun Apr 22 01:59:36 2007
|
|
Physya The Cat
Join Date:
Wed Apr 18 04:02:53 2007
Posts:19
Reputation:11
|
RE: Size of phase slips in superconducting nanowires |
Why do you think energy is conserved? What about Big Bang, which is ever lasting quantum fluctuation?
On a serious note, delataF can be very small if you allow for a phase slip which is not fully normal, but has just supressed oreder parameter. So, the time cam be very large and the size will be very long... |
| Created: Sun Apr 22 06:24:48 2007
|
|
Alexey
Join Date:
Mon Apr 2 04:58:18 2007
Posts:78
Reputation:11
|
RE: Size of phase slips in superconducting nanowires |
Why do you think in Big Bang the energy was not conserved?
(in any case, this subject might need a new thread)
deltaF can be small but not smaller than A*ksi(T)*Hc^2/8Pi.
This is the main idea of Little-to have dissipation the phase should slip and for this you must suppress the order parameter to zero. Read this paper please:
William A. Little
"Decay of persistent currents in small superconductors"
Phys.Rev. vol.156, p.396 (1967)/
So the time can not be very large in fact!!! |
| Created: Tue Apr 24 06:16:31 2007
|
|
Physya The Cat
Join Date:
Wed Apr 18 04:02:53 2007
Posts:19
Reputation:11
|
RE: Size of phase slips in superconducting nanowires |
| of course it should go to zero in ONE POINT (like in a vortex). What I mean is that in nanowire it may well be that instead of bulk xi you should use wire diameter or whatever else with similar "confined geometry" renormalization of xi. Then energy can be very small. |
| Created: Thu Apr 26 06:56:10 2007
|
|
Alexey
Join Date:
Mon Apr 2 04:58:18 2007
Posts:78
Reputation:11
|
RE: Size of phase slips in superconducting nanowires |
| Yes, so the energy of the phase slip is always delta=A*ksi*Hc^2/8Pi. Here A is the cross-section area of the wire, ksi is the coherence length or the size of the phase slip core in the direction along the wire (i.e. the length of the phase slip), and Hc^2/8Pi is the condensation energy. This energy, deltaF, can be larger or smaller than kB*T. Depending on this the wire either has a high resistance (comparable to normal resistance Rn) or an exponentially low resistance. |
| Created: Sat Apr 28 00:15:10 2007
|
|
Physya The Cat
Join Date:
Wed Apr 18 04:02:53 2007
Posts:19
Reputation:11
|
RE: Size of phase slips in superconducting nanowires |
so, you contradic your original question by postulating that the length of a phase sliip is xi.
Also, I am not sure that Hc^2/8Pi is correct energy scale in this situation. Hc is bulk property and thermodynamics on nanoscale must include the surface and dipolar (stray) fields. |
| Created: Sat Apr 28 07:05:06 2007
|
|
| Pages: 1 2 |
