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> Nanotech forum > Nanotech > CHRITCAL DIAMETR OF SUPERCONDUCTING NANOWIRES
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CHRITCAL DIAMETR OF SUPERCONDUCTING NANOWIRES |
Alexey
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Mon Apr 2 04:58:18 2007
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HOW TO GET ALPHA |
What if we try to use Tinkham eq.10.22f??
This reads:
alpha=x_m*J^2/Ef, where x_m is the fractional impurity concentration. |
| Created: Mon Apr 2 06:09:39 2007
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Tony Bollinger
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Mon Apr 2 05:22:16 2007
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
x_m J^2 / E_f ~ hbar / tau_K (de Gennes p. 264)
Also, in magnetic field effect on I_c PRl there is some tau_B (same as tau_K I beleive) vs. diameter data with a fit.
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| Created: Mon Apr 2 06:15:45 2007
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Alexey
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HOW TO GET ALPHA |
and in our paper ROGACHEV ET AL. RHYS.REV.LETT. V.97 P.137001 (2006)
we have this forumal:
tau_b=Ef/2/pi/J^2/x_m
And we also have an empirical graph which clinks tau_b with the diameter of the wire. So assuming that J^2 is the same in both paper we can say:
1/tau_b=2*pi*J^2*x_m/Ef=2*pi*alpha.
Thus:
1/2/pi/tau_b=pi*kB*T_c0/2/exp(0.577)
and
1/tau_b=2*pi*pi*kB*T_c0/2/exp(0.577)
so finally:
tau_b=exp(0.577)/pi/pi/kB/T_c0
Something is missing here...
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| Created: Mon Apr 2 06:21:43 2007
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Tony Bollinger
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
To estimate critical diameter we can use the average T_c0 of 5 K from our magnetic field effect on I_c PRL. Then alpha_c = 6.1e-23 J. This means tau_B,c ~ hbar / alpha_c ~ 1.7 ps, which corresponds to about 5 nm diameter on our magnetic field effect on I_c PRL Fig. 3.
But maybe there is a better way to get the critical diameter. |
| Created: Mon Apr 2 06:22:07 2007
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Alexey
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
| I guess Planck's constant is missing as ususal... |
| Created: Mon Apr 2 06:24:29 2007
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Alexey
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
| but what about my formula above? Is it correct? |
| Created: Mon Apr 2 06:25:14 2007
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Alexey
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
I think this formula tau_b=Ef/2/pi/J^2/x_m needs a fix. Perhaps it should be:
tau_b=h_bar*Ef/2/pi/J^2/x_m
? |
| Created: Mon Apr 2 06:26:51 2007
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Alexey
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
| I will ask Tzu-Chieh |
| Created: Mon Apr 2 06:27:55 2007
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Tony Bollinger
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
It looks right to me, except for the missing hbar you mention.
I get tau_B = [e^(0.577) hbar] / [pi^2 k_B T_c0], same as you. |
| Created: Mon Apr 2 06:28:36 2007
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Tony Bollinger
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
| Yes, Ef has units energy, J has units energy, and x_m is dimensionless. So Ef / [2 pi J^2 x_m] has units 1/energy. Multiply by hbar and you get units of time. |
| Created: Mon Apr 2 06:30:11 2007
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Alexey
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
Ok so you think this formula is right:
tau_b=hbar*exp(0.577)/pi/pi/kB/T_c0
So for Tc=1K we get:
taub=1.3ps.
From our graph we then get:
d_c= 4nm.
This seems close to what the diagram suggests, right? |
| Created: Mon Apr 2 06:37:17 2007
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Alexey
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
but somehow you got a different answer...
did you use a different formula? |
| Created: Mon Apr 2 06:38:38 2007
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