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CHRITCAL DIAMETR OF SUPERCONDUCTING NANOWIRES |
Alexey
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CHRITCAL DIAMETR OF SUPERCONDUCTING NANOWIRES |
| CHRITCAL DIAMETR OF SUPERCONDUCTING NANOWIRES |
| Created: Mon Apr 2 05:09:46 2007
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Alexey
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THE MAIN FORMULA |
I think the estimate should based on this formula:
alpha_c=pi*T_c0/2/gamma
where ln(gamma)=0.577 is the Euler constant.
From this we can get the critical depairing factor alpha_c at which the superconductivity is suppressed completely.
I got the formula from Lopatin et al Phys.Rev.Lett V.94 p.037003 (2005).
Once thing is not clear: what is gamma here? Is it 0.577 or it is exp(0.577)?
We also need to find the expression for the depairing factor expressed in terms of magnetic moments concentration. |
| Created: Mon Apr 2 05:18:08 2007
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Tony Bollinger
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
I usually see gamma used for Euler's constant with gamma = 0.577. But it appears Lopatin at al use the convention that ln(gamma) is Euler's constant and so ln(gamma) = 0.577. A bit confusing I agree.
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| Created: Mon Apr 2 05:31:30 2007
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Alexey
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
yes, we will have to ask Lopatin. For now I am not sure how to use this formula:
(1) alpha_c=pi*T_c0/2/gamma.
Which gamma to put there?
But I think this is the formula to be used, do you agree?
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| Created: Mon Apr 2 05:36:28 2007
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Tony Bollinger
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
| Yes, I think we should be able to use this formula. It is coming from the same theory Andrey used in our "influence of magnetic field on R(T) curves" PRL, correct? |
| Created: Mon Apr 2 05:43:37 2007
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Alexey
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TINKHAM BOOK FORMULA |
Tinkham book says this:
2*alpha=1.76*kB*Tc
Is this the same alpha_c as in Lopatin or not? |
| Created: Mon Apr 2 05:48:16 2007
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Alexey
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TINKHAM BOOK FORMULA |
this forumala 2*alpha=1.76*kB*Tc is given on page 392.
From the paragraph: "Depression of Tc by Magnetic Perturbations"
There is alsotime constant there:
h_bar/tau_k=2*alpha |
| Created: Mon Apr 2 05:51:17 2007
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Alexey
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
| Yes, you right, this is the same theory as Andrey used in his paper "influence of magnetic field on R(T) curves"... |
| Created: Mon Apr 2 05:52:48 2007
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Tony Bollinger
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
I think so:
1.76 = pi / e^(0.577) (See notes just above Eq. 3.51 in Tinkham through Eq. 3.52 on p.63)
so
alpha = 1.76 k_B T_c / 2 = pi k_B T_c / 2 e^(0.577)
which is the similar to Lopatin |
| Created: Mon Apr 2 05:54:16 2007
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Alexey
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FORMULA WE CAN NOT USE |
BUT WE CAN NOT USE THIS FORUMALA:
kB(T_c0-T_c)=pi*alpha/4, since this is for small suppressions only. |
| Created: Mon Apr 2 05:54:49 2007
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Alexey
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
Ok, so Tinkham book gives this mormula then:
2*alpha_c=1.76*kB*Tc;
alpha_c=1.76*kB*Tc/2=pi*kB*Tc/2/exp(0.577);
and Lopatin is this:
alpha_c=pi*kB*T_c0/2/exp(0.577).
(I assume that kB was set to 1 in Lopatin et al.)
So we get an agreement. The forumal is then this:
alpha_c=pi*kB*T_c0/2/exp(0.577)
Now what is alpha in terms of impurity fraction x_m? |
| Created: Mon Apr 2 06:03:14 2007
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Tony Bollinger
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
| My first guess is that it somehow should be coming from Lopatin Eq. 1, which contains field (coming from impurities we can say) and diameter. |
| Created: Mon Apr 2 06:05:24 2007
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