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> Nanotech forum > Nanotech > CHRITCAL DIAMETR OF SUPERCONDUCTING NANOWIRES
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CHRITCAL DIAMETR OF SUPERCONDUCTING NANOWIRES |
TzuChiehWei
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Tue Apr 3 22:52:35 2007
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
Sorry, I missed the factor gamma in x_m_cr,
corrected here:
x_m_cr = Ef/ J^2 /(S(S+1))/4/gamma * (kB Tc0).
Tzu-Chieh |
| Created: Tue Apr 3 23:25:48 2007
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Alexey
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Mon Apr 2 04:58:18 2007
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
Tzu-Chieh, thanks for clarifications!!
So do you approve our formula: tau_b_cr=exp(0.577)/pi/pi/kB/T_c0
or not really?
(An here we understand that tau_b is the same tau_b as in our PRL about local moments. Also this tau_b_cr here is the critical value of taub at which the Tc goes to zero.)
One more simple question: in your expression x_m_cr = Ef/ J^2 /(S(S+1))/4 * (kB Tc0) should we understand that x_m_cr~Tc0 or x_m_cr~1/(Tc0)?
Thanks!
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| Created: Wed Apr 4 00:45:36 2007
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Alexey
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Mon Apr 2 04:58:18 2007
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
I guess I can use Tzu-Chieh result and get tau_b and compare to our previous result:
Our old result:
tau_b=hbar*exp(0.577)/pi/pi/kB/T_c0
Tzu-Chieh result:
x_m_cr = Ef/ J^2 /(S(S+1))/4/gamma * (kB Tc0)
and
hbar/tau_b = x_m 2pi J^2/Ef
So tau_b_cr=hbar/xm/2pi/J^2*Ef
=hbar*Ef/J^2/2pi/Ef*J^2*S(S+1)*4*gamma/kB/Tc0=
=hbar/2pi*S(S+1)*4*gamma/kB/Tc0=
4*exp(0.5772)*S(S+1)*hbar/2pi/kb/Tc0=
(hbar*exp(0.577)/pi/pi/kB/T_c0)*(pi*4*S(S+1)/2).
Assuming S=1/2 we get
tau_b_cr_new=tau_b_cr_old*(pi*4*S(S+1)/2)
Or
tau_b_cr_new=(3pi/2)*tau_b_cr_old=
0.32*tau_b_cr_old
Can we all agree that this result is correct.
In other words, that:
!!!!!!!!!!!!!!!!!!
tau_b=3*hbar*exp(0.5772)/2/pi/kB/T_c0
!!!!!!!!!!!!!!!!!!
(assuming that tau_b here is the critical value at which superconductivity disappears)
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| Created: Wed Apr 4 01:12:52 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 |
Yes, I agree that using the x_m,cr from Tzu-Chieh and S = 1/2 we get
tau_b,cr = [3 * hbar * exp(0.577)] / [2 * pi * k_B * T_c0]
My thanks also to Tzu-Chieh for the explanation. |
| Created: Wed Apr 4 18:29:28 2007
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Alexey
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Mon Apr 2 04:58:18 2007
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
OK, let us assume that this is the right formula:
tau_b,cr = [3 * hbar * exp(0.577)] / [2 * pi * k_B * T_c0]
Now we need to choose Tc0. We can get it from our PRL on magnetic moments.
It is close to Tc0=5K.
If that is true then we get:
tau_b,cr=1.2ps.
From the graph in the PRL paper we then get the critical diamter:
d_cr=4nm
This is pretty close to the diagram value, right?
Let us check this one more time and we can finish this discussion. |
| Created: Wed Apr 4 22:51:33 2007
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Alexey
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Mon Apr 2 04:58:18 2007
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
One more question, perhaps somebody can figure it out.
Why do we end up with different expressions:
1. tau_b,cr = [3 * hbar * exp(0.577)] / [2 * pi * k_B * T_c0]
2. tau_b=[hbar*exp(0.577)]/[pi*pi*k_B*T_c0]
Can we identify where was the difference in the derivation?
Can we be completely sure that expression #1 is the right one? |
| Created: Thu Apr 5 02:38:55 2007
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Alexey
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Mon Apr 2 04:58:18 2007
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
2alpha=delta
delata=(pi/gamma)Tc*kB
gamma=exp(0.577) |
| Created: Thu Apr 12 23:14:11 2007
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Alexey
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Mon Apr 2 04:58:18 2007
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RE: CHRITCAL DIAMTER OF SUPERCONDUCTING NANOWIRES |
| T.C uses: alpha=S(S+1)*xm*2pi*J^2/Ef |
| Created: Thu Apr 12 23:17:17 2007
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Alexey
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Mon Apr 2 04:58:18 2007
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RE: CHRITCAL DIAMETR OF SUPERCONDUCTING NANOWIRES |
final derivation:
alpha=(3pi/2)(x_m*J^2/Ef);
2alpha=(pi/gamma)kb*Tc;
tau_b=hbar*Ef/2pi/J^2/x_m;
From this one gets:
tau_b=3*gamma*hbar/2pi/kb/Tc_0;
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| Created: Thu Apr 12 23:33:00 2007
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Physya The Cat
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Wed Apr 18 04:02:53 2007
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RE: CHRITCAL DIAMETR OF SUPERCONDUCTING NANOWIRES |
| so, what will be number for, say Pb or Al wire (in Angstrom)? |
| Created: Wed Apr 18 04:09:30 2007
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Alexey
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Mon Apr 2 04:58:18 2007
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RE: CHRITCAL DIAMETR OF SUPERCONDUCTING NANOWIRES |
| I guess we can not say much about Pb or Al till the concentration of magnetic moments on their surface is not known. This concentration might also depend on the surface conditions. So the question is not simple. We could make a prediction for MoGe since the corresponding concentration was determined for this material in the work on critical current enhancement by Rogachev et al. (http://www.nanogallery.info/nanogallery/?ipg=129) |
| Created: Wed Apr 18 04:35:52 2007
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Physya The Cat
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Wed Apr 18 04:02:53 2007
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RE: CHRITCAL DIAMETR OF SUPERCONDUCTING NANOWIRES |
| so, what is it for MoGe? |
| Created: Wed Apr 18 06:30:57 2007
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