Timeline for How to generalize BdG equation in order to match a graphene with a metal superconductor?
Current License: CC BY-SA 3.0
11 events
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| Dec 26, 2014 at 13:15 | history | tweeted | twitter.com/#!/StackPhysics/status/548467018966790144 | ||
| Nov 4, 2014 at 6:12 | comment | added | M Salehi | Finally I think we can find my answer in the above mentioned papers. | |
| Nov 4, 2014 at 6:11 | comment | added | M Salehi | About the difference between my case and Beenakker case: Beenakker used a sheet of graphene and divided it into two parts( one part a normal graphene region and another part is superconductor graphene region), but my concern is about the normal graphene region and a superconductor metal region. | |
| Nov 4, 2014 at 6:08 | comment | added | M Salehi | So thanks @FraSchelle for those interesting papers. I am going to read these. | |
| Nov 3, 2014 at 22:03 | comment | added | FraSchelle | Finally, I note that this question is the same as a previous one of yours: physics.stackexchange.com/q/144517/16689 which has been already perfectly answered by @danu ! | |
| Nov 3, 2014 at 22:00 | comment | added | FraSchelle | Well, reading again your question, I realised that what you did (or want to do) is wrong, Beenakker is right. You should replace "conducted" by "contacted" in your question I guess. When a superconductor (S) is "contacted" to graphene (G), S becomes chiral in a thin layer at the interface which is the only one which matters, and G becomes particle-hole symmetric all over. (say differently, G is particle-hole redundant, whereas S is valley redundant, so everything is fine: make a global theory, with spin it's $8\times 8$ matrix) | |
| Nov 3, 2014 at 21:49 | comment | added | FraSchelle | For two interesting papers on the relativistic version of BdG equation, see dx.doi.org/10.1103/PhysRevB.59.7140 and dx.doi.org/10.1103/PhysRevB.59.7155 by Capelle & Gross, PRB (1999). | |
| Nov 3, 2014 at 21:46 | comment | added | FraSchelle | The problem is well discussed by Beenakker in his paper : you inject the one-body Hamiltonian $H$ (eq.4 on the arXiv version, it's a $4\times 4$ matrix) in the BdG $2\times 2$-matrix (eq.1 of the arXiv version) such that you have a $8\times 8$ eigenvalues problem to resolve. Nevertheless, the valley can be switched by applying the time-reversal operator, so you need only $4$-components to resolve the problem. Since the differential equation is of first-order, you need only to match the wave-functions, not the derivative. | |
| Nov 3, 2014 at 21:42 | history | edited | FraSchelle | CC BY-SA 3.0 |
please always prefer to cite the arXiv version when available
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| Nov 3, 2014 at 12:45 | history | edited | Mostafa |
edited tags
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| Nov 3, 2014 at 9:34 | history | asked | M Salehi | CC BY-SA 3.0 |