Timeline for Mermin Wagner theorem in superconductors, massive Goldstone mode
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Jun 15, 2017 at 3:50 | history | tweeted | twitter.com/StackPhysics/status/875198921936699396 | ||
| Jun 14, 2017 at 5:41 | comment | added | JWDiddy | Regarding majorana: isn't that special for finite system? Could they really disorder the bulk? | |
| Jun 14, 2017 at 5:35 | comment | added | JWDiddy | I agree that it would be best to be more specific. I will try to work something out. However if feel that the question isn't adressed (explanations aside). a) do superconductors disorder in 2D because of a gapless collective exitation? b) what happens to Higgs-mechanism in 2D, does massless modes vanish? | |
| Jun 14, 2017 at 5:00 | comment | added | FraSchelle | Ah, and finally, there are gapless modes in 2D superconductors, for that you need a non-trivial topological superconductors, and a vortex. The gapless modes are then Majorana fermions, one more fancy concept one should discuss as well in low dimensional superconductors. | |
| Jun 14, 2017 at 4:58 | comment | added | FraSchelle | To answer the rest of the questions, perhaps it is better to start discussing models, e.g. the Abelian Higgs model or Ginzburg-Landau model or classical Galilean complex fields, and to derive results in 3D and 2D to understand the differences. Because otherwise your question relates too many different concepts with fancy names but sometimes obscure relation among themselves. I have no time this week to do that ... | |
| Jun 14, 2017 at 4:53 | comment | added | FraSchelle | The Coulomb interaction is what comes out if you integrate the fermionic modes in Galilean relativistic electromagnetism (if you prefer: when choosing the Coulomb gauge). This is the natural assumption in condensed matter problems. | |
| Jun 13, 2017 at 13:13 | comment | added | JWDiddy | Could it be that there is no massless mode in 2D? Viewing the phase mode as being promoted to the plasma frequency seems to suggest that it remains ungapped since the plasmon is ungapped in 2D (journals.aps.org/prl/pdf/10.1103/PhysRevLett.65.1482) | |
| Jun 13, 2017 at 12:46 | comment | added | JWDiddy | @FraSchelle Yes. I do now about quasi long range order (QLRO) and KTB in 2D systems. But again this is strictly for superfluids and not superconductors right? I also know that the effective screening length in 2D between superconducting vortices (Pearl length) is long and one expect the KTB to be present in small samples. However I do not understand how the derivation to show that there is QLRO for a superfluid holds for a superconductor? There should be no massless mode? Or should it? | |
| Jun 13, 2017 at 12:37 | comment | added | JWDiddy | @FraSchelle Ok but it seems that Anderson used the explicit Coulomb interaction to show that the mode phase mode acquires mass. But maybe this is because he didn't regard the gauge field as a "dynamical field". I mean coulomb is mediated by the gauge field in the field theory context. Do you have any inputs on the main question? Any hints :) | |
| Jun 13, 2017 at 12:30 | comment | added | FraSchelle | 2D systems are more rich than Mermin-Wigner-Hohenberg theorem, see for instance Kosterlitz-Thouless-Berezinskii phase transition : see Wikipedia about Mermin-Wagner theorem (i can not copy-paste the link, sorry) | |
| Jun 13, 2017 at 12:28 | comment | added | FraSchelle | Anderson mechanism is the same as Higgs mechanism: en.wikipedia.org/wiki/Higgs_mechanism second paragraph of the introduction. | |
| Jun 12, 2017 at 14:59 | comment | added | JWDiddy | But the phase has redundancy, so isn't that divergence comming from the fact that we sum over physically equivalent configurations? By "gaugeing" away the residual freedom there is no phase mode left and the real freedom should be included in the gauge invariant, now massive, gauge field. Then I cannot find any infrared divergencies | |
| Jun 12, 2017 at 14:33 | comment | added | Adam | I understand better the question. From what I gather, since the phase always appears with a gradient in the action, the inverse propagator is always proportional to $q^2$ (even though the there is a gap in the spectrum due to the Higgs mechanism). Now, the thermal physics is controlled by the zero frequency part of the propagator, which is still proportional to $1/q^2$. There is thus an infrared divergence in low dimensions, even with the gap. | |
| Jun 12, 2017 at 13:44 | history | asked | JWDiddy | CC BY-SA 3.0 |