advanced_notions:superconductivity
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | Next revision Both sides next revision | ||
|
advanced_notions:superconductivity [2017/10/10 09:23] jakobadmin [Why is it interesting?] |
advanced_notions:superconductivity [2017/10/10 10:16] jakobadmin [Researcher] |
||
|---|---|---|---|
| Line 41: | Line 41: | ||
| </note> | </note> | ||
| - | --> Common Question 1# | + | --> What about symmetry breaking in a superconductor?# |
| + | <blockquote>In fact, a gauge symmetry cannot spontaneously break down as a matter of principle, since it is not a physical symmetry of the system to begin with, but merely an invariance of description [8]. The only way to violate a gauge symmetry is by choosing a gauge, which again has only an effect on our description, but not on the physical system it- self. | ||
| + | |||
| + | We may conclude at this point that in a superfluid or superconductor, a symmetry is spontaneously violated, but this symmetry is not gauge invariance, but global U (1) phase rotation symmetry. This is already evident from the fact that the discussion above made no reference to whether the order parameter field W^yðxÞ is charged or not, and equally well applies to neutral superfluids, where W^yðxÞ carries no charge. | ||
| + | |||
| + | There is, however, a very important difference between these two cases. If the or- der parameter field is neutral, the excitation spectrum of the system contains a gap- less (or in the language of particle physics ‘‘massless’’) mode, a so-called Goldstone boson [1], which physically corresponds to very slow spatial variations in the direction (as for the case of broken rotational invariance) or phase (as for the case of a superfluid) of the classical order parameter field. If the order parameter field is charged, however, it couples to the electromagnetic gauge field, and the Goldstone boson is absent due to the Higgs mechanism. The physical principle underlying this mechanism was discovered by Anderson [13] in the context of superconductivity: as the electromagnetic interaction is long-ranged, the mode corresponding to very slow spatial variations in the phase / of the superconducting order parameter, which implies currents by the equation of motion and hence also variations in the density of the superfluid by the continuity equation, acquires a gap (or ‘‘mass’’) given by the plasma frequency. | ||
| + | |||
| + | <cite>[[https://arxiv.org/abs/cond-mat/0503400|Is electromagnetic gauge invariance spontaneously violated in superconductors?]] Martin Greiter</cite></blockquote> | ||
| <-- | <-- | ||
advanced_notions/superconductivity.txt · Last modified: 2017/11/03 09:27 by jakobadmin
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
