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advanced_notions:superconductivity [2017/10/08 14:49]
jakobadmin ↷ Links adapted because of a move operation
advanced_notions:superconductivity [2017/11/03 09:27] (current)
jakobadmin [Layman]
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 <tabbox Why is it interesting?> ​ <tabbox Why is it interesting?> ​
 +<​blockquote>​
  
 +A superconductor is simply a material in which electromagnetic gauge invariance is spontaneously broken.
 +
 +<​cite>​Weinberg QFT Vol 1</​cite>​
 +</​blockquote>​
 <tabbox Layman> ​ <tabbox Layman> ​
 +  * For a nice laymen introduction to superconductivity,​ see [[https://​thiscondensedlife.wordpress.com/​2015/​09/​12/​draw-me-a-picture-of-a-cooper-pair/​|Draw me a picture of a Cooper pair]] by Brian Skinner
 +
  
 <​blockquote>​ <​blockquote>​
-First I will explain how superconductivity arises, and then turn to the profound, and as it transpired inspirational,​ importance of [[:​symmetry_breaking|hidden symmetry]] in this case.+First I will explain how superconductivity arises, and then turn to the profound, and as it transpired inspirational,​ importance of [[advanced_notions:​symmetry_breaking|hidden symmetry]] in this case.
  
 An electron moving through a lattice of positively charged ions experiences an electrical attraction, which causes a slight distortion of the lattice.As a bell continues to ring after having been struck, so the lattice’s distortion may persist for a short while after the electron has passed. A second electron coming through finds a distorted lattice, and interacts with it. If the timing, speed, and spinning motions are right, the two interactions with the lattice cause the electrons to attract one another magnetically.They act cooperatively,​ like a single particle where the two spins, or individual magnetism, of the constituent electrons have canceled out. An electron moving through a lattice of positively charged ions experiences an electrical attraction, which causes a slight distortion of the lattice.As a bell continues to ring after having been struck, so the lattice’s distortion may persist for a short while after the electron has passed. A second electron coming through finds a distorted lattice, and interacts with it. If the timing, speed, and spinning motions are right, the two interactions with the lattice cause the electrons to attract one another magnetically.They act cooperatively,​ like a single particle where the two spins, or individual magnetism, of the constituent electrons have canceled out.
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 </​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>​
    
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advanced_notions/superconductivity.1507466950.txt.gz · Last modified: 2017/12/04 08:01 (external edit)