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A new discovery: 1D topological order beyond FQH states 精选

已有 12110 次阅读 2014-10-4 20:46 |个人分类:科普|系统分类:观点评述

http://www.scientificamerican.com/article/majorana-particle-matter-and-antimatter/ 




This is an exciting discovery. However, I must point out that the new discovery here is not a new “Majorana particle”, but the two-fold topological ground state degeneracy (see http://en.wikipedia.org/wiki/Topological_degeneracy ), which implies that the 1D wire forms a new state of quantum matter -- a topologically ordered state. In fact, the topological degeneracy is a defining property of topological order. It can appear if we put a topologically ordered state on a space with non-trivial topology (such as a torus) and/or a space with boundary (such as a two dimensional disk with holes, or one dimensional lines with ends). The current experiemnt realizes the situation of one dimensional lines with ends.


In one dimension, only fermion systems can have topological order and there is only one type of non-trivial topological order (which should be the one discovered in this experiment). In two dimensions and higher, there are infinite different types of topological order.


The two-fold topological ground state degeneracy is also referred as Majorana zero mode. As pointed out in the Wiki article http://en.wikipedia.org/wiki/Majorana_fermion "In superconducting materials, Majorana fermions can emerge as (non-fundamental) quasiparticles. This becomes possible because a quasiparticle in a superconductor is its own antiparticle". The quasiparticles in a usual BSC superconductor are already  Majorana fermions, which are more commonly referred as Bogoliubov quasiparticle in condensed matter. So Majorana fermions  were discovered long time ago in superconductors (not by this work). What was discovered by this experiment is not Majorana fermion but topological degeneracy. It is sad that such a misrepresentation is still quite wide spread.

 





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