Physics – Condensed Matter – Superconductivity
Scientific paper
2003-08-11
Physics
Condensed Matter
Superconductivity
17 pages, 5 figures
Scientific paper
We study the non-Abelian topological vortices in condensed matter physics, whose topological flux quantum number is described by $\pi_2(S^2)$, not by $\pi_1(S^1)$. We present two examples, a magnetic vortex in two-gap superconductor and a vorticity vortex in two-component Bose-Einstein condensate. In both cases the condensates exhibit a global SU(2) symmetry which allows the non-Abelian topology. We establish the non-Abelian flux quantization in two-gap superconductor by demonstrating the existence of non-Abelian magnetic vortex whose flux is quantized in the unit $4\pi/g$, not $2\pi/g$. We also discuss a genuine non-Abelian gauge theory of superconductivity which has a local SU(2) gauge symmetry, and establish the non-Abelian Meissner effect in the non-Abelian superconductor. We compare the non-Abelian vortices with the well-known Abelian Abrikosov vortex, and discuss how these non-Abelian vortices could be observed experimentally in two-gap superconductor made of ${\rm MgB_2}$ and spin-1/2 condensate of $^{87}{\rm Rb}$ atoms. Finally, we argue that the existence of the non-Abelian vortices provides a strong evidence for the existence of topological knots in these condensed matters whose topology is fixed by $\pi_3(S^2)$, which one can construct by twisting and connecting the periodic ends of the non-Abelian vortices.
Cho Young-Min
Khim Hyojoong
Yong Namsik
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