Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2011-05-11
Phys. Rev. D84:076002, 2011
Physics
High Energy Physics
High Energy Physics - Phenomenology
19 pages
Scientific paper
10.1103/PhysRevD.84.076002
Color superconductivity in high density QCD exhibits the color-flavor locked (CFL) phase. To explore zero modes in the CFL phase in the presence of a non-Abelian vortex with an SU(2) symmetry in the vortex core, we apply the index theorem to the Bogoliubov-de Gennes (BdG) Hamiltonian. From the calculation of the topological index, we find that triplet, doublet and singlet sectors of SU(2) have certain number of chiral Majorana zero modes in the limit of vanishing chemical potential. We also solve the BdG equation by the use of the series expansion to show that the number of zero modes and their chirality match the result of the index theorem. From particle-hole symmetry of the BdG Hamiltonian, we conclude that if and only if the index of a given sector is odd, one zero mode survives generically for a finite chemical potential. We argue that this result should hold nonperturbatively even in the high density limit.
Fujiwara Takanori
Fukui Takahiro
Nitta Muneto
Yasui Shigehiro
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