### Abstract

Color superconductivity in high-density QCD exhibits the color-flavor-locked phase. To explore zero modes in the color-flavor-locked 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.

Original language | English |
---|---|

Article number | 076002 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 84 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2011 Oct 6 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*84*(7), [076002]. https://doi.org/10.1103/PhysRevD.84.076002

**Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor.** / Fujiwara, Takanori; Fukui, Takahiro; Nitta, Muneto; Yasui, Shigehiro.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 84, no. 7, 076002. https://doi.org/10.1103/PhysRevD.84.076002

}

TY - JOUR

T1 - Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor

AU - Fujiwara, Takanori

AU - Fukui, Takahiro

AU - Nitta, Muneto

AU - Yasui, Shigehiro

PY - 2011/10/6

Y1 - 2011/10/6

N2 - Color superconductivity in high-density QCD exhibits the color-flavor-locked phase. To explore zero modes in the color-flavor-locked 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.

AB - Color superconductivity in high-density QCD exhibits the color-flavor-locked phase. To explore zero modes in the color-flavor-locked 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.

UR - http://www.scopus.com/inward/record.url?scp=80555146004&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevD.84.076002

DO - 10.1103/PhysRevD.84.076002

M3 - Article

AN - SCOPUS:80555146004

VL - 84

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 7

M1 - 076002

ER -