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

Journal Article · Sat Oct 01 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.84.076002· OSTI ID:21607830

Fujiwara, Takanori; Fukui, Takahiro ^[1]; Nitta, Muneto ^[2]; Yasui, Shigehiro ^[3]

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1. Department of Physics, Ibaraki University, Mito 310-8512 (Japan)
2. Department of Physics, and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521 (Japan)
3. KEK Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki, 305-0801 (Japan)

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.

• OSTI ID: 21607830
• Journal Information: Physical Review. D, Particles Fields, Vol. 84, Issue 7; Other Information: DOI: 10.1103/PhysRevD.84.076002; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOGOLYUBOV METHOD
CHIRALITY
COLOR MODEL
COMPUTERIZED SIMULATION
DENSITY
EQUATIONS
HAMILTONIANS
MAJORANA THEORY
PERTURBATION THEORY
QUANTUM CHROMODYNAMICS
SERIES EXPANSION
SU-2 GROUPS
SUPERCONDUCTIVITY
SUPERCONDUCTORS
SYMMETRY
TOPOLOGY
VORTICES
CALCULATION METHODS
COMPOSITE MODELS
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
FIELD THEORIES
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICS
PARTICLE MODELS
PARTICLE PROPERTIES
PHYSICAL PROPERTIES
QUANTUM FIELD THEORY
QUANTUM OPERATORS
QUARK MODEL
SIMULATION
SU GROUPS
SYMMETRY GROUPS