Topology of gap nodes in superfluid /sup 3/He:. pi. /sub 4/ homotopy group for /sup 3/He-B disclination

Journal Article · Thu Sep 01 00:00:00 EDT 1988 · J. Low Temp. Phys.; (United States)

DOI:https://doi.org/10.1007/BF00682148· OSTI ID:5898079

Grinevich, P G; Volovik, G E

The topologically stable zeros in the energy spectrum of Fermi excitations in superfluid /sup 3/He both in uniform phases and in textures are classified. This generalizes the classification of the defects of the order parameter in real coordinate space to the classification of zeros in the gap, which are the more general defects in coherent superfluid or superconducting states both in real space and momentum k space. The zeros are described by classes of mappings of the spherical surfaces S/sup n/, embracing the (6-n-1) dimensional manifold of zeros in six-dimensional (k, r) space, into the space of the Bogolyubov-Nambu matrices, which describe the Fermi excitations. The examples of topologically nontrivial manifolds of zeros are discussed, including the closed line of zeros in five-dimensional space, which is described by the ..pi../sub 4/ homotopy groups and exists in the core of the /sup 3/He-B disclination. This object demonstrates the coupling between the real space topology of disclination and the extended space topology of zeros in the disclination core.

• Research Organization: L.D. Landau Institute for Theoretical Physics, Moscow (USSR)
• OSTI ID: 5898079
• Journal Information: J. Low Temp. Phys.; (United States), Vol. 72:5-6
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ENERGY GAP
TOPOLOGY
HELIUM 3
ENERGY SPECTRA
EXCITATION
FERMI LEVEL
GROUP THEORY
HAMILTONIANS
HELIUM 3 A
HELIUM 3 B
MATHEMATICAL MANIFOLDS
MATHEMATICAL SPACE
ORDER PARAMETERS
PAULI SPIN OPERATORS
QUASI PARTICLES
SPIN
SUPERCONDUCTIVITY
SUPERFLUIDITY
TEXTURE
TOPOLOGICAL MAPPING
ANGULAR MOMENTUM
ANGULAR MOMENTUM OPERATORS
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
EVEN-ODD NUCLEI
HELIUM ISOTOPES
ISOTOPES
LIGHT NUCLEI
MAPPING
MATHEMATICAL OPERATORS
MATHEMATICS
NUCLEI
PARTICLE PROPERTIES
PHYSICAL PROPERTIES
QUANTUM OPERATORS
SPACE
SPECTRA
STABLE ISOTOPES
TRANSFORMATIONS
640450* - Fluid Physics- Superfluidity
656100 - Condensed Matter Physics- Superconductivity