Open AccessFermion zero-energy modes and fractional fermion numbers in a fractional vortex-fermion model
Author(s) -
Takashi Yanagisawa
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1590/1/012009
Subject(s) - fermion , physics , dirac fermion , fermion doubling , zero mode , helical dirac fermion , vortex , magnetic flux quantum , topological insulator , composite fermion , dirac equation , zero point energy , quantum hall effect , quantum mechanics , dirac sea , magnetic flux , magnetic field , quantum spin hall effect , thermodynamics
Topological materials have attracted much attention from both physicists and mathematicians recently. Topological properties are closely related to the fermion number (index) of Dirac fermions. The fermion number is given by the η invariant introduced by Atiyah, Padoti and Singer. We discuss a system of Dirac fermions interacting with a vortex and a kink. This system will be realized as a layered material of superconductors and topological insulators, where the Dirac fermion exists on the surface of the topological insulator. The fermion number is fractionalized and the fermion zero-energy excitation mode emerges when Dirac fermions interact with vortices and kinks. Our discussion includes the case where there is a half-flux quantum vortex associated with a kink in a magnetic field in a bilayer superconductor. A normalizable single-valued fermion zero-energy mode does not exist in the core of the half-flux quantum vortex.