Non-topological fractional fermion number in the Jackiw-Rossi model

Abstract

We compute the vacuum fermion current in $(2+1)$ dimensional Jackiw-Rossi model by using the $1/m$ expansion. The current is expressed through a weighted $\eta$-function with a matrix weight. In the presence of such a weight, the usual proof of topological nature of $\eta (0)$ is not longer applicable. Direct computations confirm the following surprising result: the fermion number induced by vortices in the Jackiw-Rossi model is \textit{not} topological.

arXiv comment8 pages, revtex

References in corpus (20)

• Topological insulators and superconductors
• Heat kernel expansion: user's manual
• Electron fractionalization in two-dimensional graphenelike structures
• Chiral Gauge Theory for Graphene
• Electron fractionalization for two-dimensional Dirac fermions
• The Higher Derivative Expansion of the Effective Action by the String Inspired Method. Part II
• Irrational vs. rational charge and statistics in two-dimensional quantum systems
• Nonvanishing quantum corrections to the mass and central charge of the N=2 vortex and BPS saturation
• Quantum corrections to the mass of the supersymmetric vortex
• Self-Adjointness of the Dirac Hamiltonian and Fermion Number Fractionization in the Background of a Singular Magnetic Vortex
• Covariant techniques for computation of the heat kernel
• Fermionic Vacuum Energy from a Nielsen-Olesen Vortex
• Quantum QED Flux Tubes in 2+1 and 3+1 Dimensions
• Quantum oscillations of self-dual Abrikosov-Nielsen-Olesen vortices
• Fermions in the presence of topological structures under geometric constrictions
• Fractional Fermion Number and Hall Conductivity of Domain Walls
• Quantum magnetic flux lines, BPS vortex zero modes, and one-loop string tension shifts
• Extended Chiral Transformations Including Diquark Fields as Parameters
• Zero-energy modes, fractional fermion numbers and the index theorem in a vortex-Dirac fermion system
• Hall Effect for Dirac Electrons in Graphene Exposed to an Abrikosov Flux Lattice

Cited by in corpus (3)

• Special Functions for Heat Kernel Expansion
• Edge states and the $\eta$ invariant
• Vortex Fractional Fermion Number through Heat Kernel methods and Edge States