For fermions on an Abrikosov-Nielsen-Olesen vortex, the vacuum fermion number equals [sgn(m+e sqrt(2) v)+sgn(m-e sqrt(2) v)] n/4, and disk edge states carry charge e/2.
Soliton Fermionic number from the heat kernel expansion
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abstract
We consider different methods of calculating the (fractional) fermion number of solitons based on the heat kernel expansion. We derive a formula for the localized eta function a more systematic version of the derivative expansion for spectral assymmetry and that provides a more systematic version of the derivative expansion for spectral asymmetry and compute the fermion number in a multiflavour extension of the Goldstone-Wilczek model.We also propose an improved expansionof the heat kernelthat allows the tackling ofthe convergence issues and permits an automated computation of the coefficients
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Vortex Fractional Fermion Number through Heat Kernel methods and Edge States
For fermions on an Abrikosov-Nielsen-Olesen vortex, the vacuum fermion number equals [sgn(m+e sqrt(2) v)+sgn(m-e sqrt(2) v)] n/4, and disk edge states carry charge e/2.