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

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arxiv 2103.06826 v1 pith:D7P3KZ4C submitted 2021-03-11 hep-th cond-mat.mes-hall

Caio Almeida , Alberto Alonso-Izquierdo , Rodrigo Fresneda , Juan Mateos Guilarte , Dmitri Vassilevich This is my paper · ORCID
classification hep-thcond-mat.mes-hall
keywords fermionjackiw-rossimodelcurrentnumbertopologicalweightapplicable
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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.

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  1. Vortex Fractional Fermion Number through Heat Kernel methods and Edge States

    hep-th 2025-05 conditional novelty 6.0 of 10

    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.

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