Analytical and numerical study of the Dirac equation in an interpolating Skyrme background determines that bound fermion states exist solely for electrically charged fermions with positive charge and negative angular momentum.
Soliton solutions of the fermion-Skyrmion system in (2+1) dimensions
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abstract
We study effects of backreaction of the fermionic modes localized by the baby Skyrmion in the (2+1)-dimensional Skyrme model. It is shown that there is a tower of fermionic modes of two different types, localized by the soliton, however there is only one fermionic level, which flows from positive to negative value as coupling increases. Considering the strong coupling regime we observe that the coupling of the bosonic field to the fermions may strongly deform the Skyrmion, in particular the regions of negative topological charge density appear.
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Revisiting fermion bound states in baby Skyrme background with Dzyaloshinskii Moriya interaction
Analytical and numerical study of the Dirac equation in an interpolating Skyrme background determines that bound fermion states exist solely for electrically charged fermions with positive charge and negative angular momentum.