Spin-momentum locking and fractionally charged topological quasi-particles

Fermions carrying spin and momentum in a layer are studied in presence of an external magnetic field under the three-term decomposition of the kinetic energy [1,2]. This decomposition offers a venue to introduce the spin-momentum locking condition into the Hamiltonian, which is the sum of the kinetic plus the magnetic field energies. The residual local magnetic field produced by the motion of the particles is shown to have streamlines that pierce the layer twice giving stability to the states thus giving rise to topologically stable quasi-particles. The direct inspection of this residual local magnetic field, and also the calculation of the Chern-Simons index show that these quasi-particles carry fractional magnetic flux and charge. These results are obtained in the context of recently developed new sets of doubly periodic orthonormal eigenfunctions for the Schroedinger problem of free particles in presence of an external applied magnetic field.
[1] Mauro M. Doria and Andrea Perali, Europhys. Lett. 119 (2017) 21001
[2] M. M. Doria, The European Physical Journal B 92, 64 (2019)