Zero modes of the generalized fermion-vortex system in a magnetic field

2014/03/31 by Chi-Ken Lu, Babak Seradjeh
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevb.89.245448

published as Phys. Rev. B 89, 245448 (2014) · 4 pages, 1 fig and 4+ pages, 3 figs (supplemental)

arxiv created 2014/03/31 · openalex publication_date 2014/06/30 · arxiv updated 2014/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that Dirac fermions moving in two spatial dimensions with a generalized dispersion E\ensuremath∼p^N, subject to an external magnetic field and coupled to a complex scalar field carrying a vortex defect with winding number Q acquire N|Q| zero modes. This is the same as in the absence of the magnetic field. Our proof is based on selection rules in the Landau level basis that dictate the existence and the number of the zero modes. We show that the result is insensitive to the choice of geometry and is naturally extended to general field profiles, where we also derive a generalization of the Aharonov-Casher theorem. Experimental consequences of our results are briefly discussed.

Citations

• Vortices, Zero Modes, and Fractionalization in the Bilayer-Graphene Exciton Condensate
• Zero-Energy States and Fragmentation of Spin in the Easy-Plane Antiferromagnet on a Honeycomb Lattice
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