Dirac fermions in non-Hermitian magnetic fields: Zero modes and index theorem (opens in new tab)

In a Lorentz symmetric non-Hermitian (NH) Dirac theory, containing the canonical relativistic Hamiltonian accompanied by a masslike anti-Hermitian Dirac operator, when the associated NH parameter becomes spatially modulated it couples massless Dirac fermions as NH gauge fields. With specific choices of such resulting NH gauge potential, the system experiences NH magnetic fields. When a planar Dirac system encloses a finite flux of such NH magnet...