  Skin effect, where macroscopically many bulk states are aggregated towards
the system boundary, is one of the most important and distinguishing phenomena
in non-Hermitian quantum systems. We discuss a new aspect of this effect
whereby, despite its topological origin, applying magnetic field can largely
suppress it. Skin states are pushed back into the bulk and the skin topological
area, which we define, is sharply reduced. As seen from exact solutions of
representative models this is fundamentally rooted in the fact that the applied
magnetic field restores the validity of the low-energy description that is
rendered inapplicable in the presence of non-Bloch skin states. We further
study this phenomenon using rational gauge fluxes, which reveals a unique
irrelevance of the generalized Brillouin zone in the standard non-Bloch band
theory of non-Hermitian systems.
