  It has recently been shown that signatures of non-Hermitian topology can be
realized in a conventional quantum Hall device connected to multiple current
sources. These signatures manifest as robust current-voltage characteristics,
dictated by the presence of a nontrivial, non-Hermitian topological invariant
of the conductance matrix. Chiral edge states are believed to be responsible
for this non-Hermitian response, similar to how they lead to a quantized Hall
conductivity in the presence of a single current source. Here, we go beyond
this paradigm, showing that multi-terminal conductance matrices can exhibit
non-Hermitian topological phase transitions that cannot be traced back to the
presence and directionality of a boundary-localized chiral mode. By performing
quantum transport simulations in the quantum Hall regime of monolayer graphene,
we find that when the chemical potential is swept across the zeroth Landau
level, unavoidable device imperfections cause the appearance of an additional
non-Hermitian phase of the conductance matrix. This highlights graphene as an
ideal platform for the study of non-Hermitian topological phase transitions,
and is a first step towards exploring how the geometry of quantum devices can
be harnessed to produce robust, topologically-protected transport
characteristics.
