  The Su-Schrieffer-Heeger (SSH) system is a popular model for exploring
topological insulators and topological phases in one dimension. Recent interest
in exceptional points has led to re-examination of non-Hermitian
generalizations of many physical models, including the SSH model. In such
non-Hermitian systems, singular points called exceptional points (EPs) appear
that are of interest for applications in super-resolution sensing systems and
topological lasers. Here, a non-Hermitian and non-PT-symmetric variation of the
SSH model is introduced, in which the hopping amplitudes are non-reciprocal and
vary monotonically along the chain. It is found that, while the existence of
the EPs is due to the nonreciprocal couplings, the number, position, and order
of the EPs can all be altered by the addition of the hopping amplitude
gradient, adding a new tool for tailoring the spectrum of a non-Hermitian
system.
