  We systematically investigate the finite-size effects in non-Hermitian
one-dimensional (1D) Su-Schrieffer-Heeger (SSH) and two-dimensional (2D) Chern
insulator models. Using a combination of analytical and numerical calculations,
we show that the non-Hermitian intra-cell hoppings in the SSH model can modify
the localization lengths of bulk and end states, giving rise to a complex
finite-size energy gap that exhibits an oscillating exponential decay as the
chain length grows. However, the imaginary staggered on-site potentials in the
SSH model only change the end-state energy, leaving the localization lengths of
the system unchanged. In this case, the finite-size energy gap can undergo a
transition from real values to imaginary values. We observed similar phenomena
for the finite-size effect in 2D Chern insulator systems.
