  The spontaneous symmetry breaking of a continuous symmetry in complex field
theory at the exceptional point of the parameter space is known to exhibit
interesting phenomena, such as the breakdown of a Higgs mechanism. In this
work, we derive the complex Ginzburg-Landau model from a non-Hermitian two-band
BCS model via path integral and investigate its spontaneous symmetry breaking.
We find that analog to the Higgs mechanism, the Meissner effect of the complex
Ginzburg-Landau model also breaks down at the exceptional point while the gap
parameters stay finite.
