  Negative refraction plays an important role in acoustic wave manipulation and
imaging. However, conventional systems based on acoustic metamaterials suffer
from the limits induced by loss-related and resolution issues. In this work, a
parity-time (PT)-symmetric system is introduced to realize loss-free
bidirectional acoustic negative refraction. The system is composed of a pair of
locally PT-symmetric multi-layer metasurfaces sandwiching a region of free
space, which also forms a global PT-symmetry. The property of bidirectional
negative refraction, which is rare for regular PT-symmetric structures, is
related to the coexistence of amplification and absorption in the locally
PT-symmetric metasurfaces at their PT broken phases. Such metasurfaces can
freely switch their states between coherent perfect absorber (CPA) and
amplifier depending on the direction of incidence. Our results provide a new
physical mechanism for realizing bidirectional functions in PT-symmetric
systems.
