  The phenomenon of negative refraction generally requires negative refractive
indices or phase discontinuities, which can be realized using metamaterials or
metasurfaces. Recent theories have proposed a novel mechanism for negative
refraction based on synthetic gauge fields, which affect classical waves as if
they were charged particles in electromagnetic fields, but this has not
hitherto been demonstrated in experiment. Here, we report on the experimental
demonstration of gauge-field-induced negative refraction in a twisted bilayer
acoustic metamaterial. The bilayer twisting produces a synthetic gauge field
for sound waves propagating within a projected two-dimensional geometry, with
the magnitude of the gauge field parameterized by the choice of wavenumber
along the third dimension. Waveguiding with backward propagating modes is also
demonstrated in a trilayer configuration that implements strong gauge fields.
These results provide an alternative route to achieving negative refraction in
synthetic materials.
