  Near-zero-index (NZI) materials, i.e. materials having a phase refractive
index close to zero, are known to enhance or inhibit light-matter interactions.
Most theoretical derivations of fundamental radiative processes rely on
energetic considerations and detailed balance equations, but not on momentum
considerations. Because momentum exchange should also be incorporated into
theoretical models, we investigate momentum inside the three categories of NZI
materials, i.e. inside epsilon-and-mu near-zero (EMNZ), epsilon-near-zero (ENZ)
and mu-near-zero (MNZ) materials. In the context of Abraham-Minkowski debate in
dispersive materials, we show that Minkowski-canonical momentum of light is
zero inside all categories of NZI materials while Abraham-kinetic momentum of
light is zero in ENZ and MNZ materials but nonzero inside EMNZ materials. We
theoretically demonstrate that momentum recoil, transfer momentum from the
field to the atom and Doppler shift are inhibited in NZI materials. Fundamental
radiative processes inhibition is also explained due to those momentum
considerations inside three-dimensional NZI materials. Lastly, absence of
diffraction pattern in slits experiments is seen as a consequence of zero
Minkowski momentum. Those findings are appealing for a better understanding of
fundamental light-matter interactions at the nanoscale as well as for lasing
applications.
