  Understanding the momentum of light when propagating through optical media is
not only fundamental for studies as varied as classical electrodynamics and
polaritonics in condensed matter physics, but also for important applications
such as optical-force manipulations and photovoltaics. From a microscopic
perspective, an optical medium is in fact a complex system that can split the
light momentum into the electromagnetic field, as well as the material
electrons and the ionic lattice. Here, we disentangle the partition of momentum
associated with light propagation in optical media, and develop a quantum
theory to explicitly calculate its distribution. The material momentum here
revealed, which is distributed among electrons and ionic lattice, leads to the
prediction of unexpected phenomena. In particular, the electron momentum
manifests through an intrinsic DC current, and strikingly, we find that under
certain conditions this current can be along the photonic wave vector, implying
an optical pulling effect on the electrons. Likewise, an optical pulling effect
on the lattice can also be observed, such as in graphene during plasmon
propagation. We also predict the emergence of boundary electric dipoles
associated with light transmission through finite media, offering a microscopic
explanation of optical pressure on material boundaries.
