  Time-periodic light field has emerged as a control knob for manipulating
quantum states in solid-state materials, cold atoms and photonic systems via
hybridization with photon-dressed Floquet states in the strong coupling limit,
dubbed as Floquet engineering. Such interaction leads to tailored properties of
quantum materials, for example, modifications of the topological properties of
Dirac materials and modulation of the optical response. Despite extensive
research interests over the past decade, there is no experimental evidence of
momentum-resolved Floquet band engineering of semiconductors, which is a
crucial step to extend Floquet engineering to a wide range of solid-state
materials. Here, based on time- and angle-resolved photoemission spectroscopy
measurements, we report experimental signatures of Floquet band engineering in
a model semiconductor - black phosphorus. Upon near-resonance pumping at photon
energy of 340 to 440 meV, a strong band renormalization is observed near the
band edges. In particular, light-induced dynamical gap opening is resolved at
the resonance points, which emerges simultaneously with the Floquet sidebands.
Moreover, the band renormalization shows a strong selection rule favoring pump
polarization along the armchair direction, suggesting pseudospin selectivity
for the Floquet band engineering as enforced by the lattice symmetry. Our work
demonstrates pseudospin-selective Floquet band engineering in black phosphorus,
and provides important guiding principles for Floquet engineering of
semiconductors.
