  We report the experimental discovery of orbital vortex lines in the
three-dimensional (3D) band structure of a topological semimetal. Combining
linear and circular dichroism in soft x-ray angle-resolved photoemission
(SX-ARPES) with first-principles theory, we image the winding of atomic orbital
angular momentum, thereby revealing - and determining the location of - lines
of vorticity in full 3D momentum space. Our observation of momentum-space
vortex lines with quantized winding number establishes an analogue to
real-space quantum vortices, for instance, in type-II superconductors and
certain non-collinear magnets. These results establish multimodal dichroism in
SX-ARPES as an approach to trace 3D orbital textures. Our present findings
particularly constitute the first imaging of non-trivial quantum-phase winding
at line nodes and may pave the way to new orbitronic phenomena in quantum
materials
