  A vortex beam, akin to a quantized vortex in superfluids, possesses inherent
orbital angular momentum (OAM), resulting in the propagation of a spiral-shaped
wavefront. Here we demonstrate that a pulsed vortex beam with OAM in the
terahertz frequency band can induce a spiral Higgs wave, which is a
spiral-shaped oscillation mode of the superconducting order parameter. By
utilizing the gauge-invariant theory for the superconducting order, we
demonstrate that the phase mode is driven to screen the longitudinal magnetic
field of the vortex beam, which facilitates the imprinting of the spiral-shaped
wavefront and the transfer of OAM to the condensate. Furthermore, we find that
increasing the OAM of light amplifies the intensity of the third harmonic
generation. These findings highlight the potential of terahertz vortex beams as
a spectroscopic probe of collective modes.
