  Ultrarelativistic vortex leptons with intrinsic orbital angular momenta (OAM)
have important applications in high energy particle physics, nuclear physics,
astrophysics, etc. However, unfortunately, their generation still poses a great
challenge. Here, we put forward a novel method for generating ultrarelativistic
vortex positrons and electrons through nonlinear Breit-Wheeler (NBW) scattering
of vortex $\gamma$ photons. For the first time, a complete angular
momentum-resolved scattering theory has been formulated, introducing the
angular momentum of laser photons and vortex particles into the conventional
NBW scattering framework. We find that vortex positron (electron) can be
produced when the outgoing electron (positron) is generated along the collision
axis. By unveiling the angular momentum transfer mechanism, we clarify that OAM
of the $\gamma$ photon and angular momenta of multiple laser photons are
entirely transferred to the generated pairs, leading to the production of
ultrarelativistic vortex positrons or electrons with large OAM. Furthermore, we
find that the cone opening angle and superposition state of the vortex $\gamma$
photon, distinct characteristics aside from its intrinsic OAM, can be
determined via the angular distribution of created pairs in NBW processes. Our
method paves the way for investigating strong-field quantum electrodynamics
processes concerning the generation and detection of vortex particle beams in
intense lasers.
