  In this paper, we present a systematic study of beam shifts and angular
momenta of paraxial vortex beams at air-left-handed material (LHM) interfaces.
It is shown that, compared to their counterparts at air-right-handed material
(RHM) interfaces, the spatial Goos-H\"{a}nchen (GH) and Imbert-Fedorov (IF)
shifts remains the same, while the angular GH and IF shifts are reversed, at
air-LHM interfaces. The spatial and angular shifts of paraxial vortex beams
have their respective origins in transverse angular momenta and transverse
linear momenta. The spatial GH and IF shifts remain unreversed as a result of
the both reversions of transverse angular momenta and z-component linear
momentum, while the angular GH and IF shifts are reversed due to that the
z-component linear momentum is reversed and the transverse linear momenta are
unreversed, at air-LHM interfaces. In addition, we perform a quantitative
analysis on spin-orbit angular momentum conversion and orbit-orbit angular
momentum conversion, which further helps us understand the essence of vortex
beam shifts at air-LHM interfaces and their fundamental distinctions with those
at air-RHM interfaces.
