  We present a theoretical study of the elementary electronic excitation
associated with plasmon modes in a two-dimensional hole gas (2DHG) in the
presence of spin-orbit (SO) interaction induced by the Rashba effect. The
calculation is carried out using a standard random-phase-approximation
approach. It is found that in such a spintronic system, plasmon excitation can
be achieved via intra- and inter-SO electronic transitions around the Fermi
level. As a result, the intra- and inter-SO plasmon modes can be observed. More
importantly, the plasmon modes induced by inter-SO transition are optic-like
and these modes can be directly applied to identify the Rashba spin splitting
in 2DHG systems through optical measurements. The interesting features of the
plasmon excitation in a spin split 2DHG are analyzed and discussed in details.
Moreover, the results obtained for a 2DHG are compared with those obtained for
a spin-splitting 2DEG reported very recently.
