  We investigate, within the envelope function approximation, the low-energy
states of trions in graphene quantum dots. The presence of valley pseudospin in
graphene as an electron degree of freedom apart from spin adds convolution to
the interplay between exchange symmetry and the electron-electron interaction
in the trion, leading to new states of trions as well as a low energy trion
spectrum different from those in semiconductors. Due to the involvement of
valley pseudospin, it is found that the low-energy spectrum is nearly
degenerate and consists of states all characterized by having an antisymmetric
(pseudospin) (spin) component in the wave function, with the spin (pseudospin)
part being either singlet (triplet) or triplet (singlet), as opposed to the
spectrum in a semiconductor whose ground state is known to be nondegenerate and
always a spin singlet in the case of X- trions. We investigate trions in the
various regimes determined by the competition between quantum confinement and
electron-electron interaction, both analytically and numerically. The numerical
work is performed within a variational method accounting for electron mass
discontinuity across the QD edge. The result for electron-hole correlation in
the trion is presented. Effects of varying quantum dot size and confinement
potential strength on the trion binding energy are discussed.
