  The magnetic-field dependence of the energy spectrum, wave function, binding
energy and oscillator strength of exciton states confined in a circular
graphene quantum dot (CGQD) are obtained within the configuration interaction
(CI) method. We predict that: (1) excitonic effects are very significant in the
CGQD as a consequence of a combination of geometric confinement, magnetic
confinement and reduced screening; (2) two types of excitons (intravalley and
intervalley excitons) are present in the CGQD because of the valley degree of
freedom in graphene; (3) the intravalley and intervalley exciton states display
different magnetic-field dependencies due to the different electron-hole
symmetries of the single-particle energy spectra; (4) with increasing magnetic
field, the exciton ground state in the CGQD undergoes an intravalley to
intervalley transition accompanied by a change of angular momentum; (5) the
exciton binding energy does not increase monotonically with the magnetic field
due to the competition between geometric and magnetic confinements; and (6) the
optical transitions of the intervalley and intravalley excitons can be tuned by
the magnetic field and valley-dependent excitonic transitions can be realized
in CGQD.
