  We present analytical expressions for the eigenstates and eigenvalues of
electrons confined in a graphene monolayer in the presence of a disclination.
The calculations are performed in the continuum limit approximation in the
vicinity of the Dirac points, solving Dirac equation by freezing out the
carrier radial motion. We include the effect of an external magnetic field and
show the appearence of Aharonov-Bohm oscillation and find out the conditions of
gapped and gapless states in the spectrum. We show that the gauge field due to
a disclination lifts the orbital degeneracy originating from the existence of
two valleys. The broken valley degeneracy has a clear signature on quantum
oscillations and wave packet dynamics.
