Quantum oscillation and wave packet revival in conical graphene structure

We present analytical expressions for the eigenstates and eigenvalues of electrons confined in a graphene monolayer in which the crystal symmetry is locally modified by replacing a hexagon by a pentagon, square or heptagon. 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 appearance of Aharonov-Bohm oscillations 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.