Eur. Phys. J. B (2016) 89: 57
https://doi.org/10.1140/epjb/e2016-60907-y

Regular Article

Quantum oscillations and wave packet revival in conical graphene structure

¹ TIFR Centre for Interdisciplinary Sciences, 500075 Hyderabad, India
² Statistical Physics Group, Institut Jean Lamour, UMR CNRS No 7198, Université de Lorraine, B.P. 70239, 54506 Vandœuvre les Nancy, France

^a e-mail: debabratas@tifrh.res.in

Received: 23 November 2015
Received in final form: 19 January 2016
Published online: 2 March 2016

Abstract

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.