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Using a density functional based electronic structure method, we study theeffect of perturbations on the surface state Dirac cone of a strong topologicalinsulator Bi$_2$Se$_3$ from both the intrinsic and extrinsic sources. Weconsider atomic relaxations, and film thickness as intrinsic and interfacialthin dielectric films as an extrinsic source of perturbation to the surfacestates. We find that atomic relaxations has no effect on the degeneracy of theDirac cone whereas film thickness has considerable effect on the surface statesinducing a gap which increases monotonically with decrease in film thickness.We consider two insulating substrates BN and quartz as dielectric films andshow that surface terminations of quartz with or without passivation playscritical role in preserving Dirac cone degeneracy whereas BN is more inert tothe TI surface states. The relative orbital contribution with respect to bulkis mapped out using a simple algorithm, and with the help of it we demonstratethe bulk band inversion when spin-orbit coupling is switched on. The layerprojected charge density distributions of the surface states shows that thesestates are not strictly confined to the surface. The spatial confinement ofthese states extends up to two to three quintuple layers, a quintuple layerconsists of five atomic layers of Bi and Se

Intrinsic and extrinsic perturbations on the topological insulator Bi2Se3 surface states