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Friedel oscillation is a well-known wave phenomenon, which represents theoscillatory response of electron waves to imperfection. By utilizing thepseudospin-momentum locking in gapless graphene, two recent experimentsdemonstrate the measurement of the topological Berry phase by corresponding tothe unique number of wavefront dislocations in Friedel oscillations. Here, westudy the Friedel oscillations in gapped graphene, in which thepseudospin-momentum locking is broken. Unusually, the wavefront dislocations dooccur as that in gapless graphene, which expects the immediate verification inthe current experimental condition. The number of wavefront dislocations isascribed to the invariant pseudospin winding number in gaped and gaplessgraphene. This study deepens the understanding of correspondence betweentopological quantity and wavefront dislocations in Friedel oscillations, andimplies the possibility to observe the wavefront dislocations of Friedeloscillations in intrinsic gapped two-dimensional materials, e.g., transitionmetal dichalcogenides.

Robust wavefront dislocations of Friedel oscillations in gapped graphene