  Friedel oscillation is a well-known wave phenomenon, which represents the
oscillatory response of electron waves to imperfection. By utilizing the
pseudospin-momentum locking in gapless graphene, two recent experiments
demonstrate the measurement of the topological Berry phase by corresponding to
the unique number of wavefront dislocations in Friedel oscillations. Here, we
study the Friedel oscillations in gapped graphene, in which the
pseudospin-momentum locking is broken. Unusually, the wavefront dislocations do
occur as that in gapless graphene, which expects the immediate verification in
the current experimental condition. The number of wavefront dislocations is
ascribed to the invariant pseudospin winding number in gaped and gapless
graphene. This study deepens the understanding of correspondence between
topological quantity and wavefront dislocations in Friedel oscillations, and
implies the possibility to observe the wavefront dislocations of Friedel
oscillations in intrinsic gapped two-dimensional materials, e.g., transition
metal dichalcogenides.
