Wavefronts Dislocations of Friedel Oscillations in Graphene: Trigonal Warping Effect

The electron waves of a host system exhibit an oscillating response to an external impurity, namely Friedel oscillations (FOs), extensively studied in two‐dimensional materials. Recently, wavefront dislocations, a new feature of FOs, have been revealed in graphene. However, previous analytical works have been limited to the linear dispersion of graphene. Herein, the fate of wavefront dislocations is investigated numerically in FOs beyond the linear regime. The wavefront dislocations are robust against the trigonal warping effect, crucial for high doping graphene, due to the invariant winding number of the tight‐binding energy band. Furthermore, the opening of the gap, increasing the electronic Fermi wavelength, can highlight the wavefront dislocations blurred by intravalley scattering‐induced short‐range oscillations. These results should be observable using current experimental technology. Therefore, this study not only demonstrates the robust existence of wavefront dislocations in FOs over a wide range of energies but also deepens the understanding of intervalley scattering in graphene and other two‐dimensional valleytronic materials. Recently, the unique wavefront dislocations have been identified in Friedel oscillations. Previous works are limited to the linear dispersion of graphene. Herein, the robust wavefront dislocations are found against the trigonal warping effect. These results can be explained by the invariant winding number of the tight‐binding energy band and demonstrated by using current experimental technology.