Beating feature of Friedel oscillations induced by imperfections in Mexican-hat dispersion material

Abstract

The Mexican-hat dispersion exhibits the special concentric contour Fermi surface, giving rise to novel features for scattering against the imperfections. Here, we study the mechanisms of point impurity and line defect scatterings in the material with Mexican-hat dispersion, respectively. By adopting the Green's function combined the T -matrix approximation, we calculate the local density of states (LDOS) in the momentum space (also called FT-LDOS) and real space near the point impurity. We find that the pattern of the FT-LDOS well reflects the shape of the Fermi surface. Notably, inside the Mexican-hat, three scattering processes occur with three characteristic wave vectors, i.e., the inter-scattering between the inner and outer Fermi surfaces, and the intrascattering on both Fermi surfaces, which leads to the LDOS in the real space exhibiting the beating feature. The LDOS for each scattering exhibits the asymptotic behavior with decay index x -1 similar to the parabolic dispersion, although the Mexican-hat dispersion owns the quartic form. By using the stationary phase approximation, we calculate the LDOS oscillation in the real space near the line defect. It is observed that two scatterings occur between two pairs of stationary phase points on the Fermi surfaces with two characteristic wave vectors, also leading to the beating feature for the LDOS. The LDOS for each scattering exhibit the asymptotic behavior with decay index x -1/2 also similar to the parabolic dispersion. Remarkably, the emergence of beating features for scattering against point impurity or line defect, are different from 2D electron gas and Dirac electron systems. Our results underscore a distinctive aspect of the Friedel oscillation in the Mexican-hat dispersion material, and reveal unique feature of the Fermi surfaces, which can be tested by the scanning tunneling microscope.