Scanning Tunneling Microscopy Studies of the Topological Crystalline Insulator

Abstract

The topological crystalline insulator is a topological state of matter arising from crystal symmetries. In this paper, Pb\(_{1-x}\)Sn\(_{x}\)Se with x = 0.23, where its mirror symmetries leads to topologically protected states, is studied using scanning tunneling microscopy (STM). Recent work from Fang et al [4] reveals the eigenvalues of the mirror symmetry operators, M\(_{xz}\) and M\(_{yz}\), and the orthogonality of energy bands with opposite mirror eigenvalues, leading to topologically forbidden scattering channels. Quasiparticle interference (QPI) patterns on the Fourier transformed local density of states (FT-LDOS) are measured and investigated to nd evidence for surface states, suppression of scattering channels, and the Lifshitz transition on the surface of the sample of interest. This paper con rms the existence of surface states on Pb\(_{0.77}\)Sn\(_{0.23}\)Se by comparing with measurements on the trivial PbSe. Additionally, while the QPI data closely match the shape of the joint density of states (JDOS) of the APRES data and the model, due to the small size of the Fermi surface, mirror symmetry protection is not relevant on the Pb\(_{0.77}\)Sn\(_{0.23}\)Se surface and the Lifshitz transition cannot be measured.