Electron-phonon coupling effects on the van Hove singularity in topological crystalline insulators

In this study, we examine the influence of electron–phonon coupling (EPC) on the van Hove singularities on the SnTe(001) surface as a topological crystalline insulator. To do this, we calculate the electronic density of states (DOS) and investigate its changes according to the parameters characteristic of the EPC. The effect of EPC is incorporated in the modified momentum (wave number) components along the x – and y – directions. The results show that when varying the EPC strength along the x – direction (λx), the number and position of the Van Hove singularities remain unchanged, but their height decreases significantly. As λx is sufficiently large, these singularities vanish, and an energy gap emerges. In contrast, when the EPC strength λy is altered within a range similar to λx, the change in DOS is nearly negligible, and a significant EPC is required to observe any small changes. The difference in the DOS changes with respect to EPC strength between the x- and y-directions highlights the anisotropy of the SnTe(001) surface. The findings indicate that the electronic characteristics of the SnTe(001) surface can be tuned through EPC by modifying factors influencing crystal lattice vibrations, such as temperature or substrate material.