The Wilson-loop method is widely used in topological material calculation for the reason that it efficiently determines topological invariants and surface states. I will introduce the Wilson-loop method and its application in calculating various topological invariants and surface states. Recently, the nested Wilson-loop method has been proposed to extend the Wilson-loop method from 2 dimensions to 3 dimensions to reveal the higher-order topological properties. I will introduce the application of nested Wilson-loop method in calculating hinge state invariant in SnTe and the surface Dirac cone invariant in Ba3Cd2As4.
- V. Berry Michael, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 392, 45 (1984).
- R. D. King-Smith and D. Vanderbilt, Phys. Rev. B 47, 1651 (1993).
- A. Alexandradinata, X. Dai, and B. A. Bernevig, Phys. Rev. B 89, 155114 (2014).
- H. Weng, X. Dai, and Z Fang, MRS Bulletin 39, 849 (2014).
- W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Science 357, 61 (2017).
- F. Schindler, A. M. Cook, M. G. Vergniory, Z. Wang, S. S. P. Parkin, B. A. Bernevig, and T. Neupert, Science Advances 4 (2018).
- T. Zhang, C. Yue, T. Zhang, S. Nie, Z. Wang, C. Fang, H. Weng and Z. Fang, arXiv:1905.07253.