The symmetry indicator is widely used to classify topological materials hosting inversion symmetry. We find orthorhombic LiAuBi in space group is a topological insulator with under no strain via first-principles calculations. Due to small band gaps in the = 0 plane, the band inversions can be selectively induced by moderate external strains to realize phases covering all values of = 1, 2, 3, and 0. Detailed phase diagrams are plotted under various moderate strains. The (001) surface states and their associated Fermi surfaces and spin textures are calculated. The topological surface states have different connectivities and different spin textures for the four different phases. The tunability of topological surface states via moderate strain suggests LiAuBi as an attractive topological material for device applications.
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