Doping induced topological phase transition in Bi: The role of quantum electronic stress*

Charge doping is an essential means to tailor materials’ properties. However, besides moving the Fermi level, charge doping is generally not expected to induce topological phase transition (TPT). Surprisingly, using first-principles calculations, here we demonstrate an electron doping induced TPT in bulk Bi from a higher-order topological insulator (HOTI) to a TI. The underlying mechanism is revealed to be driven by an electron doping induced quantum electronic stress (QES), which in turn induces a highly anisotropic lattice expansion to close/reopen the small energy gap in Bi band structure. Our finding significantly resolves an outstanding controversy concerning the topological characterization of bulk Bi among existing experiments and theories, and explains the physical origin of the topologic order in Bi (111) thin films. It sheds new lights to fundamental understanding of topological properties of small band gap materials in relation to doping and QES.