Topological Phase Transitions from Relativistic Many-Body Calculations

We discuss topological phase transitions (TPTs) on the basis of relativistic self-consistent GW (QSGW) calculations where the spin-orbit coupling is incorporated into the self-energy. TPTs can be caused by the variation of the thickness of a sample, the spin-orbit strength (alloying [1]), by strain, etc. The well known underestimation of band gaps in standard DFT translates into an overestimation of the inverted band gaps. This indicates that standard DFT is unable to provide the correct critical points of TPTs. As practical examples, we concentrate on semimetals Bi and Sb. In addition to the TPT that Bi undergoes under strain [2], we discuss that a thickness-mediated TPT can also occur. This sheds light on the discrepancies about the topological or trivial character of bulk-like samples of Bi. Finally, we simulate Bi_1-xSb_x alloys varying the Sb concentration to find the critical concentration for which the system becomes a topological insulator.
[1] Sanchez-Barriga et al., "Anomalous behavior of the electronic structure of (Bi_1-xIn_x)₂Se₃ across the quantum-phase transition from topological to trivial insulator" in preparation.
[2] Aguilera et al., Phys. Rev. B 91, 125129 (2015).