Temperature-Induced Topological Phase Transitions: Promoted versus Suppressed Nontrivial Topology

Abstract

We determine the topological phase diagram of BiTl(S 1−δ Se δ )2 as a function of doping and temperature from first-principles calculations. Due to electron-phonon interaction, the bands are renormalized at finite temperature, allowing for a transition between the trivial (Z2 = 0) and non-trivial (Z2 = 1) topological phase. We find two distinct regions of the phase diagram with non-trivial topology. In BiTlS2, the phonons promote the crystal to the topological phase at high temperature, while in BiTlSe2, the topological phase exists only at low temperature. This behaviour is explained by the symmetry of the phonon coupling potential, whereby the even phonon modes (whose potential is even under inversion) promote the topological phase and the odd phonon modes promote the trivial phase.PACS numbers: 63.20.kd, 63.20.dk, 71.15.Mb Recent studies on three-dimensional topological insulators have identified several materials with tunable topological phases [1]. Upon varying experimental parameters, these materials undergo a phase transition between a trivial and a topological insulator state. Such transition may occur as a function of impurity doping [2-5], pressure [6-8], or temperature [4,[9][10][11][12]. The effect of temperature becomes especially important for devices that are expected to operate under varying conditions [13]. It is thus desirable to be able to predict the topological phase diagrams of these materials and their physical origin.Electron-phonon interactions underly the temperature-induced topological phase transition. As more phonons are being thermally activated, the electronic band energies may shift and close the band gap until a band inversion occurs at some critical temperature. This process was first described in 2D and 3D topological insulators from model hamiltonians [14][15][16][17][18]. First-principles calcualtions later confirmed that lattice deformation due to phonons could flip the Z 2 invariant [19] [20].One remarkable prediction from Garate et al. [14,15] was that electron-phonon coupling could induce a trivial to topological phase transition with increasing temperature. The requirement for this scenario to happen is a negative temperature coefficients for the band edge states in the trivial phase, which promotes a band inversion at high temperature and stabilizes the topological phase. They proposed that such phenomenon could be seen in BiTl(S 1−δ Se δ ) 2 , due to the presence of light atoms and the tunability of the band gap with doping. While no temperature-dependent measurements have been reported in this particular material, those performed in Pb 1−δ Sn δ Se indicate the opposite trend-that the system goes back from a topological to a trivial phase at higher temperature [4,10,11]. * antonius@lbl.govIn this Letter, we compute from first-principles the topological phase diagram of BiTl(S 1−δ Se δ ) 2 . The electron-phonon coupling and the temperature dependence of the electronic band energies is obtained from density functional perturbation theory (DFPT) [21][22][23][24], and w...

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