312
V. Brousseau-Couture and M. Côté
By extrapolating the VBM and CBM renormalization towards the TPT within
each phase and applying this correction to the static band gap shown in Fig. 3a, we
evaluate the temperature dependence of critical pressures P C1 and P C2 . From the
above discussion, the EPI being globally unfavorable to the TI phase leads to both
critical pressures being pushed towards higher values for increasing temperature,
as seen in the topological phase diagram of Fig. 4b. Nevertheless, the stronger
renormalization of P C2 compared to P C1 leads to a widening of the WSM phase
with increasing temperature. While the WSM phase width remains small, it has
increased by ∼50% at 100K and has more than doubled by 300K. Our findings,
therefore, indicate that EPI interaction does not obstruct experimental detection of
the WSM phase in BiTeI.
4 Conclusion and Outlook
We have computed the EPI contribution to the temperature dependence of the
band gap energy for BiTeI using first-principles methods. We explain the different
possible gap behaviors in the light of a simplified heuristic two-band model. We
show that the band extrema are affected differently by EPI depending on their
leading orbital character and that EPI is globally not favorable to the non-trivial
topology in BiTeI. With increasing temperature, both critical pressures are pushed
towards higher values, and the WSM phase is widened. A complete description
of the temperature dependence of the TPT would require evaluating the thermal
expansion contribution [8]. Further analysis of the individual couplings could also
provide meaningful insight into how the Rashba interaction affects the EPI strength
within and between spin-split bands.
References
1. M.Z. Hasan, C.L. Kane, Colloquim: topological insulators. Rev. Modern Phys. 82(4), 3045–
3067 (2010). https://doi.org/10.1103/RevModPhys.82.3045
2. F. Giustino, Electron-phonon interactions from first principles. Rev. Modern Phys. 89(1),
015003 (2017). https://doi.org/10.1103/RevModPhys.89.015003
3. I. Garate, Phonon-induced topological transitions and crossovers in Dirac materials. Phys. Rev.
Lett. 110(4), 046402 (2013). https://doi.org/10.1103/PhysRevLett.110.046402
4. K. Saha, I. Garate, Phonon-induced topological insulation. Phys. Rev. B 89(20), 205103
(2014). https://doi.org/10.1103/PhysRevB.89.205103
5. G. Antonius, S.G. Louie, Temperature-induced topological phase transitions: promoted versus
suppressed nontrivial topology. Phys. Rev. Lett. 117(24), 246401 (2016). https://doi.org/10.
1103/PhysRevLett.117.246401
6. B. Monserrat, D. Vanderbilt, Temperature dependence of the bulk Rashba splitting in
the bismuth tellurohalides. Phys. Rev. Mat. 1(5), 054201 (2017). https://doi.org/10.1103/
PhysRevMaterials.1.054201
V. Brousseau-Couture and M. Côté
By extrapolating the VBM and CBM renormalization towards the TPT within
each phase and applying this correction to the static band gap shown in Fig. 3a, we
evaluate the temperature dependence of critical pressures P C1 and P C2 . From the
above discussion, the EPI being globally unfavorable to the TI phase leads to both
critical pressures being pushed towards higher values for increasing temperature,
as seen in the topological phase diagram of Fig. 4b. Nevertheless, the stronger
renormalization of P C2 compared to P C1 leads to a widening of the WSM phase
with increasing temperature. While the WSM phase width remains small, it has
increased by ∼50% at 100K and has more than doubled by 300K. Our findings,
therefore, indicate that EPI interaction does not obstruct experimental detection of
the WSM phase in BiTeI.
4 Conclusion and Outlook
We have computed the EPI contribution to the temperature dependence of the
band gap energy for BiTeI using first-principles methods. We explain the different
possible gap behaviors in the light of a simplified heuristic two-band model. We
show that the band extrema are affected differently by EPI depending on their
leading orbital character and that EPI is globally not favorable to the non-trivial
topology in BiTeI. With increasing temperature, both critical pressures are pushed
towards higher values, and the WSM phase is widened. A complete description
of the temperature dependence of the TPT would require evaluating the thermal
expansion contribution [8]. Further analysis of the individual couplings could also
provide meaningful insight into how the Rashba interaction affects the EPI strength
within and between spin-split bands.
References
1. M.Z. Hasan, C.L. Kane, Colloquim: topological insulators. Rev. Modern Phys. 82(4), 3045–
3067 (2010). https://doi.org/10.1103/RevModPhys.82.3045
2. F. Giustino, Electron-phonon interactions from first principles. Rev. Modern Phys. 89(1),
015003 (2017). https://doi.org/10.1103/RevModPhys.89.015003
3. I. Garate, Phonon-induced topological transitions and crossovers in Dirac materials. Phys. Rev.
Lett. 110(4), 046402 (2013). https://doi.org/10.1103/PhysRevLett.110.046402
4. K. Saha, I. Garate, Phonon-induced topological insulation. Phys. Rev. B 89(20), 205103
(2014). https://doi.org/10.1103/PhysRevB.89.205103
5. G. Antonius, S.G. Louie, Temperature-induced topological phase transitions: promoted versus
suppressed nontrivial topology. Phys. Rev. Lett. 117(24), 246401 (2016). https://doi.org/10.
1103/PhysRevLett.117.246401
6. B. Monserrat, D. Vanderbilt, Temperature dependence of the bulk Rashba splitting in
the bismuth tellurohalides. Phys. Rev. Mat. 1(5), 054201 (2017). https://doi.org/10.1103/
PhysRevMaterials.1.054201