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V. Brousseau-Couture and M. Côté
momentum locking in-plane allows enhanced control of the spin degree of freedom,
making this material a promising candidate for spintronic applications.
In 2012, a DFT calculation predicted that BiTeI would turn into a strong Z 2
topological insulator when subjected to hydrostatic pressure [10]. Following this
prediction, evidences of the TPT were documented experimentally, using x-ray
diffraction and infrared spectroscopy [11], electrical resistivity [12] and Shubnikov–
de Haas oscillations [13]. Liu and Vanderbilt later showed that broken inversion
symmetry imposed the existence of a mandatory (albeit narrow) Weyl semimetal
phase (WSM) between the trivial and topological insulator phases [14]. As a
consequence, the TPT of BiTeI exhibits two distinct critical pressures: the first when
the Weyl nodes are created in the H-A-L plane of the Brillouin zone, and the second
when they annihilate each other in the M-L-A mirror planes of the Brillouin zone
after migrating in the ±k z direction (see Fig. 11 of ref. [14]).
3.1 Static Lattice
Our first step was to reproduce the TPT in the static lattice approximation. To do
so, we tracked the band gap energy as a function of pressure as well as the leading
orbital character of the valence and conduction bands on either side of the TPT. The
TI phase was confirmed by computing the Z 2 topological invariant using a hybrid
Wannier charge center analysis [15]. We find the critical pressures P C1 = 2.08
GPa and P C2 = 2.28 GPa (gray vertical lines of Fig. 3a). We also observe a band
inversion between Bi-6p z and Te/I- 5p z states (Fig. 3b), as originally predicted [10].
We stress that the current implementation of our DFPT methodology assumes that
the gap energy is larger than the maximal optical phonon frequency (dashed line
on Fig. 3a). We thus restricted our EPI calculations inside this pressure range (red
markers). For more details about the underlying assumptions of our analysis of the
temperature-dependent topological phases, we refer to our forthcoming paper [8].
3.2 Phonon-Induced Gap Renormalization
Figure 4a shows the EPI induced temperature-dependent renormalization for the
CBM (upper panel), VBM (center), and band gap (bottom). Three main elements
can be highlighted from this figure. First, both band extrema show a positive
renormalization in the trivial phase, while they shift in opposite directions in the
TI phase. As a consequence, the total gap renormalization is much larger in the TI
phase, since both contributions reinforce each other rather than cancel out. Second,
the Bi extremum (CBM in trivial phase and VBM in TI phase) is almost unaffected
by the increased pressure and the change in topology, while the Te/I extremum
(VBM in trivial phase and CBM in TI phase) demonstrates a greater dependency
with respect to pressure and even changes sign as the system undergoes the TPT.
V. Brousseau-Couture and M. Côté
momentum locking in-plane allows enhanced control of the spin degree of freedom,
making this material a promising candidate for spintronic applications.
In 2012, a DFT calculation predicted that BiTeI would turn into a strong Z 2
topological insulator when subjected to hydrostatic pressure [10]. Following this
prediction, evidences of the TPT were documented experimentally, using x-ray
diffraction and infrared spectroscopy [11], electrical resistivity [12] and Shubnikov–
de Haas oscillations [13]. Liu and Vanderbilt later showed that broken inversion
symmetry imposed the existence of a mandatory (albeit narrow) Weyl semimetal
phase (WSM) between the trivial and topological insulator phases [14]. As a
consequence, the TPT of BiTeI exhibits two distinct critical pressures: the first when
the Weyl nodes are created in the H-A-L plane of the Brillouin zone, and the second
when they annihilate each other in the M-L-A mirror planes of the Brillouin zone
after migrating in the ±k z direction (see Fig. 11 of ref. [14]).
3.1 Static Lattice
Our first step was to reproduce the TPT in the static lattice approximation. To do
so, we tracked the band gap energy as a function of pressure as well as the leading
orbital character of the valence and conduction bands on either side of the TPT. The
TI phase was confirmed by computing the Z 2 topological invariant using a hybrid
Wannier charge center analysis [15]. We find the critical pressures P C1 = 2.08
GPa and P C2 = 2.28 GPa (gray vertical lines of Fig. 3a). We also observe a band
inversion between Bi-6p z and Te/I- 5p z states (Fig. 3b), as originally predicted [10].
We stress that the current implementation of our DFPT methodology assumes that
the gap energy is larger than the maximal optical phonon frequency (dashed line
on Fig. 3a). We thus restricted our EPI calculations inside this pressure range (red
markers). For more details about the underlying assumptions of our analysis of the
temperature-dependent topological phases, we refer to our forthcoming paper [8].
3.2 Phonon-Induced Gap Renormalization
Figure 4a shows the EPI induced temperature-dependent renormalization for the
CBM (upper panel), VBM (center), and band gap (bottom). Three main elements
can be highlighted from this figure. First, both band extrema show a positive
renormalization in the trivial phase, while they shift in opposite directions in the
TI phase. As a consequence, the total gap renormalization is much larger in the TI
phase, since both contributions reinforce each other rather than cancel out. Second,
the Bi extremum (CBM in trivial phase and VBM in TI phase) is almost unaffected
by the increased pressure and the change in topology, while the Te/I extremum
(VBM in trivial phase and CBM in TI phase) demonstrates a greater dependency
with respect to pressure and even changes sign as the system undergoes the TPT.