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Emergence of topological and topological crystalline phases in TlBiS2 and TlSbS2.

Zhang Q, Cheng Y, Schwingenschlögl U - Sci Rep (2015)

Bottom Line: Zero, one, and four Dirac cones are found for the (111) surfaces of both TlBiS2 and TlSbS2 when the pressure grows, which confirms trivial-nontrivial-trivial phase transitions.The Dirac cones at the points are anisotropic with large out-of-plane component.TlBiS2 shows normal, topological, and topological crystalline insulator phases under hydrostatic pressure, thus being the first compound to exhibit a phase transition from a topological to a topological crystalline insulator.

View Article: PubMed Central - PubMed

Affiliation: PSE Division, KAUST, Thuwal 23955-6900, Kingdom of Saudi Arabia.

ABSTRACT
Using first-principles calculations, we investigate the band structure evolution and topological phase transitions in TlBiS2 and TlSbS2 under hydrostatic pressure as well as uniaxial and biaxial strain. The phase transitions are identified by parity analysis and by calculating the surface states. Zero, one, and four Dirac cones are found for the (111) surfaces of both TlBiS2 and TlSbS2 when the pressure grows, which confirms trivial-nontrivial-trivial phase transitions. The Dirac cones at the points are anisotropic with large out-of-plane component. TlBiS2 shows normal, topological, and topological crystalline insulator phases under hydrostatic pressure, thus being the first compound to exhibit a phase transition from a topological to a topological crystalline insulator.

No MeSH data available.


Related in: MedlinePlus

Band structures of the TlBiS2 slab with (111)-oriented surfaces under (a) −2 GPa, (b) 2 GPa, and (c) 5 GPa pressure.The size of the red circles represents the contribution of the first eight atomic layers.
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f4: Band structures of the TlBiS2 slab with (111)-oriented surfaces under (a) −2 GPa, (b) 2 GPa, and (c) 5 GPa pressure.The size of the red circles represents the contribution of the first eight atomic layers.

Mentions: To confirm the topological phase transitions, we investigate the evolution of the surface states of TlBiS2 under hydrostatic pressure. We first obtain a tight-binding Hamiltonian from maximally localized Wannier functions36 using the WANNIER90 code37. A hexagonal supercell with 8 × 8 × 8 k points is adopted in the non-self-consistent calculation. The Tl s, p, Bi p, and S p orbitals are used for the initial projection. Once the tight-binding Hamiltonian is established, a slab of 241 atomic layers with (111)-oriented surfaces is built with Tl on both the top and bottom surfaces. Calculated band structures near the Fermi level are shown in Fig. 4. Due to the inversion symmetry of the slab, the bands related to the top and bottom surfaces are degenerate. We project the states near the Fermi level to the first eight atomic layers on the top side of the slab. According to Fig. 4(a), for −2 GPa pressure there is no state in the bulk energy gap and the surface states marked by red circles are buried in bulk states. On the other hand, for 2 GPa pressure, see Fig. 4(b), a surface state emerges in the energy gap at the point and the Dirac point is located below the Fermi level, i.e., we have a nontrivial phase. For 8 GPa pressure, see Fig. 4(c), an additional surface state arises at the point. Since there are three points in the surface Brillouin zone, we have a total of four Dirac cones. The even number again reflects a trivial phase. The contributions of the surface layers are highlighted by the size of the red circles. Comparing the surface states at the point in Fig. 4(b) and (c), we find that the proportion of the gapless states on the surface layers is determined by the pressure.


Emergence of topological and topological crystalline phases in TlBiS2 and TlSbS2.

Zhang Q, Cheng Y, Schwingenschlögl U - Sci Rep (2015)

Band structures of the TlBiS2 slab with (111)-oriented surfaces under (a) −2 GPa, (b) 2 GPa, and (c) 5 GPa pressure.The size of the red circles represents the contribution of the first eight atomic layers.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4323645&req=5

f4: Band structures of the TlBiS2 slab with (111)-oriented surfaces under (a) −2 GPa, (b) 2 GPa, and (c) 5 GPa pressure.The size of the red circles represents the contribution of the first eight atomic layers.
Mentions: To confirm the topological phase transitions, we investigate the evolution of the surface states of TlBiS2 under hydrostatic pressure. We first obtain a tight-binding Hamiltonian from maximally localized Wannier functions36 using the WANNIER90 code37. A hexagonal supercell with 8 × 8 × 8 k points is adopted in the non-self-consistent calculation. The Tl s, p, Bi p, and S p orbitals are used for the initial projection. Once the tight-binding Hamiltonian is established, a slab of 241 atomic layers with (111)-oriented surfaces is built with Tl on both the top and bottom surfaces. Calculated band structures near the Fermi level are shown in Fig. 4. Due to the inversion symmetry of the slab, the bands related to the top and bottom surfaces are degenerate. We project the states near the Fermi level to the first eight atomic layers on the top side of the slab. According to Fig. 4(a), for −2 GPa pressure there is no state in the bulk energy gap and the surface states marked by red circles are buried in bulk states. On the other hand, for 2 GPa pressure, see Fig. 4(b), a surface state emerges in the energy gap at the point and the Dirac point is located below the Fermi level, i.e., we have a nontrivial phase. For 8 GPa pressure, see Fig. 4(c), an additional surface state arises at the point. Since there are three points in the surface Brillouin zone, we have a total of four Dirac cones. The even number again reflects a trivial phase. The contributions of the surface layers are highlighted by the size of the red circles. Comparing the surface states at the point in Fig. 4(b) and (c), we find that the proportion of the gapless states on the surface layers is determined by the pressure.

Bottom Line: Zero, one, and four Dirac cones are found for the (111) surfaces of both TlBiS2 and TlSbS2 when the pressure grows, which confirms trivial-nontrivial-trivial phase transitions.The Dirac cones at the points are anisotropic with large out-of-plane component.TlBiS2 shows normal, topological, and topological crystalline insulator phases under hydrostatic pressure, thus being the first compound to exhibit a phase transition from a topological to a topological crystalline insulator.

View Article: PubMed Central - PubMed

Affiliation: PSE Division, KAUST, Thuwal 23955-6900, Kingdom of Saudi Arabia.

ABSTRACT
Using first-principles calculations, we investigate the band structure evolution and topological phase transitions in TlBiS2 and TlSbS2 under hydrostatic pressure as well as uniaxial and biaxial strain. The phase transitions are identified by parity analysis and by calculating the surface states. Zero, one, and four Dirac cones are found for the (111) surfaces of both TlBiS2 and TlSbS2 when the pressure grows, which confirms trivial-nontrivial-trivial phase transitions. The Dirac cones at the points are anisotropic with large out-of-plane component. TlBiS2 shows normal, topological, and topological crystalline insulator phases under hydrostatic pressure, thus being the first compound to exhibit a phase transition from a topological to a topological crystalline insulator.

No MeSH data available.


Related in: MedlinePlus