Topological States Ruled by Stacking Faults inBi2Se3 and Bi2Te3

Leandro Seixas, L. B. Abdalla, T. M. Schmidt, A. Fazzio and R. H. Miwa

Universidade de São PauloSão Paulo, SP, Brazil

Rensselaer Polytechnic InstituteTroy, NY, USA

Financial support

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Topological Insulators: Bi2Se3 and Bi2Te3

120° z-axisrotation of A

240° z-axisrotation of A

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Stacking Faults inBi2Se3 and Bi2Te3

IntrinsicStacking Fault

ExtrinsicStacking Fault

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Methods• First principles calculations based upon

Density Functional Theory (DFT)

• LDA functional for structural propertiesbecause weak interactions among QLs

• GGA-PBE functional for electronic propertieselectronic band structure

• PAW method

• Spin-Orbit couplingonly for electronic properties

• VASP code

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QL-QL interactionthe binding energy of two QL, in function of z-separation

three non-equivalent stacks between QLs

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Stacking Faults Energies

γISF (mJ/m2) γESF (mJ/m2)

Bi2Se3 212 107

Bi2Te3 196 82

Si[1] 33 26

Ni[2] 187 178

Th[2] 320 291

[1] M. Y. Chou, M. L. Cohen, S. G. Louie, Phys Rev. B32, 7979 (1985).[2] N. M. Rosengaard, H. L. Skriver, Phys. Rev. B47 12865 (1993).

What is the energy required to form these defects?

from our calculations

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Band Structure(Bi2Se3 Bulk)

c1

v1 v2

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Band Structure(Bi2Te3 Bulk)

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Band Structure(Bi2Te3 Bulk)

Topological metallic states

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Band Structure(QL-QL distance)

where these “topological states” come from?

without stacking faults, but with larger z-separation between QLs

2.50 3.15 4.15 7.15

2.91 3.26 3.76 7.56

Δzeq = 2.15

Δzeq = 2.56

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Band Structure(Surface)

Dirac point shift

stacking faults near the surface (about 10 Å)

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Band Structure(Surface)

Dirac point shift

stacking faults near the surface (about 10 Å)

Surface states near stacking fault

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Band Structure(Surface)

Dirac point shift

stacking faults near the surface (about 10 Å)

Pristine surface

Surface states near stacking fault

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Conclusions

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Conclusions

Stacking faults in Bi2Te3 leads topological states in bulk.

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Conclusions

Stacking faults in Bi2Te3 leads topological states in bulk.

These topological states come from the larger z-separation between QL.

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Conclusions

Stacking faults in Bi2Te3 leads topological states in bulk.

These topological states come from the larger z-separation between QL.

Interaction between surface and stacking fault shifts the Dirac point.

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Conclusions

Acknowledgement:CNPq/INCT, CAPES, CENAPAD/SP, FAPEMIG and FAPESP

Stacking faults in Bi2Te3 leads topological states in bulk.

These topological states come from the larger z-separation between QL.

Interaction between surface and stacking fault shifts the Dirac point.

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