Topological surface states protected from backscattering by chiral spin texture

Roushan, P.; Seo, Jungpil; Parker, Colin; Hor, Y. S.; Hsieh, David; Qian, Dong; Richardella, Anthony; Hasan, M. Zahid; Cava, R. J.; Yazdani, Ali

doi:10.1038/nature08308

Cited by 1,012 publications

(1,018 citation statements)

References 27 publications

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“…With regard to the backscattering protection of the SS, however, the opposite scenario τ SS τ bulk should be expected. 18 For thermoelectric applications charge carrier concentration of p = 1 × 10 19 cm −3 (cf. Figs.…”

Section: Theoretical Resultsmentioning

confidence: 99%

Impact of the Topological Surface State on the Thermoelectric Transport in Sb₂Te₃ Thin Films

et al. 2015

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Ab initio electronic structure calculations based on density functional theory and tight-binding methods for the thermoelectric properties of ptype Sb 2 Te 3 films are presented. The thicknessdependent electrical conductivity and the thermopower are computed in the diffusive limit of transport based on the Boltzmann equation. Contributions of the bulk and the surface to the transport coefficients are separated which enables to identify a clear impact of the topological surface state on the thermoelectric properties. By tuning the charge carrier concentration, a crossover between a surface-state-dominant and a FuchsSondheimer transport regime is achieved. The calculations are corroborated by thermoelectric transport measurements on Sb 2 Te 3 films grown by atomic layer deposition.Almost all proposed three-dimensional (3D) Z 2 topological insulators (TIs) 1,2 are efficient thermoelectric materials. That is not by coincidence, since the link between an efficient thermoelectric * To whom correspondence should be addressed † Institute of Physics, Martin Luther University HalleWittenberg, D-06099 Halle, Germany ‡ Institute of Nanostructure and Solid State Physics, Universität Hamburg, Jungiusstrasse 11, D-20355 Hamburg, Germany ¶ Max Planck Institute of Microstructure Physics, Weinberg 2, D-06120 Halle, Germany material and the topological character is the inverted band gap. 3,4 The last is due to spin-orbit coupling which switches parity of the bands and leads, if strong enough, to narrow band gaps which are favourable for efficient room-temperature thermoelectrics. Usually strong spin-orbit coupling is mediated by heavy elements which in turn also tend to reduce the material's lattice thermal conductivity, another requirement for desirable thermoelectrics.In the early 90's, Hicks and Dresselhaus 5,6 proposed the concept of low-dimensionality to increase further the thermoelectric efficiency; primarily in thin films, the thermopower S should be enlarged. However, in contrast to previous theoretical model calculations, 7,8 decreased values of S were found experimentally 9-11 for Bi 2 Te 3 and Sb 2 Te 3 thin films and were recently corroborated by both model 12,13 and ab initio calculations 4 of our groups.Thus, to resolve this discrepancy, the potential impact of the surface state (SS) of TIs on thermoelectricity needs to be investigated in more detail. In this Letter, we present ab initio calculations and transport measurements of the thermoelectric properties of Sb 2 Te 3 films at varying thickness, temperature and charge carrier concentration. (1/ cm)(g) Theoretical resultsIn the following, we discuss the doping-and temperature-dependent electrical conductivity and thermopower, as shown in Fig. 1, exemplary for a Sb 2 Te 3 film thickness of 18 quintuple-layer (QL), i.e. about 18 nm. A discussion of films with other thicknesses is given in the supplemental material. 14 The converged electronic structure results serve as input to obtain the thermoelectric transport properties at temperature T and fixed extri...

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Section: Theoretical Resultsmentioning

confidence: 99%

Impact of the Topological Surface State on the Thermoelectric Transport in Sb₂Te₃ Thin Films

et al. 2015

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“…The chiral nature of these Dirac states have some peculiar implications on their transport properties [8,9]. The back-scattering of these surface electrons from impurities, and therefore the localization is forbidden as long as the impurity potential does not break the TR symmetry [10].…”

Section: Introductionmentioning

confidence: 99%

Anisotropic conductivity in magnetic topological insulators

Sabzalipour

Abouie²,

Abedinpour³

2015

J. Phys.: Condens. Matter

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Abstract. We study the surface conductivity of a three dimensional topological insulator doped with magnetic impurities. The spin-momentum locking of surface electrons makes their scattering from magnetic impurities anisotropic and the standard relaxation time approximation is not applicable. Using the semiclassical Boltzmann approach together with a generalized relaxation time scheme, we obtain closed forms for the relaxation times and analytic expressions for the surface conductivities of the system as functions of the bulk magnetization and the orientation of the aligned surface magnetic impurities. We show that the surface conductivity is anisotropic, and strongly depends both on the direction of the spins of magnetic impurities and on the magnitude of the bulk magnetization. In particular, we find that the surface conductivity has its minimum value when the spin of surface impurities are aligned perpendicular to the surface of TI, and therefore the backscattering probability is enhanced due to the magnetic torque exerted by impurities on the surface electrons.PACS numbers: 72.15.Lh

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“…Recent interest in topological states 2-4 has been stimulated by the realization that the combination of time-reversal symmetry and the spin-orbit interaction can lead to topological insulating electronic phases [5][6][7][8][9][10] and by the prediction [11][12][13] and observation [14][15][16][17][18][19][20][21][22][23][24][25][26] of these phases in real materials. A topological insulator is a two-or three-dimensional material with a bulk energy gap that has gapless modes on the edge or surface that are protected by time-reversal symmetry.…”

Section: Introductionmentioning

confidence: 99%

Topological defects and gapless modes in insulators and superconductors

2010

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We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians.We consider Hamiltonians H(k,r) that vary slowly with adiabatic parameters r surrounding the defect and belong to any of the ten symmetry classes defined by time-reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topological classes to defect Hamiltonians to the presence of protected gapless modes at the defect. Many examples of line and point defects in three-dimensional systems will be discussed. These can host one dimensional chiral Dirac fermions, helical Dirac fermions, chiral Majorana fermions, and helical Majorana fermions, as well as zero-dimensional chiral and Majorana zero modes. This approach can also be used to classify temporal pumping cycles, such as the Thouless charge pump, as well as a fermion parity pump, which is related to the Ising non-Abelian statistics of defects that support Majorana zero modes. We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians. We consider Hamiltonians H͑k , r͒ that vary slowly with adiabatic parameters r surrounding the defect and belong to any of the ten symmetry classes defined by time-reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topological classes to defect Hamiltonians to the presence of protected gapless modes at the defect. Many examples of line and point defects in three-dimensional systems will be discussed. These can host one dimensional chiral Dirac fermions, helical Dirac fermions, chiral Majorana fermions, and helical Majorana fermions, as well as zero-dimensional chiral and Majorana zero modes. This approach can also be used to classify temporal pumping cycles, such as the Thouless charge pump, as well as a fermion parity pump, which is related to the Ising non-Abelian statistics of defects that support Majorana zero modes. Disciplines Physical Sciences and Mathematics | Physics

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Topological surface states protected from backscattering by chiral spin texture

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Cited by 1,012 publications

References 27 publications

Impact of the Topological Surface State on the Thermoelectric Transport in Sb₂Te₃ Thin Films

Impact of the Topological Surface State on the Thermoelectric Transport in Sb₂Te₃ Thin Films

Anisotropic conductivity in magnetic topological insulators

Topological defects and gapless modes in insulators and superconductors

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Topological surface states protected from backscattering by chiral spin texture

Abstract: SUPPLEMENTARY INFORMATION

Cited by 1,012 publications

References 27 publications

Impact of the Topological Surface State on the Thermoelectric Transport in Sb2Te3 Thin Films

Impact of the Topological Surface State on the Thermoelectric Transport in Sb2Te3 Thin Films

Anisotropic conductivity in magnetic topological insulators

Topological defects and gapless modes in insulators and superconductors

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Product

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Impact of the Topological Surface State on the Thermoelectric Transport in Sb₂Te₃ Thin Films

Impact of the Topological Surface State on the Thermoelectric Transport in Sb₂Te₃ Thin Films