Relativistic empirical tight-binding theory of the energy bands of GeTe, SnTe, PbTe, PbSe, PbS, and their alloys

We study electronic states and topological invariants of (001)-films of topological crystalline insulator (TCI) PbxSn1−xTe. Gapless surface Dirac cones on bulk TCIs become gapped in thin films due to finite-size effect, which is hybridization between those on the top and bottom surfaces. We clarify that the TCI film has the strong finite-size effect as compared to three-dimensional topological insulators such as Bi2Se3. Moreover, the energy gap oscillates with the thickness of film. The oscillation stems from topological phase transitions in two dimensions. The obtained data of the topological invariants and energy gap serve as guide to TCI-device applications.

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“…Based on the 36 × 36 model, 59 we construct a model for (001)-film of IV-VI semiconductors as The explicit forms of and t z are given by…”

Section: Discussionmentioning

confidence: 99%

Topological phase transition in a topological crystalline insulator induced by finite-size effects

et al. 2014

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“…It is important to treat films with an odd and even number of layers separately due to the difference in crystal symmetry: the former has inversion symmetry and the latter doesn't. Our calculations based on the tightbinding model of Lent et al 35 show different band structures for the two cases, as shown in Fig.1. Nonetheless, both are semiconductors with a small fundamental gap located at or near the Γ point, and a much larger band gap at M .…”

mentioning

confidence: 91%

Electrically tunable quantum spin Hall state in topological crystalline insulator thin films

Liu

2015

Phys. Rev. B

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Based on electronic structure calculations and theoretical analysis, we predict the (111) thin films of the SnTe class of three-dimensional (3D) topological crystalline insulators (TCIs) realize the quantum spin Hall phase in a wide range of thickness. The nontrivial topology originates from the inter-surface coupling of the topological surface states of TCIs in the 3D limit. The inter-surface coupling changes sign and gives rise to topological phase transitions as a function of film thickness. Furthermore, this coupling can be strongly affected by an external electric field, hence the quantum spin Hall phase can be effectively tuned under the experimentally accessible electric field.

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“…19,20 More quantitatively accurate models include also s * and d orbitals. 6,[21][22][23] However, no attempts (with the only exception of Ref. 20) have been made to fit the actual effective masses of the electrons and holes near the L-points.…”

Section: Tight-binding Parametrizationmentioning

confidence: 99%

Anomalous suppression of valley splittings in lead salt nanocrystals without inversion center

2012

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We demonstrate that confinement-induced inter-valley splittings of electron energy levels in PbSe and PbS nanocrystals are sensitive to arrangement of atoms within a nanocrystal. The splittings are strongly suppressed for stoichiometric nanocrystals of T d point symmetry lacking a center of inversion as opposed to non-stoichiometric nanocrystals of O h point symmetry having an inversion center. Our findings are supported by both atomistic sp 3 d 5 s * tight-binding calculations and a symmetry analysis.

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Relativistic empirical tight-binding theory of the energy bands of GeTe, SnTe, PbTe, PbSe, PbS, and their alloys

Cited by 53 publications

References 10 publications

Topological phase transition in a topological crystalline insulator induced by finite-size effects

Topological phase transition in a topological crystalline insulator induced by finite-size effects

Electrically tunable quantum spin Hall state in topological crystalline insulator thin films

Anomalous suppression of valley splittings in lead salt nanocrystals without inversion center

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