Model Hamiltonian for topological insulators
TLDR
In this paper, Zhang et al. gave the full microscopic derivation of the model Hamiltonian for the three-dimensional topological insulators in the Ω(n) family of materials.Abstract:
In this paper we give the full microscopic derivation of the model Hamiltonian for the three-dimensional topological insulators in the ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ family of materials (${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ and ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$). We first give a physical picture to understand the electronic structure by analyzing atomic orbitals and applying symmetry principles. Subsequently, we give the full microscopic derivation of the model Hamiltonian introduced by Zhang et al. [Nat. Phys. 5, 438 (2009)] based both on symmetry principles and the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ perturbation theory. Two different types of ${k}^{3}$ terms, which break the in-plane full rotation symmetry down to threefold rotation symmetry, are taken into account. An effective Hamiltonian is derived for the topological surface states. Both bulk and surface models are investigated in the presence of an external magnetic field, and the associated Landau level structure is presented. For a more quantitative fitting to the first principle calculations, we also present a model Hamiltonian including eight energy bands.read more
Citations
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Topological insulators and superconductors
Xiao-Liang Qi,Shou-Cheng Zhang +1 more
TL;DR: Topological superconductors are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors and are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time reversal symmetry.
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Topological Insulator Materials
TL;DR: Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surface states that show up due to a topological character of the bulk wave functions.
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Low-energy effective Hamiltonian involving spin-orbit coupling in silicene and two-dimensional germanium and tin
TL;DR: In this article, the authors derived the low energy effective Hamiltonian involving spin-orbit coupling (SOC) for silicene, which is the analog to the graphene quantum spin Hall effect (QSHE) Hamiltonian.
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Topological Insulator Materials
TL;DR: Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surface states that show up due to a topological character of the bulk wave functions as mentioned in this paper.
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Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4
TL;DR: This work probes quantum transport in MnBi2Te4 thin flakes—a topological insulator with intrinsic magnetic order that becomes ferromagnetic when the sample has an odd number of septuple layers and establishes MnBi 2Te4 as an ideal arena for further exploring various topological phenomena with a spontaneously broken time-reversal symmetry.
References
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Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
TL;DR: In this article, the quantum spin Hall (QSH) effect can be realized in mercury-cadmium telluride semiconductor quantum wells, a state of matter with topological properties distinct from those of conventional insulators.
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Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface
TL;DR: In this article, first-principles electronic structure calculations of the layered, stoichiometric crystals Sb2Te3, Bi2Se3, SbSe3 and BiSe3 were performed.
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Quantum Spin Hall Insulator State in HgTe Quantum Wells
Markus König,Steffen Wiedmann,Steffen Wiedmann,Christoph Brüne,Christoph Brüne,Andreas Roth,Andreas Roth,Hartmut Buhmann,Hartmut Buhmann,Laurens W. Molenkamp,Laurens W. Molenkamp,Xiao-Liang Qi,Xiao-Liang Qi,Shou-Cheng Zhang,Shou-Cheng Zhang +14 more
TL;DR: The quantum phase transition at the critical thickness, d = 6.3 nanometers, was independently determined from the magnetic field–induced insulator-to-metal transition, providing experimental evidence of the quantum spin Hall effect.
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Topological insulators with inversion symmetry
Liang Fu,Charles L. Kane +1 more
TL;DR: In this paper, it was shown that the parity of the occupied Bloch wave functions at the time-reversal invariant points in the Brillouin zone greatly simplifies the problem of evaluating the topological invariants.