Topological insulators from the Perspective of first-principles calculations

Abstract

Topological insulators are new quantum states with helical gapless edge or surface states inside the bulk band gap.These topological surface states are robust against the weak time-reversal invariant perturbations, such as lattice distortions and non-magnetic impurities. Recently a variety of topological insulators have been predicted by theories, and observed by experiments. First-principles calculations have been widely used to predict topological insulators with great success. In this review, we summarize the current progress in this field from the perspective of first-principles calculations. First of all, the basic concepts of topological insulators and the frequently-used techniques within first-principles calculations are briefly introduced. Secondly, we summarize general methodologies to search for new topological insulators. In the last part, based on the band inversion picture first introduced in the context of HgTe, we classify topological insulators into three types with s-p, p-p and d-f, and discuss some representative examples for each type.

10 pages, 7 figures

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• Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice
• Ideal Weyl semimetals in the chalcopyrites CuTlSe2, AgTlTe2, AuTlTe2 and ZnPbAs2
• Theoretical Prediction of Two-Dimensional Functionalized MXene Nitrides as Topological Insulators
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• Exploration and prediction of topological electronic materials based on first-principles calculations
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• A single nodal loop of accidental degeneracies in minimal symmetry: triclinic CaAs${}_3$
• The rhombohedral Sb2Se3 is also an intrinsic topological insulator
• Photoemission Spectroscopic Evidence for the Dirac Nodal Line in Monoclinic Semimetal SrAs${}_3$
• Mesoscopic transport in two-dimensional topological insulators
• Topological insulators based on HgTe
• Ab initio study of topological surface states of strained HgTe
• Topological surface states on Bi(111) based on empirical tight-binding calculations
• Two distinct topological phases in the mixed valence compound YbB6 and its differences from SmB6
• VASP2KP: kp models and Lande g-factors from ab initio calculations
• SmO thin films: a flexible route to correlated flat bands with nontrivial topology
• Two Dimensional Multigap Superconductivity in Bulk 2H-TaSSe
• Interacting topological mirror excitonic insulator in one dimension
• Transformation of an energy spectrum and wave functions in the crossover from two- to three-dimensional topological insulator in HgTe quantum wells: long and thorny way
• Interplay between spin-orbit coupling and crystal-field effect in topological insulators
• A programmable $k\cdot p$ Hamiltonian method and application to magnetic topological insulator MnBi${}_2$Te${}_4$
• A first-principles investigation of band inversion in topologically nontrivial Na2AgX (X= As, Sb and Bi) full Heusler compounds