Exploration and prediction of topological electronic materials based on first-principles calculations

Abstract

The class of topological insulator materials is one of the frontier topics of condensed matter physics. The great success of this field is due to the conceptual breakthroughs in theories for topological electronic states and is strongly motivated by the rich variety of material realizations, thus making the theories testable, the experiments operable, and the applications possible. First-principles calculations have demonstrated unprecedented predictive power for material selection and design. In this article, we review recent progress in this field with a focus on the role of first-principles calculations. In particular, we introduce the Wilson loop method for the determination of topological invariants and discuss the band inversion mechanism for the selection of topological materials. Recent progress in quantum anomalous Hall insulators, large-gap quantum spin Hall insulators, and correlated topological insulators are also covered.

29 pages, 3 figures

References in corpus (28)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Topological Insulators with Inversion Symmetry
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Topological Crystalline Insulators
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Nearly-flat bands with nontrivial topology
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Quantum Anomalous Hall Effect in Hg${}_{1-y}$Mn${}_y$Te Quantum Wells
• The space group classification of topological band insulators
• Topological Mott Insulators
• Fractional quantum Hall effect in the absence of Landau levels
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Wannier representation of Z_2 topological insulators
• Spectral and Fermi surface properties from Wannier interpolation
• Correlated Topological Insulators with Mixed Valence
• Helical edge and surface states in HgTe quantum wells and bulk insulators
• Fractional topological insulators in three dimensions
• Electronic Structures and Surface States of Topological Insulator Bi${}_{1-x}$Sb${}_x$
• Ab Initio Models of Dislocations
• Determining topological order from a local ground state correlation function

Cited by in corpus (13)

• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Topological Node-Line Semimetal in Three Dimensional Graphene Networks
• Theoretical Prediction of Two-Dimensional Functionalized MXene Nitrides as Topological Insulators
• Quantum Spin Hall Effect in 2D Transition Metal Dichalcogenide Haeckelites
• Evidence of topological insulator state in the semimetal LaBi
• Topological Insulator to Dirac Semimetal Transition Driven by Sign Change of Spin-Orbit Coupling in Thallium Nitride
• Observation of Open-Orbit Fermi Surface Topology in Extremely Large Magnetoresistance Semimetal MoAs${}_2$
• Surface-state-dominated transport in crystals of the topological crystalline insulator In-doped Pb${}_{1-x}$Sn${}_x$Te
• Prediction of Topological Crystalline Insulator and Topological Phase Transitions in Two-dimensional PbTe Films
• Long-Time Magnetic Relaxation in Antiferromagnetic Topological Material EuCd${}_2$As${}_2$
• Electronic structure and open-orbit Fermi surface topology in isostructural semimetals NbAs${}_2$ and W${}_2$As${}_3$ with extremely large magnetoresistance
• Spectroscopic Evidence on Realization of a Genuine Topological Nodal Line Semimetal in LaSbTe
• Emergent topological states via digital (001) oxide superlattices