Topological Phases in Two-Dimensional Materials: A Brief Review

Abstract

Topological phases with insulating bulk and gapless surface or edge modes have attracted much attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this review, we mainly focus on the recent progress in the engineering of topologically nontrivial phases (such as ${\mathbb{Z}}_2$ topological insulators, quantum anomalous Hall effects, quantum valley Hall effects \textit{etc.}) in two-dimensional material systems, including quantum wells, atomic crystal layers of elements from group III to group VII, and the transition metal compounds.

Invited review article for Reports on Progress in Physics

References in corpus (127)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Half-Metallic Graphene Nanoribbons
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Topological Crystalline Insulators
• Quantum Spin Hall Effect and Topological Field Effect Transistor in Two-Dimensional Transition Metal Dichalcogenides
• Dissipationless Quantum Spin Current at Room Temperature
• The Valley Hall Effect in MoS2 Transistors
• Valley filter and valley valve in graphene
• High temperature fractional quantum Hall states
• Semiconducting layered blue phosphorus: A computational study
• Valley Dependent Optoelectronics from Inversion Symmetry Breaking
• The electronic properties of bilayer graphene
• Fractional quantum Hall states at zero magnetic field
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Valley-Polarized Metals and Quantum Anomalous Hall Effect in Silicene
• Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps
• Spin-orbit gap of graphene: First-principles calculations
• Dirac materials
• High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator
• Nearly-flat bands with nontrivial topology
• Arsenene: Two-dimensional buckled and puckered honeycomb arsenic systems
• The Quantum Spin Hall Effect: Theory and Experiment
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• Detecting Topological Currents in Graphene Superlattices
• Quantum Anomalous Hall Effect in Hg${}_{1-y}$Mn${}_y$Te Quantum Wells
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• Electronic structures and theoretical modelling of two-dimensional group-VIB transition metal dichalcogenides
• Quantum Anomalous Hall Effect in Graphene from Rashba and Exchange Effects
• Trajectory of Anomalous Hall Effect toward the Quantized State in a Ferromagnetic Topological Insulator
• Topological Mott Insulators
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling
• Scale-Invariant Dissipationless Chiral Transport in Magnetic Topological Insulators beyond the Two-Dimensional Limit
• Topological Anderson Insulator
• Proximity-induced ferromagnetism in graphene revealed by anomalous Hall effect
• Topological confinement in bilayer graphene
• Quantum anomalous Hall effect and related topological electronic states
• Spin Filtered Edge States and Quantum Hall Effect in Graphene
• Graphene valley filter using a line defect
• Electric Field Induced Topological Phase Transition in Two-Dimensional Few-layer Black Phosphorus
• The Rare Two-Dimensional Materials with Dirac Cones
• Quantum Anomalous Hall Effect in Graphene Proximity Coupled to an Antiferromagnetic Insulator
• Intervalley scattering, long-range disorder, and effective time reversal symmetry breaking in graphene
• One-dimensional Topological Edge States of Bismuth Bilayers
• Edge states in Graphene: from gapped flat band to gapless chiral modes
• Scalar spin chirality and quantum Hall effect on a triangular lattice
• Origin of band gaps in graphene on hexagonal boron nitride
• Evidence for crossed Andreev reflection in superconductor-ferromagnet hybrid structures
• Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
• Realistic Time-Reversal Invariant Topological Insulators With Neutral Atoms
• Spin-Valleytronics in Silicene: Quantum-Spin-Quantum-Anomalous Hall Insulators and Single-Valley Semimetals
• Prediction of Near-Room-Temperature Quantum Anomalous Hall Effect on Honeycomb Materials
• Organic Topological Insulators in Organometallic Lattices
• Dissipative Quantum Hall Effect in Graphene near the Dirac Point
• Flat Chern Band in a Two-Dimensional Organometallic Framework
• Epitaxial growth of large-gap quantum spin Hall insulator on semiconductor surface
• High-fidelity transmission of entanglement over a high-loss freespace channel
• Quantum Anomalous Hall State in Bilayer Graphene
• Quantized Anomalous Hall Effects in Skyrmion Crystal
• Electronic Highways in Bilayer Graphene
• Large-Gap Quantum Spin Hall Insulator in single layer bismuth monobromide Bi${}_4$Br${}_4$
• Zero Energy Modes and Gate-Tunable Gap in Graphene on hexagonal Boron Nitride
• Compact Skyrmions, Merons and Bimerons in Thin Chiral Magnetic Films
• Valley-Hall Kink and Edge States in Multilayer Graphene
• Pseudospin valve in bilayer graphene: towards graphene-based pseudospintronics
• Orbital analogue of quantum anomalous Hall effect in $p$-band systems
• Adatoms and clusters of 3d transition metals on graphene: Electronic and magnetic configurations
• Tuning phase transition between quantum spin Hall and ordinary insulating phases
• Spin-Valley Optical Selection Rule and Strong Circular Dichroism in Silicene
• Realizing and Detecting the Haldane's Quantum Hall effect with Ultracold Atoms
• Strained bilayer graphene: Band structure topology and Landau level spectrum
• Room Temperature Quantum Spin Hall Insulators with a Buckled Square Lattice
• New Family of Robust 2D Topological Insulators in van der Waals Heterostructures
• Chern insulators from heavy atoms on magnetic substrates
• Fractionalized Topological Insulators
• The dependence of topological Anderson insulator on the type of disorder
• sd2 Graphene: Kagome Band in Hexagonal lattice
• Spin-orbit coupling and Berry phase with ultracold atoms in 2D optical lattices
• Dirac Cones, Topological Edge States, and Nontrivial Flat Bands in Two-Dimensional Semiconductors with a Honeycomb Nanogeometry
• Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices
• Transport Properties of Graphene Nanoroads in Boron-Nitride Sheets
• Edge and Interfacial States in a 2D Topological Insulator:Bi(111) Bilayer on Bi${}_2$Te${}_2$Se
• Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions
• Functionalized Bismuth Films: Giant Gap Quantum Spin Hall and Valley-Polarized Quantum Anomalous Hall States
• One-Dimensional Edge States with Giant Spin Splitting in a Bismuth Thin Film
• Topological phases in a two-dimensional lattice: Magnetic field versus spin-orbit coupling
• Band topology and quantum spin Hall effect in bilayer graphene
• Perfect Valley Filter in Topological Domain Wall
• Three-dimensional phase diagram of disordered HgTe/CdTe Quantum spin-Hall wells
• Observation of Valley-polarized Landau Levels in Strained Graphene
• Marginality of bulk-edge correspondence for single-valley Hamiltonians
• Quantum Spin Hall Effect in Strip of Stripes Model
• Phase diagram of the Kane-Mele-Coulomb model
• Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetry
• Single-Valley Engineering in Graphene Superlattices
• Quantum spin Hall effect on germanene nanoroad embedded in a completely hydrogenated germanene
• Quantum spin Hall effect induced by electric field in silicene
• Topological states in multi-orbital HgTe honeycomb lattices
• Valley-polarized quantum anomalous Hall phase and disorder induced valley-filtered chiral edge channels
• Quantum Anomalous Hall Effect in Magnetic Insulator Heterostructure
• Disorder-Induced Multiple Transition involving Z2 Topological Insulator
• Topological Phase Transition and Electrically Tunable Diamagnetism in Silicene
• One-dimensional quantum channel in a graphene line defect
• Valley-polarized quantum anomalous Hall phases and tunable topological phase transitions in half-hydrogenated Bi honeycomb monolayers
• Topological phases in gated bilayer graphene: Effects of Rashba spin-orbit coupling and exchange field
• Integer and Fractional Quantum Anomalous Hall Effect in a Strip of Stripes Model
• Correlated spinless fermions on the honeycomb lattice revisited
• Fractional Topological Insulators: from sliding Luttinger Liquids to Chern-Simons theory
• Multiple Quantum Phases in Graphene with Enhanced Spin-Orbit Coupling: From the Quantum Spin Hall Regime to the Spin Hall Effect and a Robust Metallic State
• The edge engineering of topological Bi(111) bilayer
• Topological Crystalline Insulator and Quantum Anomalous Hall States in IV-VI based Monolayers and their Quantum Wells
• Topological phases in Iridium oxide superlattices: quantized anomalous charge or valley Hall insulators
• Quantum anomalous Hall phase in (001) double-perovskite monolayers via intersite spin-orbit coupling
• Quantum Anomalous Hall effect in graphene coupled to skyrmions
• Gate-Tunable Exchange Coupling Between Cobalt Clusters on Graphene
• Ferromagnetism and quantum anomalous Hall effect in one-side-saturated buckled honeycomb lattices
• Size Effects on Transport Properties in Topological Anderson Insulators
• Unbalanced edge modes and topological phase transition in gated trilayer graphene
• Landau Levels in Strained Optical Lattices
• High-Chern-number bands and tunable Dirac cones in $\beta$-graphyne
• The Coexistence and Decoupling of Bulk and Edge States in Disordered Two-dimensional Topological Insulators

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• Valley kink states and topological channel intersections in substrate-integrated photonic circuitry
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• Chirality as Generalized Spin-Orbit Interaction in Spintronics
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• Tuning the Berry curvature in 2D Perovskite
• Emerging chiral edge states from the confinement of a magnetic Weyl semimetal in Co${}_3$Sn${}_2$S${}_2$
• Protected pseudohelical edge states in proximity graphene ribbons and flakes
• Theory and Experimental Investigation of the Quantum Valley Hall Effect
• Experimental evidence of robust acoustic valley Hall edge states in a non-resonant topological elastic waveguide
• Canted Spin Texture and Quantum Spin Hall Effect in WTe2
• Quantum anomalous Hall effect in atomic crystal layers from in-plane magnetization
• Topological carbon materials: a new perspective
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• Designing multi-directional energy-splitters and topological valley supernetworks
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• Classification of topological insulators and superconductors out of equilibrium
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• Two Dimensional Antiferromagnetic Chern Insulator NiRuCl6
• Quantum Spin-Valley Hall Kink States: From Concept to Materials Design
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• Theoretical realization of hybrid Weyl state and associated high catalytic performance for hydrogen evolution in NiSi
• Mixed Weyl semimetals and dissipationless magnetization control in insulators by spin-orbit torques
• Topological Valley Hall Edge State Lasing
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• The valence band energy spectrum of HgTe quantum wells with inverted band structures
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