Berry phase effects on electronic properties
2009/07/12 by Di Xiao, Ming-Che Chang, Qian Niu · 5,259 citations
Materials Science · Physics and Astronomy · #Berry connection and curvature #Condensed matter physics #Electron #Geometric phase #Graphene research and applications #Physics #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Semiclassical physics #Theoretical physics #Topological Materials and Phenomena #Wave function #cond-mat.mes-hall #cond-mat.mtrl-sci
paper · pdf · doi:10.1103/revmodphys.82.1959
published in Reviews of Modern Physics 82(3), 1959-2007 (American Physical Society) · 48 pages, 16 figures, submitted to RMP
arxiv created 2009/07/12 · openalex publication_date 2010/07/06 · arxiv updated 2010/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Abstract
Ever since its discovery the notion of Berry phase has permeated through all branches of physics. Over the past three decades it was gradually realized that the Berry phase of the electronic wave function can have a profound effect on material properties and is responsible for a spectrum of phenomena, such as polarization, orbital magnetism, various (quantum, anomalous, or spin) Hall effects, and quantum charge pumping. This progress is summarized in a pedagogical manner in this review. A brief summary of necessary background is given and a detailed discussion of the Berry phase effect in a variety of solid-state applications. A common thread of the review is the semiclassical formulation of electron dynamics, which is a versatile tool in the study of electron dynamics in the presence of electromagnetic fields and more general perturbations. Finally, a requantization method is demonstrated that converts a semiclassical theory to an effective quantum theory. It is clear that the Berry phase should be added as an essential ingredient to our understanding of basic material properties.
Citations
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- Anomalous ferromagnetism and magneto-optical Kerr effect in semiconducting double perovskite Ba2NiOsO6 and its (111) (Ba2NiOsO6)/(BaTiO3)10 superlattice
- Magnetotransport in multi-Weyl semimetals: a kinetic theory approach
- Cold atoms meet lattice gauge theory
- Spontaneous Quantum Hall States in Chirally Stacked Few-Layer Graphene Systems
- Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
- Chiral Phonons at High-Symmetry Points in Monolayer Hexagonal Lattices
- BCS-BEC crossover in spin-orbit-coupled two-dimensional Fermi gases
- Spin-orbit-coupled Bose gases at finite temperatures
- Determination of the Spin Axis in Quantum Spin Hall Insulator Candidate Monolayer WTe2
- Gapped Dirac cones and spin texture in thin film topological insulator
- Spectrum Collapse of Disordered Dirac Landau Levels as Topological Non-Hermitian Physics
- A impessoalidade e a magistratura em Sant'Ana do Livramento
- Gauge potential formulations of the spin Hall effect in graphene
- Quantum-limit Hall effect with large carrier density in topological semimetals
- Topological characterization of one-dimensional open fermionic systems
- Gate-tunable topological flat bands in twisted monolayer-bilayer graphene
- Berry Curvature Effects on Quasiparticle Dynamics in Superconductors
- Analytically solvable model to the spin Hall effect with Rashba and Dresselhaus spin-orbit couplings
- Carboneyane: A nodal line topological carbon with sp−sp2 −sp3 chemical bonds
- Berry phase jumps and giant nonreciprocity in Dirac quantum dots
- Conserved current of nonconserved quantities
- Characterization of topological phase transitions via topological properties of transition points
- Monitoring nonadiabatic avoided crossing dynamics in molecules by ultrafast X-ray diffraction
- Topological phases of a dimerized Fermi–Hubbard model for semiconductor nano-lattices
- Exposing the quantum geometry of spin-orbit-coupled Fermi superfluids
- Correlation length, universality classes, and scaling laws associated with topological phase transitions
- Optically Controlled Orbitronics on a Triangular Lattice
- Su-Schrieffer-Heeger model inspired acoustic interface states and edge states
- Anomalous Bloch oscillations in one-dimensional parity-breaking periodic potentials
- Properties and application of SO(3) Majorana representation of spin: Equivalence with Jordan-Wigner transformation and exact Z2 gauge theories for spin models
- Pseudospin order in monolayer, bilayer and double-layer graphene
- Tuning Anti-Klein to Klein Tunneling in Bilayer Graphene
- Topological Hall effect in inhomogeneous superconductors
- Fulde-Ferrell-Larkin-Ovchinnikov state to topological superfluidity transition in bilayer spin-orbit-coupled degenerate Fermi gases
- Holonomic Quantum Control by Coherent Optical Excitation in Diamond
- Quantum Geometry of Finite XY Chains: A Comparison of Neveu-Schwarz and Ramond Sectors
- Topological spin Hall effect in antiferromagnetic skyrmions
- Novel phenomena in transition-metal oxide thin films and heterostructures with strong correlations and spin-orbit coupling
- Behavior of Floquet Topological Quantum States in Optically Driven Semiconductors
- Accessing quasi-flat f-bands to harvest large Berry curvature in NdGaSi
- Noncoplanar multiple-Q spin textures by itinerant frustration: Effects of single-ion anisotropy and bond-dependent anisotropy
- Band structure and topological properties of graphene in a superlattice spin exchange field
- Antiferromagnetic chiral spin density wave and strain-induced Chern insulator in the square lattice Hubbard model with frustration
- Valley-Hall-like second-order photonic topological insulators in Kagome lattice
- Complementary local-global approach for phonon mode connectivities
- Switchable valley filter based on a graphene p−n junction in a magnetic field
- Nontrivial Berry phase in magnetic BaMnSb 2 semimetal
- Semiconductor Bloch-equations formalism: Derivation and application to high-harmonic generation from Dirac fermions
- Quantum geometry from the Moyal product: quantum kinetic equation and non-linear response
- Topological aspects in the photonic-crystal analog of single-particle transport in quantum Hall systems
- Symmetry-protected spinful magnetic Weyl nodal loops and multi-Weyl nodes in 5dn cubic double perovskites (n=1,2)
- Berry curvature-induced transport signature for altermagnetic order
- Effects of Berry Curvature and Orbital Magnetic Moment in the Magnetothermoelectric Transport of Bloch Electron Systems
- Engineering photonic environments for two‐dimensional materials
- Non-reciprocal waves in two-dimensional electron systems with temperature gradient
- Breakdown of Bulk-Radiation Correspondence in Radiative Photonic Lattices
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