Orbital angular momentum of Bloch electrons: equilibrium formulation, magneto-electric phenomena, and the orbital Hall effect

Abstract

The investigation of orbital angular momentum (OAM) of delocalised Bloch electrons has advanced our understanding of magnetic, transport, and optical phenomena in crystals, drawing widespread interest across various materials science domains, from metals and semiconductors to topological and magnetic materials. Here, we review OAM dynamics in depth, focusing on key concepts and non-equilibrium systems, and laying the groundwork for the thriving field of {\it orbitronics}. We review briefly the conventional understanding of the equilibrium OAM based on the modern theory of orbital magnetisation. Following this, we explore recent theoretical and experimental developments in out-of-equilibrium systems. We focus on the generation of an OAM density via the orbital magneto-electric, or Edelstein effect, the generation of an OAM current via the orbital Hall effect, the orbital torque resulting from them, along with their reciprocal non-equilibrium counterparts -- the inverse orbital Edelstein and inverse orbital Hall effects, as well as OAM conservation. We discuss the most salient achievements and the most pressing challenges in this rapidly evolving field, and in closing we highlight the future prospects of {\it orbitronics}.

arXiv comment25 pages, 8 figures

References in corpus (168)

• Spintronics: Fundamentals and applications
• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Berry Phase Effects on Electronic Properties
• Spin torque switching with the giant spin Hall effect of tantalum
• Maximally localized Wannier functions: Theory and applications
• Dissipationless Quantum Spin Current at Room Temperature
• Spin Torque Ferromagnetic Resonance Induced by the Spin Hall Effect
• Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
• Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
• Intrinsic quantized anomalous Hall effect in a moiré heterostructure
• Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
• Spin Hall Magnetoresistance Induced by a Non-Equilibrium Proximity Effect
• Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
• Graphene Bilayers with a Twist
• Theory of spin Hall magnetoresistance
• Observation of the nonlinear Hall effect under time reversal symmetric conditions
• Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moiré Superlattice
• The Quantum-Mechanical Position Operator in Extended Systems
• Study of Intrinsic Spin Hall Effect and Orbital Hall Effect in 4d- and 5d- Transition Metals
• Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands
• Berry phase effect in anomalous thermoelectric transport
• Berry phase correction to electron density of states in solids
• Roadmap of spin-orbit torques
• Comparative Measurements of Inverse Spin Hall and Magnetoresistance in YIG|Pt and YIG|Ta
• Intrinsic Spin and Orbital Hall Effects from Orbital Texture
• Orbital magnetization in periodic insulators
• Suppression of the Persistent Spin Hall Current by Defect Scattering
• On A Proper Definition of Spin Current
• Nonlinear Hall Effects
• Observation of the orbital Hall effect in a light metal Ti
• Giant Orbital Hall Effect in Transition Metals: Origin of Large Spin and Anomalous Hall Effects
• Electrical switching of magnetic order in an orbital Chern insulator
• Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and metals
• Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach
• Harnessing non-local orbital-to-spin conversion of interfacial orbital currents for efficient spin-orbit torques
• Gigantic intrinsic orbital Hall effects in weakly spin-orbit coupled metals
• Berry phase, hyperorbits, and the Hofstadter spectrum
• Quantum Theory of Orbital Magnetization and its Generalization to Interacting Systems
• Orbitronics: the Intrinsic Orbital Hall Effect in p-Doped Silicon
• Spin-orbit driven ferromagnetic resonance: A nanoscale magnetic characterisation technique
• Orbitronics: Orbital Currents in Solids
• Orbital-Angular-Momentum Based Origin of Rashba-Type Surface Band Splitting
• Disorder-induced nonlinear Hall effect with time-reversal symmetry
• Orbital Torque: Torque Generation by Orbital Current Injection
• Intrinsic nonlinear Hall effect in antiferromagnetic tetragonal CuMnAs
• Gyrotropic magnetic effect and the magnetic moment on the Fermi surface
• Quantum valley Hall effect, orbital magnetism, and anomalous Hall effect in twisted multilayer graphene systems
• Diffuse transport and spin accumulation in a Rashba two-dimensional electron gas
• Observation of long-range orbital transport and giant orbital torque
• Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models
• Giant orbital Hall effect and orbital-to-spin conversion in 3d, 5d, and 4f metallic heterostructures
• Imaging orbital ferromagnetism in a moiré Chern insulator
• Valley Magnetoelectricity in Single-Layer MoS2
• Observation of the Orbital Rashba-Edelstein Magnetoresistance
• Hanle Magnetoresistance in Thin Metal Films with Strong Spin-Orbit Coupling
• Strain-engineering of Berry curvature dipole and valley magnetization in monolayer MoS${}_2$
• Theories for the correlated insulating states and quantum anomalous Hall phenomena in twisted bilayer graphene
• The insulator/Chern-insulator transition in the Haldane model
• Magneto-Optical Detection of the Orbital Hall Effect in Chromium
• Magneto-Optical Detection of the Spin Hall Effect in Pt and W Thin Films
• Gyrotropic effects in trigonal tellurium studied from first principles
• Chiral orbital-angular-momentum in the surface states of Bi2Se3
• Theory of Current-Induced Angular Momentum Transfer Dynamics in Spin-Orbit Coupled Systems
• Berry curvature dipole senses topological transition in a moiré superlattice
• Disentangling orbital and valley Hall effects in bilayers of transition metal dichalcogenides
• Topological-chiral magnetic interactions driven by emergent orbital magnetism
• Orbital Hall effect as an alternative to valley Hall effect in gapped graphene
• Quantum theory of the nonlinear Hall effect
• Non-trivial charge-to-spin conversion in ferromagnetic metal/Cu/Al2O3 by orbital transport
• Magnetoresistance due to edge spin accumulation
• Platinum thickness dependence of the inverse spin-Hall voltage from spin pumping in a hybrid YIG/Pt system
• Symmetry and Quantum Kinetics of the Non-linear Hall Effect
• Surface orbitronics: new twists from orbital Rashba physics
• Orbital Edelstein effect as a condensed-matter analog of solenoid
• Giant Intrinsic Spin and Orbital Hall Effects in Sr2MO4 (M=Ru,Rh,Mo)
• Orbital Rashba effect in surface oxidized Cu film
• Time-domain observation of ballistic orbital-angular-momentum currents with giant relaxation length in tungsten
• Giant Orbital Magneto-electric effect and Current-driven Magnetization Switching in Twisted Bilayer Graphene
• Spin and Valley States in Gate-defined Bilayer Graphene Quantum Dots
• Extrinsic spin Hall effect induced by resonant skew scattering in graphene
• Imaging Chern mosaic and Berry-curvature magnetism in magic-angle graphene
• Coherent wave-packet evolution in coupled bands
• Orbitally Dominated Rashba-Edelstein Effect in Noncentrosymmetric Antiferromagnets
• Nonlinear anomalous Hall effect for Néel vector detection
• Intrinsic orbital moment and prediction of a large orbital Hall effect in the 2D transition metal dichalcogenides
• Nonlinear Hall effect with time-reversal symmetry: Theory and material realizations
• Nonexistence of intrinsic spin currents
• Detection of long-range orbital-Hall torques
• Role of Berry phase theory for describing orbital magnetism: From magnetic heterostructures to topological orbital ferromagnets
• Theory of spin Hall magnetoresistance (SMR) and related phenomena
• Vertex Corrections on the Anomalous Hall Effect in Spin-polarized Two-dimensional Electron Gases with Rashba Spin-orbit Interaction
• Orbital Hall Insulating Phase in Transition Metal Dichalcogenide Monolayers
• Quantum geometry induced second harmonic generation
• Wannier-based calculation of the orbital magnetization in crystals
• A single hole spin with enhanced coherence in natural silicon
• Spin and orbital Edelstein effect in an oxide two-dimensional electron gas: theory and application to AlO${}_x$/SrTiO${}_3$
• Microscopic Theory of Rashba Interaction in Magnetic Metal
• First-principles theory of the orbital magnetization
• Excited states in bilayer graphene quantum dots
• Intrinsic orbital and spin Hall effects in monolayer transition metal dichalcogenides
• Inter-band Coherence Response to Electric Fields in Crystals
• Valley Zeeman effect and spin-valley polarized conductance in monolayer MoS${}_2$ in a perpendicular magnetic field
• Anomalous Hall effect with massive Dirac fermions
• Voltage-Controlled Magnetic Reversal in Orbital Chern Insulators
• Unveiling the mechanisms of the spin Hall effect in Ta
• Orbital Hanle Magnetoresistance in a 3d Transition Metal
• Connecting Higher-Order Topology with the Orbital Hall Effect in Monolayers of Transition Metal Dichalcogenides
• Tunable Valley Splitting due to Topological Orbital Magnetic Moment in Bilayer Graphene Quantum Point Contacts
• Orbital Hall effect in bilayer transition metal dichalcogenides: From the intra-atomic approximation to the Bloch states orbital magnetic moment approach
• Mixed topological semimetals driven by orbital complexity in two-dimensional ferromagnets
• Recent advances in hole-spin qubits
• Intrinsic Nonlinear Spin Magnetoelectricity in Centrosymmetric Magnets
• Magnetoelectric Effects in Gyrotropic Superconductors
• Designing spin and orbital sources of Berry curvature at oxide interfaces
• Tunable valley splitting and bipolar operation in graphene quantum dots
• Topologically non-trivial valley states in bilayer graphene quantum point contacts
• Valley Zeeman effect and Landau levels in Two-Dimensional Transition Metal Dichalcogenides
• Evidence of orbital ferromagnetism in twisted bilayer graphene aligned to hexagonal boron nitride
• Influence of minivalleys and Berry curvature on electrostatically induced quantum wires in gapped bilayer graphene
• Theory of Spin Hall Magnetoresistance from a Microscopic Perspective
• Adiabatically Induced Orbital Magnetization
• Time-Reversal-Even Nonlinear Current Induced Spin Polarization
• Prototypical topological orbital ferromagnet $\gamma$-FeMn
• Nonlinear Valley Hall Effect
• Anomalous Hall effect in 2D Rashba ferromagnet
• Study of intrinsic spin and orbital Hall effects in Pt based on a (6s, 6p, 5d) tight-binding model
• Thermoelectric Generation of Orbital Magnetization in Metals
• Semiclassical equations of motion for disordered conductors: extrinsic interband velocity, corrected collision integral and spin-orbit torques
• Dominance of extrinsic scattering mechanisms in the orbital Hall effect: graphene, transition metal dichalcogenides and topological antiferromagnets
• Orbital Hall effect and orbital edge states caused by s electrons
• Spin precession and alternating spin polarization in spin-3/2 hole systems
• Orbital Hall physics in two-dimensional Dirac materials
• Colossal orbital-Edelstein effect in non-centrosymmetric superconductors
• Intrinsic Hall conductivities induced by the orbital magnetic moment
• Orbital magnetoelectric effect in zigzag nanoribbons of p-band systems
• Orbital momentum Hall effect in p-doped graphane
• Current-induced orbital magnetization in systems without inversion symmetry
• Giant efficiency of long-range orbital torque in Co/Nb bilayers
• Exploring orbital-charge conversion mediated by interfaces with copper through spin-orbital pumping
• Intrinsic Spin and Orbital Hall Effects in Heavy Fermion Systems
• Quantum Kinetic Theory of Nonlinear Optical Currents: Finite Fermi surface and Fermi sea contributions
• Role of Disorder in the Intrinsic Orbital Hall Effect
• Berry curvature induced nonlinear magnetoresistivity in two dimensional systems
• Orbital magnetoelectric effect in nanoribbons of transition metal dichalcogenides
• Orbital Rashba effect as a platform for robust orbital photocurrents
• Imaging the valley and orbital Hall effect in monolayer MoS2
• Spin supercurrent in two-dimensional superconductors with Rashba spin-orbit interaction
• Kinetic orbital moments and nonlocal transport in disordered metals with nontrivial geometry
• Disorder in the non-linear anomalous Hall effect of $\mathcal{P}\mathcal{T}$-symmetric Dirac fermions
• X-ray circular dichroism versus orbital magnetization
• Intrinsic Superspin Hall Current
• Orbital magnetic susceptibility of graphene and MoS2
• Magneto-orbital effect without spin-orbit interactions --- noncentrosymmetric zeolite-templated carbon structure
• Optical rotation in thin chiral/twisted materials and the gyrotropic magnetic effect
• Topological nature of the proper spin current and the spin-Hall torque
• Giant surface Edelstein effect in $d$-wave superconductors
• Electrical operation of hole spin qubits in planar MOS silicon quantum dots
• Quantum theory of the Intrinsic Orbital Magnetoelectric Effect in itinerant electron systems at finite temperatures
• Kinetic magnetoelectric effect in topological insulators
• Spin-Hall effect due to the bulk states of topological insulators: Extrinsic contribution to the conserved spin current
• Orbital gyrotropic magneto-electric effect and its strain engineering in monolayer Nb$X_2$
• Non-conservation of the valley density and its implications for the observation of the valley Hall effect
• Low-dissipation edge currents without edge states
• Bulk photospin effect: Calculation of electric spin susceptibility to second order in an electric field
• Green function theory of orbital magnetic moment of interacting electrons in solids
• Semiclassical kinetic theory for systems with non-trivial quantum geometry and the expectation value of physical quantities
• Modern Theory for the Orbital Moment in a Superconductor
• Magnetoresistance in Noncentrosymmetric Two-dimensional Systems

Cited by in corpus (24)

• Role of Disorder in the Intrinsic Orbital Hall Effect
• Topological orbital Hall effect caused by skyrmions and antiferromagnetic skyrmions
• Planar Hall Effect in Quasi-Two-Dimensional Materials
• Orbital Hall Responses in Disordered Topological Materials
• Quantum correction to the orbital Hall effect
• The Streda Formula for Floquet Systems: Topological Invariants and Quantized Anomalies from Cesaro Summation
• Dominant orbital magnetization in the prototypical altermagnet MnTe
• Orbital origin of fourfold anisotropic magnetoresistance in Dirac materials
• Intrinsic nonlinear Nernst and Seebeck effect
• Spin and orbital Edelstein effect in spin-orbit coupled noncentrosymmetric superconductor
• Topological Nature of Orbital Chern Insulators
• Symmetry-driven Intrinsic Nonlinear Pure Spin Hall Effect
• Orbital magnetization in Sierpinski fractals
• Planar Nernst effect from hidden band geometry in layered two-dimensional materials
• Orbital currents in lattice multiorbital systems: Continuity equation, torques, and RKKY interaction
• Orbital magnetization from interface reflections in a conductor with charge current
• Orbital splitter effect and spatial resolution of current-induced orbital accumulation
• Odd-parity longitudinal magnetoconductivity in time-reversal symmetry broken materials
• Average density of Bloch electrons in a homogeneous magnetic field: A second-order response
• Charge-to-spin conversion in epitaxial and polycrystalline Bi and Bi/Ag layers
• Ge as an orbitronic platform: giant in-plane orbital magneto-electric effect in a 2-dimensional hole gas
• Semiclassical theory for the orbital magnetic moment of superconducting quasiparticles
• Quantum Christoffel Nonlinear Magnetization
• Quantum geometric map of magnetotransport