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}.

25 pages, 8 figures

References in corpus (39)

• Dissipationless Quantum Spin Current at Room Temperature
• Theory of spin Hall magnetoresistance
• Study of Intrinsic Spin Hall Effect and Orbital Hall Effect in 4d- and 5d- Transition Metals
• Berry phase effect in anomalous thermoelectric transport
• Orbital magnetization in periodic insulators
• On A Proper Definition of Spin Current
• Giant Orbital Hall Effect in Transition Metals: Origin of Large Spin and Anomalous Hall Effects
• Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach
• Quantum Theory of Orbital Magnetization and its Generalization to Interacting Systems
• Orbitronics: Orbital Currents in Solids
• Giant orbital Hall effect and orbital-to-spin conversion in 3d, 5d, and 4f metallic heterostructures
• The insulator/Chern-insulator transition in the Haldane model
• Theory of Current-Induced Angular Momentum Transfer Dynamics in Spin-Orbit Coupled Systems
• Magnetoresistance due to edge spin accumulation
• Giant Intrinsic Spin and Orbital Hall Effects in Sr2MO4 (M=Ru,Rh,Mo)
• Orbital Rashba effect in surface oxidized Cu film
• Vertex Corrections on the Anomalous Hall Effect in Spin-polarized Two-dimensional Electron Gases with Rashba Spin-orbit Interaction
• Microscopic Theory of Rashba Interaction in Magnetic Metal
• Excited states in bilayer graphene quantum dots
• Intrinsic orbital and spin Hall effects in monolayer transition metal dichalcogenides
• Valley Zeeman effect and spin-valley polarized conductance in monolayer MoS${}_2$ in a perpendicular magnetic field
• Orbital Hanle Magnetoresistance in a 3d Transition Metal
• Orbital Hall effect in bilayer transition metal dichalcogenides: From the intra-atomic approximation to the Bloch states orbital magnetic moment approach
• Adiabatically Induced Orbital Magnetization
• Prototypical topological orbital ferromagnet $\gamma$-FeMn
• Nonlinear Valley Hall Effect
• Study of intrinsic spin and orbital Hall effects in Pt based on a (6s, 6p, 5d) tight-binding model
• Dominance of extrinsic scattering mechanisms in the orbital Hall effect: graphene, transition metal dichalcogenides and topological antiferromagnets
• Spin precession and alternating spin polarization in spin-3/2 hole systems
• Intrinsic Hall conductivities induced by the orbital magnetic moment
• Orbital momentum Hall effect in p-doped graphane
• Exploring orbital-charge conversion mediated by interfaces with copper through spin-orbital pumping
• Intrinsic Spin and Orbital Hall Effects in Heavy Fermion Systems
• Role of Disorder in the Intrinsic Orbital Hall Effect
• Disorder in the non-linear anomalous Hall effect of $\mathcal{P}\mathcal{T}$-symmetric Dirac fermions
• Electrical operation of hole spin qubits in planar MOS silicon quantum dots
• Spin-Hall effect due to the bulk states of topological insulators: Extrinsic contribution to the conserved spin current
• Quantum theory of the Intrinsic Orbital Magnetoelectric Effect in itinerant electron systems at finite temperatures
• Orbital gyrotropic magneto-electric effect and its strain engineering in monolayer Nb$X_2$

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