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

Rhonald Burgos Atencia, Amit Agarwal, Dimitrie Culcer

Published 2024-03-11Version 1

The investigation of orbital angular momentum (OAM) of delocalised Bloch electrons has significantly 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, mainly focusing on key concepts and non-equilibrium systems, laying the groundwork for the thriving field of {\it orbitronics}. We begin by dissecting the conventional understanding of equilibrium OAM and identify two primary contributions. The {\it atomic}-OAM contribution is rooted in the angular momentum of parent atomic orbitals and is prevalent in inversion-symmetric systems. The other {\it itinerant}-OAM contribution arises from the rotation of the electron wave packet around its center of mass and it is dominant in systems lacking inversion symmetry. Following this, we explore recent theoretical and experimental developments in out-of-equilibrium systems. We specifically 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. Beyond discussing the current excitement and challenges in this rapidly evolving field, we highlighted the future prospects of {\it orbitronics}.