Orbitronics in Two-dimensional Materials

TL;DR

Orbitronics aims to manipulate orbital angular momentum (OAM) currents without relying on spin–orbit coupling, unlocking non-magnetic materials for information processing. The paper surveys the theoretical framework for OHE, OREE, and OT, and examines orbital textures, Bloch orbital magnetization, and their 2D realizations, including topological phases such as orbital Chern insulators and HOTIs in 2D TMDs. It analyzes how 2D materials enable robust OAM transport through orbital topology, symmetry breaking, and heterostructure engineering while discussing disorder and extrinsic contributions that shape real devices. The review identifies promising directions for controllable OAM in 2D systems, including strain, proximity, and magnetic 2D materials, and highlights key challenges in separating orbital from spin signals and achieving long-range OAM propagation.

Abstract

Orbitronics explores the control and manipulation of electronic orbital angular momentum in solid-state systems, opening new pathways for information processing and storage. One significant advantage of orbitronics over spintronics is that it does not rely on spin-orbit coupling, thereby broadening the range of non-magnetic materials that can be utilized for these applications. It also introduces new topological features related to electronic orbital angular momentum, and clarifies some long-standing challenges in understanding experiments that rely on the conventional concept of valley transport. This review highlights recent advances in orbitronics, particularly in relation to two-dimensional materials. We examine the fundamental principles underlying the generation, transport, and dynamics of orbital angular momentum to illustrate how the unique properties of two-dimensional materials can promote orbitronic phenomena. We also outline potential future research directions and address some outstanding questions in this field.

Figures (4)

• Figure 1: OHE in a 2D system. Schematic representation of the orbital Hall effect [Eq.(\ref{['OHE']})]. A longitudinal charge current (black arrow) driven by an external electric field (red arrow) leads to a transverse flow of orbital angular momentum (OAM). This orbital current results in the accumulation of opposite OAM at the lateral edges of the sample, represented by golden arrows and phase rings. The color gradient in the rings indicates the phase structure of the electron wavefunctions associated with nonzero OAM. The splitting of the charge current line is purely pictorial, used to illustrate the opposite deflection of electrons carrying different signs of OAM. No transverse charge current is present.
• Figure 2: Berry and Orbital Berry Curvature in 2H-TMD Monolayers. (a) Schemmatic illustration of the calculated energy bands for non-centrosymmetric 2H-TMD monolayer (a typical massive Dirac material) around the bottom of its conduction band and the top of the valence bands located at ${\bf K}$ and ${\bf K'}$ valleys of Brillouin zone (BZ). The black curve shows the spectrum without considering spin-orbit coupling (SOC). The dashed brown ($s=\uparrow$) and dotted purple ($s=\downarrow$) curves show the spin splitting of the valence bands caused by SOC. (b) The valence band Berry curvature near the valleys of the BZ. (c) The z-component of orbital angular momentum (OAM) near the valleys of the BZ. (d) The valence band orbital Berry curvature near the valleys of the BZ for a 2H-TMD monolayer. In the panels (c) and (d), the blue curves represent the results in the intra-atomic approximation, while the red curves show the results for OAM originating from the magnetic moment of Bloch states Cysne2022. In panels (b)–(d), the SOC of the TMD is not considered, and a spin-degeneracy factor is included in the results for the Berry and orbital Berry curvatures. The low-energy theory of 2H-TMD monolayer with parameters for MoS$_2$ is used in these results.
• Figure 3: OREE in a 2D system. Schematic representation of orbital Rashba-Edelstein Effect [component $\beta_{zx}$ of Eq.(\ref{['OEE2']})]. An electric current passing through the material induces an orbital magnetization (golden arrows) oriented perpendicular to the current. The circulating electrons, driven by the phase gradient of their wavefunctions (color gradient in the rings), give rise to the orbital angular momentum.
• Figure 4: Aspects of electronic structure, lattice symmetry, OAM transport, and topology of 2H-TMDs. (a) Side view of a bilayer of 2H-TMD. $\mathcal{I}$ represents the inversion-symmetry point. (b) The OHC plateau predicted by the low-energy theory for a bilayer of 2H-TMD. The blue curve represents the result obtained using the intra-atomic approximation, while the red curve represents the results derived from the Bloch OMM formulation. The dashed line marks the quantized value of the OHE plateau. (c) The energy spectrum of a MoS$_2$ nanoribbon with zigzag edges reveals OAM-polarized edge states that cross the bulk band and can transport OHC. (d) Energy spectra of triangular nanoflakes of MoS$_2$ with in-gap corner states and the corresponding image of the distribution probability associated with the corner-states wave function. Figures adapted from Refs. Cysne2021aCysne2022Costa2023.