Orbital Edelstein Effect at Edges: Absence of Bulk-Boundary Correspondence

Core Concepts

The orbital Edelstein effect (OEE), characterized by the accumulation of orbital angular momentum at edges, arises from the specific shape of the edge and the resulting electron motion, independent of bulk properties.

Abstract

This research paper investigates the orbital Edelstein effect (OEE) arising from the inter-atomic contribution of orbital angular momentum (OAM) in various two-dimensional lattice models.

Research Objective: The study aims to examine the OAM texture within edge states and understand the OEE's dependence on edge shape and its relation to higher-order topological insulators (HOTIs).

Methodology: The researchers employed tight-binding calculations to analyze the OAM of edge states in different slab geometries (straight and zigzag) for various models: a simple square lattice, a Chern insulator (π-flux model), and two HOTI models (Benalcazar-Bernevig-Hughes and breathing kagome lattice). They calculated the OAM texture in momentum space and the OAM accumulation under an applied electric field.

Key Findings:

• The presence of well-localized edge states alone does not guarantee a finite OAM texture.
• Zigzag edge geometries, which induce oscillatory electron motion, exhibit finite OAM and OEE, while straight edges do not.
• This suggests an absence of bulk-boundary correspondence for OEE, unlike the orbital Hall effect (OHE).
• OEE is observed in HOTI models, indicating a potential link between higher-order topology and orbital dynamics.

Main Conclusions:

• The shape of the edge significantly influences the OAM texture and the emergence of OEE.
• OEE arises from the self-rotation of localized electrons at edges, independent of bulk properties.
• The study provides direct evidence for the relationship between HOTIs and orbital dynamics.

Significance: This research enhances the understanding of orbital physics in condensed matter, particularly the role of edge geometry in OAM dynamics and its implications for OEE. It also sheds light on the connection between HOTIs and orbital effects, opening avenues for further exploration in this area.

Limitations and Future Research: The study primarily focuses on non-interacting electron models. Incorporating electron-electron interactions and orbital relaxation dynamics could provide a more comprehensive understanding of OEE in real materials. Further investigation into the interplay between OEE and OHE, especially in systems with broken symmetries, is also warranted.

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Orbital Edelstein effect of electronic itinerant orbital motion at edges

by Jongjun M. L... at arxiv.org 11-04-2024

https://arxiv.org/pdf/2411.00353.pdf

Deeper Inquiries

How would the incorporation of electron-electron interactions and spin-orbit coupling affect the observed OAM textures and OEE in these models?

Incorporating electron-electron interactions and spin-orbit coupling (SOC) would significantly enrich the physics of OAM textures and OEE, pushing the system beyond the non-interacting picture. Here's a breakdown of their potential effects:
Electron-electron interactions:

Modification of band structure: Interactions can renormalize the band structure, potentially shifting the energy levels and group velocities of edge states. This could enhance or suppress the OEE depending on the specific interaction details.
Emergent phases: Strong interactions might drive the system into novel phases with exotic properties. For instance, in the presence of strong correlations, the system could exhibit a Mott insulating phase, fundamentally altering the electronic structure and potentially quenching the OEE. Conversely, interactions could give rise to unconventional superconducting states, where the interplay of OAM and superconductivity could lead to novel phenomena.
Many-body effects on OAM: Interactions could modify the OAM operator itself, leading to a renormalization of the OAM texture. This could be particularly relevant in systems with strong correlations, where the single-particle picture breaks down.
Spin-orbit coupling:

Entanglement of spin and orbital degrees of freedom: SOC directly couples the spin and orbital degrees of freedom, leading to intertwined spin and orbital transport phenomena. This could manifest as a spin-orbital Edelstein effect, where an applied electric field generates a spin accumulation at the edges, in addition to the OAM accumulation.
Modification of topological properties: SOC can induce topological phase transitions, potentially transforming a trivial insulator into a topological insulator or vice versa. This could drastically alter the edge state structure and consequently the OEE.
Anisotropic OEE: The specific form of SOC (e.g., Rashba, Dresselhaus) can introduce anisotropy in the OEE, making the response dependent on the direction of the applied electric field.
Investigating these effects would require advanced theoretical techniques beyond the simple tight-binding approach, such as mean-field theory, dynamical mean-field theory, or tensor network methods. These methods could capture the interplay of interactions, SOC, and OAM, providing a more complete understanding of the OEE in realistic materials.

Could the lack of bulk-boundary correspondence in OEE be exploited for novel device functionalities, particularly in spintronics or valleytronics?

The lack of bulk-boundary correspondence in OEE, where the edge response is decoupled from bulk properties, presents intriguing possibilities for device engineering, particularly in spintronics and valleytronics:
Spintronics:

Edge-confined spin manipulation: By carefully designing the edge geometry and applying electric fields, one could selectively manipulate spin accumulation at specific edges without affecting the bulk spin polarization. This could lead to novel spin transistors or logic gates with enhanced functionality and reduced power consumption.
Enhanced spin-orbit torques: The OEE-induced spin accumulation at edges could generate significant spin-orbit torques on adjacent magnetic layers. This could enable efficient magnetization switching using electric fields, paving the way for low-power spintronic memory and logic devices.
Valleytronics:

Valley filtering and separation: In materials with multiple valleys, the OEE could be employed to selectively populate or deplete specific valleys at the edges. This valley filtering effect could be utilized to create valleytronic devices, where information is encoded in the valley degree of freedom.
Valley-dependent OEE: In systems with valley-contrasting OAM textures, the OEE could exhibit a valley dependence, leading to different responses for different valleys. This could be exploited for valley-selective charge-to-spin conversion or spin current generation.
Furthermore, the edge-confined nature of OEE could be advantageous for miniaturization, as it allows for the realization of functionalities within a smaller footprint compared to bulk-based effects. However, challenges remain in controlling and characterizing the OEE at the nanoscale, requiring further experimental and theoretical efforts to fully exploit its potential for technological applications.

If the universe can be considered a closed system with boundaries, how might the concept of "edge states" in condensed matter physics offer insights into cosmological phenomena?

While highly speculative, drawing parallels between the universe and condensed matter systems with boundaries could potentially offer intriguing insights into cosmological phenomena. Here are a few speculative ideas:

Cosmic "edge states" and dark energy: If the universe possesses boundaries, could there exist cosmological analogs of "edge states" localized near these boundaries? These hypothetical "cosmic edge states" might possess unique properties and interact differently with the known forces, potentially contributing to the observed dark energy or dark matter.
Topological defects as "edges": Cosmological topological defects, like cosmic strings or domain walls, could be considered as "edges" within the fabric of spacetime. Just as edge states in condensed matter systems exhibit unique properties, these cosmological "edges" might harbor exotic physics and potentially influence the evolution of the early universe.
Holographic principle and boundary information: The holographic principle suggests that the information content of a region of space is encoded on its boundary. The concept of "edge states" in condensed matter systems, where information about the system's topology is encoded in the edge, might offer a tangible analogy for understanding how information is stored and processed at the boundaries of the universe.
However, it's crucial to emphasize that these are highly speculative connections. The energy scales and physics governing the universe are vastly different from those in condensed matter systems. Nevertheless, exploring such analogies, even if speculative, could potentially spark new avenues of research and lead to a deeper understanding of both the cosmos and the fundamental laws of physics.