Non-equilibrium angular momentum selectivity and filtering in chiral carbon nanotubes

Abstract: Carbon nanotubes (CNTs) constitute a highly tunable platform for probing the interplay between structural chirality and quantum transport in quasi-one-dimensional systems. Here, we perform a systematic study of the non-equilibrium orbital response across a broad set of metallic and semiconducting chiral CNTs. We find that the orbital Edelstein susceptibility depends strongly on both chirality and nanotube diameter, revealing that the orbital response cannot be captured by a universal scaling law. Instead, distinct families of CNTs emerge, forming characteristic orbital-response branches uniquely determined by the chiral wrapping vector. We further investigate the role of metallic contacts on orbital-current generation and orbital selectivity. While metallic CNTs rapidly recover their intrinsic orbital response away from the contact region, semiconducting CNTs display pronounced oscillatory behavior arising from interference between transport channels carrying different angular momenta injected by wide-band metallic contacts. Finally, by incorporating angular correlations into the contact self-energy, we demonstrate that chiral CNTs can operate as efficient orbital-angular-momentum filters, selectively transmitting orbitally textured electronic states in accordance with the crystal angular momentum of the propagating bands.

• The paper demonstrates a non-universal, chirality-dependent orbital Edelstein response in CNTs, with responses varying by up to a factor of two across 86 chiralities.
• It employs NEGF and Landauer–Büttiker methods to reveal how contact geometry and wrapping symmetry critically shape orbital magnetization profiles.
• It introduces an angular momentum filtering mechanism that achieves near-unity selectivity for electron transmission, positioning CNTs for orbitronic applications.

Non-equilibrium Angular Momentum Selectivity and Filtering in Chiral Carbon Nanotubes

Introduction

This work presents a comprehensive theoretical analysis of the non-equilibrium orbital response in chiral carbon nanotubes (CNTs), with a focus on current-driven orbital Edelstein effects and angular momentum filtering. The investigation advances the microscopic understanding of chirality-induced orbital selectivity (CIOS) by systematically characterizing both metallic and semiconducting CNT families across 86 distinct chiralities, including detailed consideration of contact effects and angular momentum–resolved transport.

Chirality-Dependent Orbital Transport

The study rigorously quantifies the orbital Edelstein susceptibility, $\chi_z^{L_z}$, as a function of diameter, chirality (wrapping vector), and contact geometry for metallic and semiconducting CNTs. Calculations employ a nearest-neighbor tight-binding model and NEGF formalism, combined with the Landauer--Büttiker approach for non-equilibrium steady-state current distributions.

Key findings include:

• Non-universality of Orbital Response: $\chi_z^{L_z}$ does not scale universally with diameter. Instead, it exhibits distinct, chirality-dependent branches in the $(n, m)$ parameter space. CNTs with identical diameters but different chiral indices manifest orbital susceptibilities differing by up to a factor of two.
• Branch Structures and Family Trends: Similar to optical properties captured in Kataura plots, the orbital response branches are directly correlated with the family index associated with the chiral vector, elucidating the critical joint role of geometric and electronic structure on the orbital transport.

In metallic CNTs, armchair and zigzag families display bifurcation in orbital response, with smaller chiral angle (near-zigzag) tubes supporting enhanced azimuthal current components and larger orbital magnetizations. For semiconducting CNTs, van Hove singularities in the density of states lead to enhanced and energy-dependent Edelstein susceptibility, characterized by pronounced family-dependent branching and sign alternation attributable to the angular-momentum structure of transport subbands.

Contact Geometry and Angular Momentum Injection

The study systematically contrasts ideal (CNT-based) and wide-band metallic contacts with varying spatial coupling (end and side contacts):

• Charge Conductance: Total conductance is relatively insensitive to contact geometry within the wide-band approximation, maintaining mode-matching in single-channel (metallic) and multi-channel (semiconducting) regimes as expected.
• Orbital Magnetization Profile: In metallic CNTs, angular-momentum-eigenstate populations and bulk orbital response are rapidly recovered within a few unit cells from the contact interface, regardless of contact geometry. In semiconducting CNTs, by contrast, metallic contacts induce persistent oscillations in the spatial profile of the orbital moment, resulting from coherent beating between modes with different quantized angular momenta.

The presence and spatial extent of non-equilibrium orbital magnetization are thus deeply influenced by both lead type and the contact’s imposed angular correlation structure. Importantly, side contacts—which break rotational symmetry—can generate substantial transverse orbital components, offering a practical degree of control over the direction of induced orbital magnetization.

Angular Momentum Filtering Mechanism

The manuscript introduces a well-defined model for selectively injecting electrons with prescribed orbital angular texture by modifying the contact self-energy to project onto specific angular momentum channels.

Theoretical Foundation

• The filtering operates via quantization of crystal angular momentum $\mathfrak{m}$, determined by the $C_{\mathfrak{n}}$ symmetry of the CNT.
• The selection rule $l \equiv \mathfrak{m} \pmod{\mathfrak{n}}$ is demonstrated: only those injected angular momenta matching a propagating channel's $\mathfrak{m}$ are transmitted, while others are completely blocked, leading to angular-momentum-resolved transport gaps.

Results

• In armchair-class CNTs, only $l \equiv 0 \pmod{\mathfrak{n}}$ is transmitted near the Fermi level.
• In zigzag-class CNTs, the simultaneous presence of two distinct low-energy $\mathfrak{m}$ values allows for injection-selective, channel-resolved transmission—effectively a nanoscale demultiplexer for orbital angular momentum.
• Filtering efficiencies can approach unity with well-designed injection and contact geometries; contact imperfection only diminishes transmission amplitude without compromising angular discrimination.

Implications and Future Directions

This study establishes that chiral CNTs function as highly efficient orbitronic elements for angular-momentum-resolved current manipulation, with immediate relevance for emerging orbitronics device designs. The results delineate the parameter space where orbital Edelstein effects and filtering are maximized, providing a roadmap for experimental implementation:

• For devices relying on CIOS, optimal performance is achieved in large-diameter, small-chiral-angle (near-zigzag) CNTs, particularly in semiconducting families.
• The selection of contact geometry presents a practical axis for engineering both the magnitude and orientation of the non-equilibrium orbital moment.
• The demonstrated filtering effect positions CNTs as minimalistic, symmetry-defined elements for angular-momentum multiplexing and demultiplexing in nanoelectronic and quantum devices.

Open theoretical directions include full ab initio modeling of realistic metal–nanotube interfaces, incorporation of phonon and disorder effects on angular-momentum-selective transport, and extension of these filtering principles to other low-dimensional chiral materials.

Conclusion

This work provides a systematic and quantitative foundation for understanding and exploiting non-equilibrium orbital selectivity and angular-momentum filtering in chiral CNTs. The interplay of quantum transport, chirality, and contact engineering yields a diverse set of phenomenology, including non-universal, family-resolved orbital responses, rapid angular-momentum equilibration in metallic tubes, persistent mode-beating in semiconducting tubes, and robust orbital angular momentum filtering governed exclusively by the CNT’s discrete rotational symmetry. These results position chiral CNTs as archetypal platforms for both fundamental investigation and technological application of orbitronic phenomena.