Light Can Now Pull on Carbon Nanotubes, Defying Conventional Forces

Tomer Berghaus and colleagues at Tel Aviv University have revealed that light can pull on carbon nanotubes, identifying a phenomenon linked to the unique nonlocal conductivity within these materials. Their theory explains this optical pulling effect, showing it arises from the spatial dispersion of conductivity and disappears when conductivity is considered local. This advances theoretical understanding of optomechanical interactions in low-dimensional conductors, providing a key insight into how light and matter interact at a nanoscale.

Nonlocal electron behaviour explains previously unobserved negative optical forces on carbon

Optical forces on carbon nanotubes (CNTs) are now demonstrably negative, representing a 180-degree shift from the previously understood behaviour of light always exerting a pushing force. Traditionally, the interaction between light and matter at the nanoscale has been predicted using models based on the assumption of ‘local conductivity’, where the electron response is considered instantaneous and confined to a single point. However, observing this “optical pulling effect” proved impossible within the framework of these local conductivity models. The current findings reveal this effect only manifests when electron behaviour within the CNT is considered ‘nonlocal’, meaning electrons respond to electromagnetic signals over a finite distance, exhibiting a delayed and spatially distributed response. This nonlocal behaviour is a direct consequence of the unique electronic band structure of CNTs and the way electrons propagate along their axis.

This discovery necessitates a move beyond conventional dipole approximations in optomechanical modelling, instead employing an integral-equation-based approach to accurately map interactions. The dipole approximation, while computationally efficient, breaks down when dealing with materials exhibiting strong spatial dispersion of conductivity. The researchers’ integral-equation approach solves for the surface current density on the CNT, directly relating it to the axial electric field and, consequently, the optical force. A theoretical framework developed rigorously accounts for ‘edge effects’, the behaviour at the ends of finite-length CNTs, a key refinement absent in earlier calculations. These edge effects arise from the reflection of surface currents at the CNT’s boundaries, significantly influencing the overall optical force, particularly for shorter nanotubes. Manipulating the electronic properties of a carbon nanotube, such as its doping concentration or chirality, can tune the optical force acting upon it. The emergence of negative optical forces, a pulling effect, is valid across a broad frequency range from terahertz to visible light, suggesting potential applications in a wide range of optical technologies.

This analysis details how the analysis incorporates both interband and intraband transitions contributing to the overall conductivity, with the non-local component arising from a second-order Taylor series expansion of spatial dispersion. Interband transitions involve electrons moving between different energy bands, while intraband transitions occur within the same band. The inclusion of both is crucial for accurately modelling the CNT’s optical response. The model accounts for the behaviour of electrons near specific points within the CNT’s structure, termed K-points, which represent the extrema of the energy bands and significantly influence electron transport. Carefully modelled finite-length CNTs, applying additional boundary conditions to account for reflections, were used in the calculations. These findings provide a vital benchmark for existing models, exposing where simplifications introduce errors in predicting how light interacts with these tiny structures, and will guide the development of more accurate simulations. The magnitude of the negative optical force is directly related to the degree of nonlocal conductivity, providing a quantifiable metric for assessing the effectiveness of this effect.

Nonlocal electron behaviour governs light-nanotube interactions

The ability to manipulate light at the nanoscale promises advances across diverse fields, from improved sensors to novel optical devices, including nanophotonic circuits and high-precision actuators. Many simulations, however, assume a ‘local conductivity’, where electron behaviour is confined to a single point, effectively ignoring the broader spatial distribution of electrons within the nanotube. This simplification fails to capture the vital nonlocal effects demonstrated here, potentially leading to inaccurate predictions of optical forces and hindering the design of effective nanoscale optomechanical systems. The assumption of local conductivity is often made for computational convenience, but it introduces a significant error when dealing with materials where electron coherence lengths are comparable to the dimensions of the structure, as is the case with carbon nanotubes.

Calculations rely on approximations of complex electron behaviour, but this does not diminish their value. The integral-equation approach, while computationally demanding, provides a more accurate representation of the physical processes involved. Understanding these limitations is vital, enabling the rational design of advanced nanoscale devices for sensing and optomechanics, even if further refinement of the underlying theory is needed. For example, the current model does not account for the effects of electron-phonon interactions, which could further modify the optical force. This work establishes a theoretical framework for understanding optical forces on carbon nanotubes, moving beyond conventional models that assume electron behaviour is limited to a specific point. By employing an integral-equation-based approach, calculations accurately modelled how electrons respond over a distance within these nanoscale cylinders, accounting for behaviour at the tube’s ends, and demonstrating that light can exert a pulling force on carbon nanotubes, a phenomenon dependent on this property and absent when electrons are considered to behave locally. The researchers’ work opens avenues for exploring similar nonlocal effects in other low-dimensional materials, potentially leading to a broader understanding of light-matter interactions at the nanoscale and the development of entirely new optoelectronic technologies. The precise control over optical forces offered by exploiting nonlocal conductivity could enable the creation of highly sensitive nanoscale sensors capable of detecting minute changes in their environment.

The research demonstrated that light can exert a pulling force on carbon nanotubes, a behaviour originating from the way electrons move within the material over a distance. This pulling effect occurs because of nonlocal conductivity and is not present when electron behaviour is limited to a single point. By using an integral-equation approach, scientists accurately modelled optical forces on finite-length carbon nanotubes, accounting for edge effects. The authors suggest this framework can be extended to investigate similar phenomena in other low-dimensional materials, improving understanding of light-matter interactions at the nanoscale.