Tractor Beam Physics: Carbon Nanotubes Feel a Pulling Force from Light

In a result that reads like science fiction made rigorous, a team of theorists has shown that a beam of light can pull a carbon nanotube backward, against the very direction in which the light travels. The study, published in the open-access journal iScience by Tomer Berghaus, Touvia Miloh, and Gregory Ya. Slepyan, demonstrates that this counterintuitive optical pulling force arises from a subtle quantum-mechanical property of the nanotube’s electrons known as non-local conductivity. Crucially, the effect vanishes entirely if the nanotube is described by the conventional local models that physicists have relied on for decades, meaning the pulling force is not a small correction to existing theory but a genuinely new manifestation of how light and matter exchange momentum at the nanoscale.

The story of optical forces begins more than a century ago, with the pioneering measurements of radiation pressure by Pyotr Lebedev and by Ernest Nichols and Gordon Hull in 1901. The modern era, however, is usually dated to Arthur Ashkin’s work in the 1970s and 1980s, which showed that focused laser beams could trap and steer microscopic dielectric and metallic particles. That line of research produced optical tweezers, tools now ubiquitous in biology and chemistry, and earned a share of the 2018 Nobel Prize in Physics. In the classical picture, light exerts two kinds of forces: a gradient force that draws particles toward regions of high intensity, and a scattering force that pushes them along the beam’s propagation direction through the transfer of photon momentum. Under almost all ordinary circumstances, the net result is pushing.

Over the past two decades, researchers have discovered that the nanoscale world harbors exceptions. Chirality, plasmonic resonances, optical gain, metamaterial architectures, and excitonic effects can all conspire to produce negative optical forces, in which an object is drawn toward the light source rather than pushed away from it. These tractor-beam effects have been demonstrated or predicted for Janus particles, plasmonic nanorods, and engineered metamaterial structures. What distinguishes the new work is the physical mechanism. The pulling force in a carbon nanotube does not come from clever geometry or exotic materials design; it emerges from the spatial dispersion of the nanotube’s conductivity, the fact that the current induced at any given point along the tube depends on the electric field in its neighborhood, not just at that point.

To understand why non-locality matters, it helps to recall how electrons behave in a carbon nanotube. A single-wall nanotube is essentially a rolled-up sheet of graphene, and its low-energy electronic states mimic those of graphene: the energy depends linearly on momentum, with the Fermi velocity playing the role of the speed of light in an effective relativistic description. In graphene, electrons roam freely across a two-dimensional plane. In a nanotube, however, the transverse direction is wrapped up and quantized, so the electron momentum is discrete around the circumference and continuous only along the tube axis. The authors adapted the Kubo formalism of linear response theory, treating the electrons as a pseudo-spin liquid in the collision-free, low-temperature regime, to compute how the axial conductivity depends on both frequency and wavevector. This wavevector dependence is precisely what local models discard.

Mathematically, the non-local conductivity can be expanded in powers of the wavevector, and symmetry ensures that the first correction term vanishes, leaving a second-order contribution. Transforming back to real space, this term becomes a second spatial derivative of the electric field multiplied by a complex non-locality factor. The physical meaning is direct: the current at a point on the tube is the sum of a local Ohmic response and a non-local component that senses the field’s curvature along the axis. The non-locality factor obeys Kramers-Kronig relations and splits into interband and intraband parts, just as the conductivity itself does. The interband component dominates at high frequencies, while the Drude-like intraband component governs the low-frequency response, and the crossover between them sits near the energy where the photon energy equals twice the electrochemical potential.

The geometry of the problem turns out to be just as important as the electronic physics. Most previous treatments modeled nanotubes as infinitely long, one-dimensional objects, which conveniently sidesteps what happens at the ends. Berghaus and colleagues insisted on a finite-length tube, and that choice has profound consequences. Electrons traveling along the tube reflect from the open ends, and these reflections are captured through so-called additional boundary conditions that supplement Maxwell’s equations. The induced current near the terminations behaves like an effective multipole, absent in the local limit, and it is these end-induced multipoles that ultimately reverse the direction of the optical force. The non-locality of the conductivity, in other words, manifests itself entirely through edge effects.

Computing the force itself required careful handling of the Maxwell stress tensor, the mathematical object whose integral over a closed surface yields the total electromagnetic force on an object. For a slender nanotube, the axial force is determined by the off-diagonal components of the tensor, which couple the radial and longitudinal field components. Here the authors encountered a striking result: a purely local conductivity model produces non-integrable singularities in the diagonal tensor elements, rendering the force calculation mathematically ill-defined. Including spatial dispersion removes these singularities and makes the integral convergent. Non-locality, in this sense, is not optional refinement but a prerequisite for a physically consistent theory of optomechanical forces in nanotubes.

To obtain quantitative predictions, the team formulated a Fredholm integral equation of the second kind for the axial surface current, a framework long used in the electrodynamics of nanotube antennas. The kernel of this equation contains a weak singularity, and naive numerical treatment produces unphysical oscillations in the current density near the tube ends, a pathology familiar from classical microwave antenna theory. The authors adapted renormalization techniques from that literature and regularized the singular part analytically using properties of Hankel functions. They then solved the equation numerically in MATLAB and, in parallel, derived an approximate analytical solution from the zeroth-order term of a Neumann series. The two approaches agreed closely, lending confidence to the central prediction: a narrow, sharp peak of negative force appears near the critical frequency where the photon energy matches twice the electrochemical potential of the nanotube’s electrons.

The parameter dependence of the effect is rich and experimentally testable. Pulling occurs for relatively short tubes, roughly 100 to 200 nanometers long, and only in the frequency regime where intraband transitions dominate. As the tube lengthens, the relative importance of the end effects diminishes, the force turns positive, and it settles into a linear dependence on length, exactly the behavior of the classical Ashkin-like pushing regime. The force also depends strongly on the angle of incidence and on the electrochemical potential, which suggests practical applications: measuring the doping level of a nanotube optically, sorting nanotubes by length or radius with light, and developing nanotube-based mechanical sensors. The calculated force magnitudes, in the tens of femtonewtons for incident powers of 50 to 100 milliwatts, fall squarely within the range already measured in optical trapping experiments on nanotubes, so the predicted pulling should be within reach of existing instrumentation.

The theoretical framework is deliberately simple in its baseline configuration, a single achiral, open-ended, metallic nanotube suspended in vacuum and illuminated by a plane wave, but the authors outline natural extensions to tubes in fluids, in waveguides or optical cavities, and in the presence of neighboring structures, all of which could enhance the force. Structured light such as Gaussian or Bessel beams offers another route to strengthening the pull. Limitations remain, including the restriction to achiral tubes and the simplified treatment of nonlinear saturation effects, which the authors show are negligible at the field strengths considered since the saturation intensity of metallic nanotube films exceeds the simulation intensity by nearly two orders of magnitude. Still, the message of the work is clear and likely to resonate across nanophotonics: at the nanoscale, the response of matter to light is fundamentally non-local, and ignoring that fact can make the difference between a beam that pushes and one that pulls. The study’s data and code have been deposited publicly on Zenodo, and the authors explicitly welcome experimental validation of the newly predicted tractor-beam effect.

Subject of Research: Optical pulling forces on carbon nanotubes arising from non-local conductivity

Article Title: Optical pulling force in carbon nanotubes: Manifestation of non-local conductivity

Article References: Berghaus, T., Miloh, T., & Slepyan, G. Y. (2026). Optical pulling force in carbon nanotubes: Manifestation of non-local conductivity. iScience, 29(11), Article 117817. https://doi.org/10.1016/j.isci.2026.117817

Image Credits: AI Generated

DOI: 10.1016/j.isci.2026.117817

Keywords: carbon nanotubes, optical pulling force, non-local conductivity, spatial dispersion, optical tweezers, Maxwell stress tensor, Kubo formalism, tractor beam, nanophotonics, Landau damping, integral equation, edge effects