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arXiv:2601.00489

Casimir interactions between two parallel graphene sheets carrying steady-state drift currents

Modi Ke, Dai-Nam Le, Lilia M. Woods

quant-phcond-mat.mes-hallcond-mat.mtrl-sciphysics.app-phphysics.opticsSubmitted Jan 1, 2026• Announced Jan 5, 2026• Revised Jan 13, 2026 (v2)
v1 · Jan 1, 2026v2 · Jan 13, 2026
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Abstract

We investigate the fluctuation-induced Casimir interactions between two parallel graphene sheets carrying steady-state drift currents. The graphene properties are modeled based on the shifted Fermi disk model to capture the non-equilibrium optical response of the system. We find that the drift current introduces a repulsive correction to the perpendicular to the layers Casimir interaction, thereby reducing the overall attractive force. Although the correction is repulsive, it does not overcome the underlying attraction between the layers. It also generates a lateral force that opposes the carrier flow direction. Both contributions are studied in terms of distance and drift velocity functionalities showing pathways for Casimir force control.

DOI
10.1103/84n7-1r3b
Comments
10 pages, 5 figures. To be published on Physical Review B

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We investigate the fluctuation-induced Casimir interactions between two parallel graphene sheets carrying steady-state drift currents. The graphene properties are modeled based on the shifted Fermi disk model to capture the non-equilibrium optical response of the system. We find that the drift current introduces a repulsive correction to the perpendicular to the layers Casimir interaction, thereby reducing the overall attractive force. Although the correction is repulsive, it does not overcome the underlying attraction between the layers. It also generates a lateral force that opposes the carrier flow direction. Both contributions are studied in terms of distance and drift velocity functionalities showing pathways for Casimir force control.
Casimir forces, arising from quantum and thermal fluctuations, depend strongly on the electromagnetic susceptibilities of the interacting materials. Here, we theoretically investigate the Casimir force between two graphene sheets separated by a nanometer-thin layer of liquid water. We find that deviations from the bulk case can be as large as 24 \%, mostly due to the static susceptibility components. This effect does not decrease monotonically as a function of the layer thickness: it increases up to a maximum at 70 nm and it slowly declines to the bulk limit only at 1 micron. This is due to two competing effects: on one hand, the anisotropy decreases with the layer thickness; on the other hand, the relative contribution of the most anisotropic, static susceptibility components increases.
Casimir–Lifshitz forces arising from quantum electromagnetic fluctuations provide a fundamental mechanism for momentum transfer at the nanoscale. In this work, we investigatehow graphene-based nanostructures and periodic gratings enable active control of these forcesin three representative configurations. First, we analyze the Casimir–Lifshitz interaction between a gold plate and a graphene-covered dielectric grating. We show that the combinationof graphene and periodic structuring leads to a strong enhancement of the force, reachingup to 130%, with pronounced thermal effects at submicron separations.Second, we study tunable nonadditivity effects in the Casimir–Lifshitz force between twographene strip gratings. Using a rigorous scattering-matrix framework, we demonstrate thatthe interaction strongly depends on geometry and graphene chemical potential, leading todeviations from additive approximations of up to 30%, which can be tuned in situ.Finally, we investigate normal and lateral Casimir forces acting on a nanoparticle above agraphene grating. We reveal stable and unstable lateral equilibrium positions and identifytwo regimes governed by the ratio between separation distance and grating period. Our results highlight the breakdown of additive approximations and demonstrate new opportunitiesfor controlling nanoscale momentum transfer using graphene-based nanophotonic structures.
We explore the possibility to create hybrid quantum systems that combine ultracold atoms with graphene membranes. We investigate a setup in which a cold atom cloud is placed close to a free-standing sheet of graphene at distances of a few hundred nanometers. The atoms then couple strongly to the graphene membrane via Casimir-Polder forces. Temporal changes in the atomic state of the atomic cloud changes the Casimir-Polder interaction, thereby leading to the creation of a back-action force in the graphene sheet. This setup provides a controllable way to engineer ripples in a graphene sheet with cold atoms.
We study a massless Dirac field subjected to two alternative boundary conditions on two parallel thin walls, in d + 1 dimensions. The two configurations correspond to the system being even or odd under reflection about the midplane between the two walls, and lead to qualitatively different behaviors. The even (symmetric) configuration produces an attractive Casimir force, whereas the odd (antisymmetric) one yields repulsion, in agreement with a general theorem linking parity to the sign of the fermionic Casimir effect. We complement this result by studying two phenomena associated with the vacuum fluctuations responsible for the Casimir interaction, both of which are also sensitive to parity: the correlation between currents concentrated on the walls, and the induced bulk current under the influence of an external electric field. For the latter we show that, in 2 + 1 dimensions, an induced transverse (Hall-like) current arises, whose spatial profile inherits the symmetry of the confining potential.
We demonstrate quantum levitation controlled by Casimir forces acting between a polystyrene surface and a Teflon-coated metallic substrate immersed in a mixture of Toluene and magnetite particles. This system experiences repulsion-attraction transitions in the Casimir interaction for distances where the effect is measurable. This Casimir trapping can be controlled by clever choices of metallic and ferrofluid materials, which are directly linked to the emergence of the trapping effect. Thermal and quantum contributions are investigated in detail, showing how the optical and magnetic properties of the ferrofluid and other materials affect the magnitude of the trapping and its distance range of observability.
We investigate the Casimir force on thin suspended dielectric layers covered with graphene, both theoretically and experimentally. Thermal effects of the Casimir force on graphene occur at separations significantly smaller compared to ordinary metals and dielectrics. At such small separations, the Casimir force is sufficiently strong to be measured experimentally. However, the presence of substrates to support the graphene significantly reduces the enhancement. We show theoretically that replacing the solid substrate beneath graphene with a thin dielectric membrane partially restores this strong thermal dependence. One of the interacting objects is a solid gold plate. The other object is a suspended dielectric membrane made of either 15 nm of silicon oxide or 13 nm silicon nitride, covered with graphene. At a separation of $\sim$500 nm, theoretical predictions yield changes in the Casimir pressure of up to 54 % and 40 % for silicon oxide and silicon nitride, respectively, when the temperature is increased from 10 K to 294 K. Measurements were performed for graphene on a suspended silicon nitride membrane at room temperature, using a gold-coated sphere attached to a cantilever as the force sensor. The measured force gradient is consistent with the theoretical prediction, although the thermal dependence could not be resolved, in part because of uncertainties in the optical properties of silicon nitride. Replacing a bulk substrate with a thin dielectric membrane covered with graphene provides a substantial reduction of the Casimir force, which may facilitate the stable operation of neutral nanomechanical elements at small separations.