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arXiv:2609.23609

Casimir force in a water nanolayer confined by graphene sheets

Wijnand Broer, Jure Dobnikar

quant-phcond-mat.softSubmitted Sep 20, 2026• Announced Sep 22, 2026
v1 · Sep 20, 2026v2 · Sep 29, 2026
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Abstract

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, at thicknesses up to 3.4 nm, the confinement reduces the Casimir force by up to 26 % compared to the bulk case. At larger thicknesses, the bulk model underestimates the Casimir force by up to 42 % due to the interface effect. 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 2 microns. We separately assess the effect of nanoscale confinement on the electronic response of graphene, which has no effect on the Casimir force.

Comments
9 pages, 6 figures

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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, at thicknesses up to 3.4 nm, the confinement reduces the Casimir force by up to 26 % compared to the bulk case. At larger thicknesses, the bulk model underestimates the Casimir force by up to 42 % due to the interface effect. 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 2 microns. We separately assess the effect of nanoscale confinement on the electronic response of graphene, which has no effect on the Casimir force.
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.
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The Casimir effect for two parallel slabs immersed in an ideal Fermi sea is investigated at both zero and nonzero temperatures. It is found that the Casimir effect in a Fermi gas is distinctly different from that in an electromagnetic field or a massive Bose gas. In contrast to the familiar result that the Casimir force decreases monotonically with the increase of the separation L between two slabs in an electromagnetic field and a massive Bose gas, the Casimir force in a Fermi gas oscillates as a function of L. The Casimir force can be either attractive or repulsive, depending sensitively on the magnitude of L. In addition, it is found that the amplitude of the Casimir force in a Fermi gas decreases with the increase of the temperature, which also is contrary to the case in a Bose gas, since the bosonic Casimir force increases linearly with the increase of the temperature in the region T < T c , where T c is the critical temperature of the Bose—Einstein condensation.
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.