The Casimir-Lifshitz force is an interaction between two neutral bodies based on the quantum and thermal fluctuations of the electromagnetic field and that depends on the geometry, the temperature, and the relative values of the dielectric function of the materials involved. Although this interaction is strongly determined by the materials at the surface of the interacting bodies, as the interaction penetrates the bodies, the arrangement of the materials behind the surfaces of the bodies also influences the Casimir-Lifshitz force of the system. In this context, multilayer structures can help modulate the interaction between two bodies by balancing the attractive and repulsive contributions introduced by layers of different materials and different thicknesses, in particular when a fluid mediates the interaction. Herein, the Casimir-Lifshitz force between two planar objects of two exemplary systems stratified at the nanoscale and finite temperature is investigated. The aim is to show the relevance of this material arrangement on the Casimir-Lifshitz force and its implications.
On the one hand, layering results in optical interference effects that give rise to modification of the optical losses, which, as stated by the fluctuation-dissipation theorem, should affect the Casimir-Lifshitz interaction. On these grounds, we demonstrate that, by nanostructuring the same volume of dielectric materials in diverse multilayer configurations, it is possible to access Casimir-Lifshitz force of attractive or repulsive nature, even getting canceled, at specific separation distances . We show this behaviour for experimentally accessible systems made of commonly found materials such as silicon dioxide, polystyrene, glycerol, and silicon, at thermal equilibrium at room temperature.
On the other hand, the formation of a thin water layer on the ice at the triple point of water was theoretically predicted by the Casimir-Lifshitz force theory . Here we study how the addition of a rocky material behind the ice, simulating for example permafrost, influences the formation of such water layer on ice according to the equilibrium of repulsive and attractive Casimir-Lifshitz forces . We find that the initial conditions of ice and water thickness largely determine the resulting melt ice layer at the triple point.
Our results demonstrate the interest of studying multilayer nanostructures for the rational design and fine-tuning of the Casimir-Lifhsitz force in complex nanostructures and the deeper understanding of fundamental phenomena driven by the Casimir-Lifshitz interaction in nanolayered structures.
 V. Esteso, S. Carretero-Palacios, H. Míguez, Phys. Rev. A, 101, 033815 (2020).
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