How to observe the giant thermal effect in the Casimir force for graphene systems

A differential measurement scheme is proposed which allows for clear observation of the giant thermal effect for the Casimir force, which was recently predicted to occur in graphene systems at short separation distances. The difference among the Casimir forces acting between a metal-coated sphere and the two halves of a dielectric plate, one uncoated and the other coated with graphene, is calculated in the framework of the Dirac model using the rigorous formalism of the polarization tensor. It is shown that in the proposed configuration both the difference among the Casimir forces and its thermal contribution can be easily measured using existing experimental setups. An observation of the giant thermal effect should open opportunities for modulation and control of dispersion forces in micromechanical systems based on graphene and other novel two-dimensional (2D) materials.

Figure 1

The experimental configuration of a Au sphere moving back and forth above a Si plate, half of which is covered with graphene (shown by dashes). The measured quantity is the differential Casimir force $F_{\mathrm{diff}}$ between the Au sphere and the two halves of the plate when the sphere tip is far away from their boundaries. The figure displays the two extreme positions of the sphere during its motion. The size of the sphere is shown not to scale.

Figure 2

The differences $F_{\mathrm{diff}}$ among the Casimir forces calculated at $T=300\mathrm{K}$ (top lines) and at $T=0\mathrm{K}$ (bottom lines) are shown as functions of separation over four different separation intervals.

Figure 3

The relative thermal correction ${\mathrm{\Delta }}_T{F}_{\mathrm{diff}}/F_{\mathrm{diff}}$ to the difference among the Casimir forces (solid line). The short-dashed line shows the relative contribution ${\mathrm{\Delta }}_T^{\left(1\right)}{F}_{\mathrm{diff}}/F_{\mathrm{diff}}$ to the thermal correction arising from the explicit temperature dependence of the polarization tensor of graphene, while the long-dashed line shows the relative contribution ${\mathrm{\Delta }}_T^{\left(2\right)}{F}_{\mathrm{diff}}/F_{\mathrm{diff}}$ originating from the combined effect of the temperature dependence of the Au relaxation frequency together with the implicit temperature dependence brought about by the discrete summation over the Matsubara frequencies.