Demonstration of an Unusual Thermal Effect in the Casimir Force from Graphene

We report precision measurements of the gradient of the Casimir force between an Au-coated sphere and graphene sheet deposited on a silica plate. The measurement data are compared with exact theory using the polarization tensor found in the framework of the Dirac model including effects of the nonzero chemical potential and energy gap of the graphene sample with no fitting parameters. The very good agreement between experiment and theory demonstrates the unusually big thermal effect at separations below $1\mu \mathrm{m}$ which has never been observed for conventional 3D materials. Thus, it is confirmed experimentally that for graphene the effective temperature is determined by the Fermi velocity rather than by the speed of light.

Figure 1

The residual potential difference between a Au-coated sphere and a graphene sample is shown by the dots as a function of separation.

Figure 2

The mean gradient of the Casimir force is shown by the crosses as a function of separation. The top and bottom theoretical bands are computed at $T=294\mathrm{K}$ and 0 K, respectively (see the text for further discussion).