Low-temperature increase in the van der Waals friction force with the relative motion of metal plates

The van der Waals friction force (dissipative fluctuation electromagnetic force) between metallic plates during their relative motion at temperatures close to $1$ K is calculated within the Levin–Polevoi–Rytov fluctuation electromagnetic theory. It is shown that the van der Waals friction force for gold plates with a small number of defects and low residual resistance ${{\rho }_{0}}$ can increase by six to eight orders of magnitude with a decrease in the temperature below $100$ K, reaching a maximum value proportional to ${{\rho }_{0}}^{{ - 4/5}}$. For superconducting metals, an increase in friction can be observed when the temperature decreases to the critical transition temperature, after which friction disappears. Another important result is the weak dependence of the friction force on the distance $a$ between the plates (${\propto}\, a^{-q} $ with $q<1$). The absolute values of the friction forces are achievable for measurements in experiments using the modern atomic force microscopy technique.