Thermal van der Waals interaction between graphene layers

The van de Waals interaction between two graphene sheets is studied at finite temperatures. Graphene's thermal length $({\ensuremath{\xi}}_{T}=\ensuremath{\hbar}v/{k}_{B}T)$ controls the force versus distance $(z)$ as a crossover from the zero temperature results for $z⪡{\ensuremath{\xi}}_{T}$, to a linear-in-temperature, universal regime for $z⪢{\ensuremath{\xi}}_{T}$. The large separation regime is shown to be a consequence of the classical behavior of graphene's plasmons at finite temperature. Retardation effects are largely irrelevant, both in the zero and finite temperature regimes. Thermal effects should be noticeable in the van de Waals interaction already for distances of tens of nanometers at room temperature.