  The nonequilibrium Casimir-Polder force between a nanoparticle and a graphene
sheet kept at different temperatures is investigated in the framework of Dirac
model using the formalism of the polarization tensor. It is shown that the
force magnitude increases with increasing temperature of a graphene sheet. At
larger separations an impact of nonequilibrium conditions on the force becomes
smaller. According to our results, the attractive Casimir-Polder force vanishes
at some definite nanoparticle-graphene separation and becomes repulsive at
larger separations if the temperature of a graphene sheet is smaller than that
of the environment. This effect may find applications both in fundamental
investigations of graphene and for the control of forces in microdevices of
bioelectronics.
