Casimir-Lifshitz force with graphene: Role of spatial nonlocality and of losses
Phys. Rev. B 112, 035412 – Published 11 July, 2025
DOI: https://doi.org/10.1103/vwm1-x3vw
Abstract
We analyze the impact of spatial nonlocality and losses in the electromagnetic response of graphene on the Casimir-Lifshitz interaction. To this purpose, we calculate the Casimir-Lifshitz force (CLF) between a gold sphere and a graphene-coated plane and compare our finding with the recent experiment in M. Liu et al. [Phys. Rev. Lett. 126, 206802 (2021) and Phys. Rev. B 104, 085436 (2021)]. We calculated the CLF using three different models for the electromagnetic response of graphene: electric conductivity using a nonlocal and lossy Kubo model, electric conductivity using the local and lossy Kubo model, and the nonlocal and lossless polarization operator model. The relation between these three models has been recently explored in P. Rodriguez-Lopez et al. [Phys. Rev. B 111, 115428 (2025)]. We show that, for the parameters of the available experiments, the theoretical predictions for the Casimir-Lifshitz force using the three models are practically identical (having relative differences smaller than ). This implies that for those given experiments, both nonlocal and lossy effects in the graphene response are completely negligible. We also find that this experiment cannot distinguish between the Drude and Plasma prescriptions for the involved materials (gold and graphene). Our findings are relevant for present and future comparisons with experimental measurement of the Casimir-Lifshitz force involving graphene structures. Indeed, we show that an extremely simple local Kubo model for the electric conductivity, explicitly depending on Dirac mass, chemical potential, losses and temperature, is largely enough for a totally comprehensive comparison with typical experimental configurations. We also show how the Polarization tensor must be used and modified in general, for phenomena needing a more fine response function, i.e., requiring both the spatial nonlocality and losses.
