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The Casimir and Casimir-Polder interactions are investigated in a stack ofequally spaced graphene layers. The optical response of the individual grapheneis taken into account using gauge invariant components of the polarizationtensor extended to the whole complex frequency plane. The planar symmetry forthe electromagnetic boundary conditions is further used to obtain explicitforms for the Casimir energy stored in the stack and the Casimir-Polder energybetween an atom above the stack. Our calculations show that these fluctuationinduced interactions experience strong thermal effects due to the grapheneDirac-like energy spectrum. The spatial dispersion and temperature dependencein the optical response are also found to be important for enhancing theinteractions especially at smaller separations. Analytical expressions for lowand high temperature limits and their comparison with corresponding expressionsfor an infinitely conducting planar stack are further used to expand ourunderstanding of Casimir and Casimir-Polder energies in Dirac materials. Ourresults may be useful to experimentalists as new ways to probe thermal effectsat the nanoscale in such universal interactions.

Thermal Casimir and Casimir-Polder interactions in $N$ parallel 2D Dirac materials