  The electrocaloric (EC) effect is the reversible change in temperature and/or
entropy of a material when it is subjected to an adiabatic electric field
change. Our tight-binding calculations linked to Fermi statistics, show that
the EC effect is sensitive to the stacking arrangement in trilayer graphene
(TLG) structures connected to a heat source, and is produced by changes of the
electronic density of states (DOS) near the Fermi level when external gate
fields are applied on the outer graphene layers. We demonstrate the AAA-stacked
TLG presents an inverse EC response (cooling), whereas the EC effect in
ABC-stacked TLG remains direct (heating) regardless of the applied gate field
potential strength. We reveal otherwise the TLG with Bernal-ABA stacking
geometry generates both the inverse and direct EC response in the same sample,
associated with a gate-dependent electronic entropy transition at finite
temperature. By varying the chemical potential to different Fermi levels, we
find maxima and minima of the DOS are located near the extremes of the
electronic entropy, which are correlated with sign changes in the differential
entropy per particle, giving a particular experimentally measurable electronic
entropy spectrum for each TLG geometry. The EC effect in quantum
two-dimensional layered systems may bring a wide variety of prototype van der
Waals materials that could be used as versatile platforms to controlling the
temperature in nanoscale electronic devices required in modern portable on-chip
technologies.
