Abstract
We study the neutral filling ABC-stacked trilayer graphene with a long-range Coulomb interaction. The extremely large density of states near Dirac points leads to more plausible formation of spin ferromagnets, and our calculation indicates that the spin split energy approximates to 32 meV. Electron and hole carriers coexist in this spontaneous ferromagnetic system. The Coulomb interaction between carriers with opposite charge leads to triplet exciton condensation, namely, a spin superconductor. Using a BCS-type self-consistent calculation, we demonstrate the exciton condensation energy gap is about $7.8$ meV. Further, we consider the thermal fluctuations and determine the Berezinskii-Kosterlitz-Thouless critical temperature to be around 11 K.
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