Temperature-dependent zero-field splittings in graphene

Graphene is a quantum spin Hall insulator with a 45 mu eV-wide nontrivial topological gap induced by the intrinsic spin-orbit coupling. Even though this zero-field spin splitting is weak, it makes graphene an attractive candidate for applications in quantum technologies, given the resulting long spin-relaxation time. On the other side, the staggered sublattice potential, resulting from the coupling of graphene with its boron nitride substrate, compensates intrinsic spin-orbit coupling and decreases the nontrivial topological gap, which may lead to the phase transition into trivial band insulator state. In this work, we present extensive experimental studies of the zero-field splittings in monolayer and bilayer graphene in a temperature range 2-12 K by means of subterahertz photoconductivity-based electron spin-resonance technique. Surprisingly, we observe a decrease of the spin splittings with increasing temperature. We discuss the origin of this phenomenon by considering possible physical mechanisms likely to induce a temperature dependence of the spin-orbit coupling. These include the difference in the expansion coefficients between the graphene and the boron nitride substrate or the metal contacts, the electron-phonon interactions, and the presence of a magnetic order at low temperature. Our experimental observation expands knowledge about the nontrivial topological gap in graphene.