Lifshitz transition and thermoelectric properties of bilayer graphene

This is a numerical study of thermoelectric properties of ballistic bilayer graphene in the presence of a trigonal warping term in the effective Hamiltonian. We find, in the mesoscopic samples of the length $L>10\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ at sub-Kelvin temperatures, that both the Seebeck coefficient and the Lorentz number show anomalies (the additional maximum and minimum, respectively) when the electrochemical potential is close to the Lifshitz energy, which can be attributed to the presence of the van Hove singularity in a bulk density of states. At higher temperatures the anomalies vanish, but measurable quantities characterizing the remaining maximum of the Seebeck coefficient still unveil the presence of massless Dirac fermions and make it possible to determine the trigonal warping strength. Behavior of the thermoelectric figure of merit ($ZT$) is also discussed.