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Stacking-order dependence in thermoelectric transport of biased trilayer graphene

We numerically study the thermoelectric and thermal transport in trilayer graphene with different stacking orders in the presence of interlayer bias under a strong perpendicular magnetic field. In biased ABA-stacked case, we find that the thermoelectric conductivity displays different asymptotic behaviors with the varying of the temperature, similar to that of monolayer graphene. In the high temperature regime, the transverse thermoelectric conductivity $α_{xy}$ saturates to a universal value $2.77 k_B e/h$ at the center of each LL, while it displays a linear temperature dependence at low temperatures limit. The calculated transverse thermal conductivity $κ_{xy}$ exhibits two plateaus away from the band center. The transition between the two plateaus is continuous, which is accompanied by a pronounced peak in the longitudinal thermal conductivity $κ_{xx}$. In biased ABC-stacked case, it is found that both the thermoelectric conductivity and thermal conductivity have similar properties to the biased bilayer graphene, which is consistent with the behavior of a band insulator. The obtained results demonstrate the sensitivity of the thermoelectric conductivity to the band gap near the Dirac point. We also verify the validity of the Mott-relation and the generalized Wiedemann-Franz law.