This is a numerical study of thermoelectric properties of ballistic bilayer graphene in the presence of trigonal warping term in the effective Hamiltonian. We find, in the mesoscopic samples of the length L > 10 µm 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 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.

The Corbino geometry allows one to investigate the propagation of electric current along ap-n interface in ballistic graphene in the absence of edge states appearing for the familiar Hall-bar geometry. Using the transfer matrix in the angular-momentum space we find that for sufficiently strong magnetic fields the current propagates only in one direction, determined by the magnetic field direction and the interface orientation, and the two valleys, K and K′, are equally occupied. Spatiallyanisotropic effective mass may suppress one of the valley currents, selected by the external electric field, transforming the system into amesoscopic version of the valley filter. The filtering mechanism can be fully understood within the effective Dirac theory, without referring to atomic-scale effects which are significant in proposals operating on localized edge states.

Unlike in conventional semiconductors, both the chemical potential and the band gap in bilayer graphene (BLG) can be tuned via application of external electric field. Among numerous device implications, this property also designates BLG as a candidate for high-performance thermoelectric material. In this theoretical study we have calculated the Seebeck coefficients for abrupt interface separating weakly-and heavily-doped areas in BLG, and for a more realistic rectangular sample of mesoscopic size, contacted by two electrodes. For a given band gap (∆) and temperature (T ) the maximal Seebeck coefficient is close to the Goldsmid-Sharp value |S| GS max = ∆/(2eT ), the deviations can be approximated by the asymptotic expression |S| GS max −|S|max = (kB/e)× 1 2 ln u + ln 2 − 1 2 + O(u −1 ) , with the electron charge −e, the Boltzmann constant kB, and u = ∆/(2kBT ) 1. Surprisingly, the effects of trigonal warping term in the BLG low-energy Hamiltonian are clearly visible at few-Kelvin temperatures, for all accessible values of ∆ 300 meV. We also show that thermoelectric figure of merit is noticeably enhanced (ZT > 3) when a rigid substrate suppresses out-of-plane vibrations, reducing the contribution from ZA phonons to the thermal conductivity.with f BE (T, ω) = 1/ [ exp ( ω/k B T ) − 1 ] the Bose-Einstein distribution function and T ph (ω) the phononic transmission spectrum. We calculate T ph (ω) by adopting the procedure developed by Alofi and Srivastava [30] to the two systems considered in this work (see Supplementary Information, Sec. IV ).