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.
We discuss, by means of mode-matching analysis for the Dirac equation, how splittings of the Landau-level (LL) degeneracies associated with spin, valley, and layer degrees of freedom affect the ballistic conductance of graphene bilayer. The results show that for wide samples (W L) the Landauer-Büttiker conductance reaches the maximum G se 2 /(πh) × W/L at the resonance via each LL, with the prefactor varying from s = 8 if all three degeneracies are preserved, to s = 1 if all the degeneracies are split. In the absence of bias between the layers, the degeneracies associated with spin and layer degrees of freedom may be split by manipulating the doping and magnetic field; the conductance at the zeroth LL is twice as large, while the conductance at any other LL equals to the corresponding conductance of graphene monolayer. The presence of bias potential allows one also to split the valley degeneracy. Our results show that the charge transfer at each LL has pseudodiffusive character, with the second and third cumulant quantified by F = 1/3 and R = 1/15 (respectively). In case the electrochemical potential is allowed to slowly fluctuate in a finite vicinity of LL, the resulting charge-transfer characteristics are still quantum limited, with F 0.7 and R 0.5 in the limit of large fluctuations. Analogously, the above values of F and R are predicted to be approached in the limit of high source-drain voltage difference applied. The possible effects of indirect interlayer hopping integrals are also briefly discussed.
We study the ballistic conductivity of graphene bilayer in the presence of next-nearest neighbor hoppings between the layers. An undoped and unbiased system was found in Ref.[1] to show a nonuniversal (length-dependent) conductivity σ(L), approaching the value of σ = 3/π 0.95 for large L. Here we demonstrate one-parameter scaling and determine the scaling function β(σ) = d lnσ/d lnL. The scaling flow has an attractive fixed point [ β(σ ) = 0, β (σ ) < 0 ] reproducing the scenario predicted for random impurity scattering of Dirac fermions with Coulomb repulsion, albeit the system considered is perfectly ballistic and interactions are not taken into account. The role of electrostatic bias between the layers is also briefly discussed.
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