Thermoelectric properties of gapped bilayer graphene

Abstract

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 ($\Delta$) and temperature ($T$) the maximal Seebeck coefficient is close to the Goldsmid-Sharp value $|S{|}_{\max }^{\mathrm{GS}}=\Delta /(2eT)$, the deviations can be approximated by the asymptotic expression $|S{|}_{\max }^{\mathrm{GS}}-|S{|}_{\max }=(k_B/e)\times \left[\frac{1}{2}\ln u+\ln 2-\frac{1}{2}+\mathcal{O}(u^{-1})\right]$, with the electron charge $-e$, the Boltzmann constant $k_B$, and $u=\Delta /(2k_{B}T)\gg 1$. 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 $\Delta ⩽300$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.

arXiv commentMinor revisions; notation clarified, a comment effective doping added. RevTeX; 9 pages; 5 figures

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• Wiedemann-Franz law for massless Dirac fermions with implications for graphene
• Transport signatures of Van Hove singularities in mesoscopic twisted bilayer graphene
• Thermoelectric properties of the Corbino disk in graphene
• Conductivity scaling and the effects of symmetry-breaking terms in bilayer graphene Hamiltonian
• Sub-Sharvin conductance and incoherent shot-noise in graphene disks at magnetic field