Thermoelectric properties of gapped bilayer graphene

TL;DR

This theoretical study explores the thermoelectric properties of bilayer graphene with tunable band gaps, calculating Seebeck coefficients and revealing effects of trigonal warping and substrate conditions on thermoelectric efficiency.

Contribution

The paper provides a detailed theoretical analysis of thermoelectric properties in bilayer graphene, including Seebeck coefficients and the impact of trigonal warping and substrate effects, which was previously unexplored.

Findings

Maximal Seebeck coefficient approaches Goldsmid-Sharp limit.

Trigonal warping effects are significant at low temperatures.

Thermoelectric figure of merit ZT exceeds 3 with substrate suppression of phonons.

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 $|S|_{\rm max}^{\rm GS}=\Delta/(2eT)$, the deviations can be approximated by the asymptotic expression $|S|_{\rm max}^{\rm GS}-|S|_{\rm max}=(k_B/e)\times\left[\frac{1}{2}\ln{u}+\ln{}2-\frac{1}{2}+{\cal O}(u^{-1})\right]$, with the electron charge $-e$, the Boltzmann constant $k_B$, and $u = \Delta/(2k_BT)\gg{}1$. 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 $\Delta\leqslant{}300\,$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.