Lifshitz transition and thermoelectric properties of bilayer graphene

TL;DR

This study numerically investigates how Lifshitz transition influences thermoelectric properties of ballistic bilayer graphene, revealing anomalies near the Lifshitz energy at low temperatures and providing insights into Dirac fermions and trigonal warping effects.

Contribution

It introduces a numerical analysis of thermoelectric anomalies in bilayer graphene caused by Lifshitz transition and trigonal warping, highlighting measurable effects at sub-Kelvin temperatures.

Findings

Seebeck coefficient exhibits an additional maximum near Lifshitz energy.

Lorentz number shows a minimum close to Lifshitz energy.

Anomalies disappear at higher temperatures, but signatures remain detectable.

Abstract

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 $L>10\,\mu{}$m 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.