A Theoretical Study of Thermoelectric Effect for Cross-plane Transport Across Twisted Bilayer Graphene

Abstract

The thermoelectric effect and the linear response theory is one of the most studied areas in condensed matter physics. In the last few years, the study of Van Der Waals heterostructure has become one of the most promising domains of research in physics and nanoscience both theoretically and experimentally. Twisted bilayer graphene is synthesized by stacking one graphene layer on top of another and introducing a relative twist between them. In this project, we have looked at the cross-plane electrical and thermal transport and the thermoelectric effect across twisted bilayer graphene. We have tried to give a theoretical framework based on the experiments performed in Prof. Arindam Ghosh's lab. In the entire project, we only looked at the thermoelectric transport for a large incommensurate twist angle (>10 degree). For these twist angles, the entire structure does not form any Moire superlattice and the two graphene layers become effectively decoupled. The cross-plane transport across TBG is essentially ballistic so we have constructed a phenomenological framework using the Landauer formula to determine the current. In TBG, the inter-planer transport can take place via two processes, (1) The incoherent electronic tunneling which follows the Landauer formalism with a given transmission coefficient T(E) and (2) The phonon drag effect where the electrons are kicked out form a graphene plane by the thermally excited phonons having polarization mode perpendicular to the graphene plane. Experimentally it was found that at low temperature, the thermopower is governed by the incoherent electronic transmission process whereas, at high temperature, the phonon drag effect determines the form of Seebeck Coefficient. In this project, we have discussed the incoherent electronic transmission part both qualitatively and quantitatively. Here the cross-plane transport is considered as a perfect (zero scattering) ballistic transport and hence the transmission coefficient T(E) is taken as 1.This idea came from a purely phenomenological point of view which was first discussed in this paper arXiv:1801.01269. We have shown that at the low-temperature regime, the thermopower saturates to the Mott value. For thermal transport, the Wiedemann-Franz law is holding at the low-temperature regime. In the high-temperature regime, the proportionality constant between the ratio of thermal to electrical conductivity and absolute temperature of the system saturates to a finite value. In the end, we have also calculated the thermoelectric figure of merit (the ZT factor) for the inter-planner electronic transport across TBG and derived the efficiency as a function of absolute temperature.