Quantifying the Charge Carrier Interaction in Metallic Twisted Bilayer Graphene Superlattices

The mechanism of charge carrier interaction in twisted bilayer graphene (TBG) remains an unresolved problem, where some researchers proposed the dominance of the electron-phonon interaction, while the others showed evidence for electron-electron or electron-magnon interactions. Here we propose to resolve this problem by generalizing the Bloch-Gruneisen equation and using it for the analysis of the temperature dependent resistivity in TBG. It is a well-established theoretical result that the Bloch-Gruneisen equation power-law exponent, p, exhibits exact integer values for certain mechanisms. For instance, p = 5 implies the electron-phonon interaction, p = 3 is associated with the electron-magnon interaction and p = 2 applies to the electron-electron interaction. Here we interpret the linear temperature-dependent resistance, widely observed in TBG, as p -> 1, which implies the quasielastic charge interaction with acoustic phonons. Thus, we fitted TBG resistance curves to the Bloch-Gruneisen equation, where we propose that p is a free-fitting parameter. We found that TBGs have a smoothly varied p-value (ranging from 1.4 to 4.4) depending on the Moire superlattice constant, lambda, or the charge carrier concentration, n. This implies that different mechanisms of the charge carrier interaction in TBG superlattices smoothly transition from one mechanism to another depending on, at least, lambda and n. The proposed generalized Bloch-Gruneisen equation is applicable to a wide range of disciplines, including superconductivity and geology.