Quantifying the charge carrier interaction in metallic twisted graphene superlattices

TL;DR

This paper analyzes charge carrier interactions in twisted bilayer graphene by generalizing the Bloch-Grüneisen equation, revealing a transition from electron-phonon to other interactions depending on the Moiré pattern and carrier concentration.

Contribution

It introduces a generalized Bloch-Grüneisen equation with a variable exponent n to interpret temperature-dependent resistivity in TBG, linking n to different charge interaction mechanisms.

Findings

Linear resistance in TBG corresponds to n≈1, indicating quasielastic phonon interactions.

The exponent n varies from 1.4 to 4.4 depending on the Moiré pattern and carrier density.

Different charge interaction mechanisms transition smoothly as n changes.

Abstract

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-Gr\"uneisen equation and using it for the analysis of the temperature dependent resistivity in TBG. It is a well-established theoretical result that the Bloch-Gr\"uneisen equation power-law exponent, n, exhibits exact integer values for certain mechanisms. For instance, n=5 implies the electron-phonon interaction, n=3 is associated with electron-magnon interaction and n=2 applies to the electron-electron interaction. Here we interpret the linear temperature-dependent resistance, widely observed in TBG, as n$\rightarrow$1, which implies the quasielastic charge interaction with acoustic phonons. Thus, we fitted TBG resistance curves to the Bloch-Gr\"uneisen equation, where we propose that n is a free-fitting parameter. We found that TBGs have a smoothly varied n-value (ranging from 1.4 to 4.4) depending on the Moir\'e superlattice constant, $\lambda$, or the charge carrier concentration. This implies that different mechanisms smoothly transition from one to another. The proposed generalized Bloch-Gr\"uneisen equation is applicable to a wide range of problems, including the Earth geology.