Linear response of twisted bilayer graphene: continuum vs. tight-binding models

TL;DR

This study compares continuum and tight-binding models for twisted bilayer graphene's linear response, confirming qualitative features and exploring differences in magnetic and current responses near the neutrality point.

Contribution

It provides a detailed comparison between continuum and tight-binding models for twisted bilayer graphene's linear response, validating the continuum approach and analyzing magnetic properties.

Findings

Qualitative features are consistent across models.

Quantitative agreement improves at smaller twist angles.

Orbital paramagnetism dominates the equilibrium response.

Abstract

We present a linear response calculation for twisted bilayer graphene. The calculation is performed for both the continuum and tight-binding models, with the aim of assessing the validity of the former. All qualitatively important features previously reported by us [T. Stauber et al. Phys. Rev. Lett. 120, 046801 (2018)] for the Drude matrix in the continuum model are also present in the tight-binding calculation, with increasing quantitative agreement for decreasing twist angle. These features include the chiral longitudinal magnetic moment associated with plasmonic modes, and the anomalous counterflow around the neutrality point, better interpreted as a paramagnetic response. We have addressed the differences between Drude and equilibrium response, and shown that orbital paramagnetism is the equilibrium response to a parallel magnetic field over a substantial doping region around the neutrality point. Chirality also makes the equilibrium response to exhibit a non trivial current structure associated with the non-vertical character of interlayer bonds in the tight-binding calculation.