Does filling-dependent band renormalization aid pairing in twisted bilayer graphene?

TL;DR

This paper investigates how filling-dependent band renormalization in twisted bilayer graphene enhances superconductivity by increasing the density of states and optimizing Wannier function localization, explaining experimental robustness of superconductivity.

Contribution

It demonstrates that Coulomb interaction-driven band renormalization enhances superconductivity through increased density of states and Wannier function localization, providing a simple explanation for experimental observations.

Findings

Filling-dependent band flattening increases the density of states.

Interaction-induced Wannier function renormalization enhances phase stiffness.

Model explains the robustness of superconductivity across various fillings.

Abstract

Magic-angle twisted bilayer graphene exhibits a panoply of many-body phenomena that are intimately tied to the appearance of narrow and well-isolated electronic bands. The microscopic ingredients that are responsible for the complex experimental phenomenology include electron-electron (phonon) interactions and non-trivial Bloch wavefunctions associated with the narrow bands. Inspired by recent experiments, we focus on two independent quantities that are considerably modified by Coulomb interaction driven band renormalization, namely the density of states and the minimal spatial extent associated with the Wannier functions. First, we show that a filling-dependent enhancement of the density of states, caused by band flattening, in combination with phonon-mediated attraction due to electron-phonon umklapp processes, increases the tendency towards superconducting pairing in a range of angles around magic-angle. Second, we demonstrate that the minimal spatial extent associated with the Wannier functions, which contributes towards increasing the superconducting phase stiffness, also develops a non-trivial enhancement due to the interaction induced renormalization of the Bloch wavefunctions. While our modeling of superconductivity assumes a weak electron-phonon coupling and does not consider many of the likely relevant correlation effects, it explains simply the experimentally observed robustness of superconductivity in the wide range of angles that occurs in the relevant range of fillings.