Singlet superconductivity enhanced by charge order in nested twisted bilayer graphene Fermi surfaces

TL;DR

This paper investigates how charge order can enhance singlet superconductivity in twisted bilayer graphene, revealing that Fermi surface reconstructions and nesting conditions significantly influence the competition between various electronic orders.

Contribution

It introduces a hot-spot model and RPA analysis to explain the interplay of charge order and superconductivity in twisted bilayer graphene, providing new insights into the phase diagram near the magic angle.

Findings

Charge order enhances singlet superconductivity.

Fermi surface reconstruction leads to van Hove singularities.

Nesting conditions influence the dominance of charge or spin order.

Abstract

Using the continuum model for low energy non-interacting electronic structure of moir\'e van der Waals heterostructures developed by Bistritzer and MacDonald [1], we study the competition between spin, charge, and superconducting order in twisted bilayer graphene. Surprisingly, we find that for a range of small angles inclusive of the so-called magic angle, this model features robust Fermi pockets that preclude any Mott insulating phase at weak coupling. However, a Fermi surface reconstruction at $\theta \gtrsim 1.2^{\circ}$ gives emergent van Hove singularities without any Fermi pockets. Using a hot-spot model for Fermi surface patches around these emergent saddle points, we develop a random-phase approximation from which we obtain a phase diagram very similar to that obtained recently by Isobe, Yuan, and Fu using the parquet renormalization group [2] but with additional insights. For example, our model shows strong nesting around time-reversal symmetric points at a moderate doping of $\sim 2 \times 10^{11} \text{cm}^{-2}$ away from the van Hove singularity. When this nesting dominates, we predict that charge-order enhances singlet superconductivity, while spin-order suppresses superconductivity. Our theory also provides additional possibilities for the case of unnested Fermi surfaces.