[Paper Review] Unconventional Superconductivity and Density Waves in Twisted Bilayer Graphene

Hiroki Isobe, Noah F. Q. Yuan+1 more|DSpace@MIT (Massachusetts Institute of Technology)|May 16, 2018

Graphene research and applicationsMaterials Science3 citations

TL;DR

This paper investigates unconventional superconductivity and density wave order in twisted bilayer graphene near $n=2$ filling using a renormalization group (RG) approach in a hot-spot model. It identifies $d$- and $p$-wave superconductivity and charge/spin density waves as leading instabilities driven by Coulomb repulsion, with the density wave state exhibiting a gapped spectrum and a single doubly degenerate pocket upon doping, consistent with experimental observations.

ABSTRACT

We study electronic ordering instabilities of twisted bilayer graphene with $n=2$ electrons per supercell, where correlated insulator state and superconductivity are recently observed. Motivated by the Fermi surface nesting and the proximity to Van Hove singularity, we introduce a hot-spot model to study the effect of various electron interactions systematically. Using renormalization group method, we find $d$/$p$-wave superconductivity and charge/spin density wave emerge as the two types of leading instabilities driven by Coulomb repulsion. The density wave state has a gapped energy spectrum at $n=2$ and yields a single doubly-degenerate pocket upon doping to $n>2$. The intertwinement of density wave and superconductivity and the quasiparticle spectrum in the density wave state are consistent with experimental observations.

Motivation & Objective

• To understand the origin of superconductivity and correlated insulator states observed in twisted bilayer graphene at $n=2$ electrons per supercell.
• To investigate how electron correlations drive instabilities near the Van Hove singularity and Fermi surface nesting.
• To determine the nature of competing orders—particularly superconductivity and density waves—using a weak-coupling approach.
• To connect theoretical predictions with experimental observations, including the superconducting dome and quasiparticle spectrum in doped samples.

Proposed method

• A hot-spot model is constructed based on Fermi surface nesting and proximity to Van Hove singularities in twisted bilayer graphene at small twist angles.
• The renormalization group (RG) method is applied to analyze the flow of coupling constants under energy scale reduction, focusing on interactions at hot spots near the Van Hove energy.
• The model includes valley and spin degrees of freedom ($N_v = 2$, $N_s = 2$) and accounts for particle number $n_p = 3$ at the hot spots.
• The RG equations are derived for 16 coupling constants $g_{ij}$, with interactions split into particle-particle and particle-hole channels, and include terms sensitive to nesting vectors $Q^+$, $Q^-$, and $Q'$.
• Susceptibilities for various orders (superconducting and density wave) are computed from the RG flow to identify leading instabilities.
• The analysis is validated by reproducing known results for cuprates ($n_p=2$, $N_v=1$) and monolayer graphene ($n_p=3$, $N_v=1$), confirming consistency.

Experimental results

Research questions

• RQ1 What types of electron correlation-driven instabilities emerge in twisted bilayer graphene near $n=2$ filling, given the proximity to Van Hove singularities and Fermi surface nesting?
• RQ2 How do $d$- and $p$-wave superconducting states arise in the presence of Coulomb repulsion in this system?
• RQ3 What is the nature of the density wave state in terms of its energy spectrum and quasiparticle structure upon doping?
• RQ4 How does the interplay between superconductivity and density wave order manifest in the quasiparticle spectrum and experimental observables?

Key findings

• Coulomb repulsion drives $d$- and $p$-wave superconductivity as leading instabilities in the RG flow, with $d$-wave pairing favored in the presence of strong nesting.
• Charge and spin density wave states also emerge as leading instabilities, with the spin density wave state exhibiting a gapped spectrum at $n=2$.
• Upon doping to $n>2$, the density wave state yields a single doubly degenerate Fermi pocket, consistent with angle-resolved photoemission spectroscopy (ARPES) and transport data.
• The interplay between density wave and superconducting order is consistent with the observed superconducting dome and quasiparticle spectrum in twisted bilayer graphene.
• The RG flow shows nontrivial scaling of coupling constants due to Fermi surface nesting, with interference effects between multiple hot spots enhancing instabilities.
• The model successfully reproduces known results for cuprates and monolayer graphene when $N_v=1$, validating its applicability to twisted bilayer graphene with $N_v=2$.