[Paper Review] Emergent Superconductivity in the weak Mott insulator phase of bilayer Graphene Moiré Superlattice

Xiao-Chuan Wu, Kelly Ann Pawlak+2 more|arXiv (Cornell University)|May 17, 2018

Graphene research and applications1 references20 citations

TL;DR

This paper proposes that emergent superconductivity in twisted bilayer graphene's weak Mott insulator phase arises from the interplay of strong electron correlations and the two-dimensional nature of the moiré superlattice. Using an effective two-orbital Hubbard model on a triangular lattice with SU(4) symmetry and spin-triplet pairing favored by Hund's coupling, the authors show that a spin density wave order with finite momentum gaps the Fermi surface, leading to a weak Mott insulator that becomes superconducting at low temperatures due to residual pairing fluctuations, with a transition temperature Tc ≈ 1 K.

ABSTRACT

We propose a phenomenological understanding of the recently discovered weak Mott insulator in the moiré superlattice of twisted bilayer graphene, especially the emergent superconductivity at low temperature within the weak Mott insulator phase, namely while lowering temperature, the longitudinal resistivity first grows below temperature $T_m$, but then rapidly drops to zero at even lower temperature $T_c$. An emergent superconductor in an insulator phase is very unusual. Here we propose that this phenomenon is due to the pure two-dimensional nature of the bilayer graphene moiré superlattice. We also compare our results with other theories proposed so far.

Motivation & Objective

• To explain the unusual coexistence of weak Mott insulating behavior and emergent superconductivity in twisted bilayer graphene at low temperatures.
• To understand why resistivity increases below Tm ≈ 4–5 K but then drops to zero below Tc ≈ 1 K in the same phase.
• To show that the weak Mott insulator can be understood via Fermi surface nesting and order parameter formation without requiring strong correlations or Dirac physics.
• To demonstrate that the system's two-dimensional nature and SU(4) symmetry breaking via Hund's coupling enable a spin-triplet superconducting instability within the insulating phase.

Proposed method

• Formulates an effective two-orbital extended Hubbard model on a triangular lattice to describe the moiré superlattice, with orbitals corresponding to the two valleys in bilayer graphene.
• Introduces a spin-triplet, valley-singlet pairing state favored by a negative Hund's coupling, which stabilizes a noncollinear spin density wave order.
• Uses the nonlinear sigma model (NLSM) with a target manifold deformed by an external Zeeman field to describe the noncollinear spin order and its geometric flow.
• Applies the Ricci flow formalism to the NLSM metric to derive the renormalization group (RG) flow of coupling constants g1 and g2, capturing the effect of anisotropy from the Zeeman field.
• Analyzes the RG flow at the point X_i = 0 (corresponding to the ordered state favored by Zeeman field) to extract the critical scaling behavior and instability toward superconductivity.
• Compares the model’s predictions with experimental resistivity data showing resistivity rise below Tm and drop to zero below Tc, confirming the emergence of superconductivity within the insulating phase.

Experimental results

Research questions

• RQ1 How can superconductivity emerge within a Mott insulator phase in twisted bilayer graphene, given that insulators typically suppress superconducting pairing?
• RQ2 Why does resistivity increase below Tm ≈ 4–5 K but then drop to zero below Tc ≈ 1 K, indicating a superconducting instability within an insulating state?
• RQ3 What role does the two-dimensional nature of the moiré superlattice play in enabling superconductivity in a weak Mott insulator?
• RQ4 How does the interplay between spin-triplet pairing and Fermi surface nesting via finite-momentum order parameters lead to a stable insulating state that remains susceptible to superconducting fluctuations?
• RQ5 Can the observed resistivity behavior be explained by a non-Fermi liquid state with a spin density wave order that supports emergent superconductivity?

Key findings

• The weak Mott insulator phase in twisted bilayer graphene is stabilized by a spin-triplet, valley-singlet order that gaps the Fermi surface via nesting and Brillouin zone folding.
• The system exhibits a resistivity peak at Tm ≈ 4–5 K due to insulating behavior, followed by a sharp drop to zero at Tc ≈ 1 K, indicating emergent superconductivity within the insulating phase.
• The superconducting instability is driven by residual pairing fluctuations in the spin-triplet channel, which remain active even after the formation of the spin density wave order.
• The RG flow analysis shows that the coupling constants g1 and g2 evolve under the Ricci flow, with g1 and g2 both diverging logarithmically at the same energy scale, signaling a quantum phase transition to superconductivity.
• The model explains the suppression of superconductivity by weak magnetic fields: when SC is suppressed, the resistivity continues to grow at low temperatures, confirming the system is a normal Mott insulator.
• The results are robust to microscopic details and do not require Dirac band crossings or specific valley order, relying instead on Fermi surface physics and symmetry-breaking via Hund's coupling.