Spontaneous symmetry breaking in a honeycomb lattice subject to a periodic potential

Abstract

Motivated by recent developments in twisted bilayer graphene moiré superlattices, we investigate the effects of electron-electron interactions in a honeycomb lattice with an applied periodic potential using a finite-temperature Wilson-Fisher momentum shell renormalization group (RG) approach. We start with a low-energy effective theory for such a system, at first giving a discussion of the most general case in which no point group symmetry is preserved by the applied potential, and then focusing on the special case in which the potential preserves a $D_3$ point group symmetry. As in similar studies of bilayer graphene, we find that, while the coupling constants describing the interactions diverge at or below a certain "critical temperature" $T=T_c$, it turns out that ratios of these constants remain finite and in fact provide information about what types of orders the system is becoming unstable to. However, in contrast to these previous studies, we only find isolated fixed rays, indicating that these orders are likely unstable to perturbations to the coupling constants. Our RG analysis leads to the qualitative conclusion that the emergent interaction-induced symmetry-breaking phases in this model system, and perhaps therefore by extension in twisted bilayer graphene, are generically unstable and fragile, and may thus manifest strong sample dependence.

16+$\epsilon$ pages, 6 figures. Added a better explanation of the tree-level scaling of the coupling constants. Added a new section demonstrating the existence of Dirac cones in a tight-binding model on a honeycomb lattice subject to a periodic potential. Published in Phys. Rev. Research

References in corpus (6)

• Observation of Moiré Excitons in WSe2/WS2 Heterostructure Superlattices
• Electronic multicriticality in bilayer graphene
• Gap Opening in Twisted Double Bilayer Graphene by Crystal fields
• Identification of superconducting pairing symmetry in twisted bilayer graphene using in-plane magnetic field and strain
• Electron-phonon and electron-electron interaction effects in twisted bilayer graphene
• Quantum multicriticality of bilayer graphene in the presence of a tunable energy gap

Cited by in corpus (5)

• Correlation-induced triplet pairing superconductivity in graphene-based moiré systems
• Topological superconductivity, ferromagnetism, and valley-polarized phases in moire systems: Renormalization group analysis for twisted double bilayer graphene
• Functional renormalization group for a large moiré unit cell
• Twisted bilayer graphene at charge neutrality: competing orders of SU(4) Dirac fermions
• Bipolaron formed through electron-hole excitation