Classification of massive and gapless phases in bilayer graphene

TL;DR

This paper classifies all gapped and gapless phases in bilayer graphene, identifying 8 insulating, 4 superconducting, and 8 semimetallic states, including novel gapless superconductors with broken translational symmetry.

Contribution

It provides a comprehensive symmetry-based classification of all possible ordered phases in bilayer graphene, including new gapless superconducting states.

Findings

Identified 8 insulating and 4 superconducting phases in bilayer graphene.

Discovered novel gapless superconducting states breaking translational symmetry.

Analyzed the role of Coulomb interactions and proposed experimental detection methods.

Abstract

We here classify of all the fully gapped \emph{massive} and \emph{gapless} phases in bilayer graphene. The effective low energy theory in bilayer graphene is constructed, and various discrete and continuous symmetries of the non-interacting system is analyzed. Spinless fermions, placed in a quantizing magnetic field is considered. The quantum anomalous Hall insulator is properly defined. Constructing a particle-hole doubled 16 component Nambu-Dirac spinor, we recognize all the possible fully gapped, and the gapless states, which, on the other hand, split the parabolic dispersion into two anisotropic Dirac like conical ones. A thorough symmetry analysis of all the ordered states is performed. Altogether there are 8 insulating and 4 superconducting phases in bilayer graphene, that can lead to fully gapped spectrum. Among the gapped superconductors, \emph{three} are spin-singlet, which include uniform s-wave and two spatially inhomogeneous, translational symmetry breaking Kekule superconductors. The triplet pairing exhibits an f-wave symmetry. Besides the gapped phases, there are 8 semimetallic and 8 gapless superconducting states in total, available for fermions to condense into. We also find novel gapless superconducting states, which break the translational symmetry, dubbed as \emph{gapless-Fulde-Farrell-Larkin-Ovchinikov} superconductors. We also discuss the role of Coulomb interaction, and propose various experimental tools to determine the underlying ordered states.