Symmetry-broken metallic orders in spin-orbit-coupled Bernal bilayer graphene

TL;DR

This paper investigates the complex phase diagram of Bernal bilayer graphene with Coulomb interactions, Hund's coupling, and spin-orbit effects, revealing symmetry-broken metallic states and potential insights into superconductivity.

Contribution

It introduces a comprehensive self-consistent Hartree-Fock study of the interplay between interactions and spin-orbit coupling in bilayer graphene, uncovering new metallic phases.

Findings

Identification of intervalley coherent and spin-canted states.

Observation of phase transitions involving $ ext{U}(1)$ symmetry breaking.

Potential implications for spin-orbit-enabled superconductivity.

Abstract

We explore Bernal bilayer graphene in the presence of long-range Coulomb interactions, short-range Hund's coupling, and proximity-induced Ising spin-orbit coupling using self-consistent Hartree-Fock simulations. We show that the interplay between these three ingredients produces an intricate phase diagram comprising a multitude of symmetry-broken metallic states tunable via doping and applied displacement field. In particular, we find intervalley coherent and spin-canted ground states that may hold the key to understanding spin-orbit-enabled superconductivity observed in this platform. We also investigate various phase transitions where a continuous $\mathrm{U}(1)$ symmetry is broken to ascertain the possible role of critical fluctuations on pairing.