# Quantum Hall ferroelectric helix in bilayer graphene

## TL;DR

This paper investigates the ground states of bilayer graphene at odd integer filling factors, revealing a transition from incoherent to helical ferroelectric phases, and suggests experimental tuning to stabilize these states.

## Contribution

It provides evidence that bilayer graphene transitions directly into a helical ferroelectric phase, challenging previous assumptions of uniform states, through exact diagonalization analysis.

## Key findings

- No uniform coherent state observed; transition directly to helical phase.
- Helical ferroelectric state can be stabilized by tuning interlayer electric field.
- Exact diagonalization supports the existence of the helical phase.

## Abstract

We re-examine the nature of the ground states of bilayer graphene at odd integer filling factors within a simplified model of nearly degenerate $n=0$ and $n=1$ Landau levels. Previous Hartree-Fock studies have found that ferroelectric states with orbital coherence can be stabilized by tuning the orbital splitting between these levels. These studies indicated that, in addition to a uniform ferroelectric state, a helical ferroelectric phase with spontaneously broken translational symmetry is possible. By performing exact diagonalization on the torus, we argue that the system does not have a uniform coherent state but instead transitions directly from the uniform incoherent state into the ferroelectric helical phase. We argue that there is a realistic prospect to stabilize the helical ferroelectric state in bilayer graphene by tuning the interlayer electric field in a model that includes all single particle corrections to its zero energy eight-fold multiplet of Landau levels.